Free Math Worksheets

Evaluate. a) \(-14-19\) b) \(22-(-11)\) c) \(-35-(-15)\) d) \(8-23\)

A submarine is at \(-150\,\text{m}\) relative to sea level and then descends another \(75\,\text{m}\). Write an integer addition equation and find its new position.

A weather station records a temperature of \(-9\,^\circ\text{F}\) one winter morning. During the morning, the temperature rises by \(14\,^\circ\text{F}\). What temperature does the station now show?

What number is \(58\) greater than \(-33\)? Write and evaluate an equation.

\(7 \frac{5}{12} - \left(3 \frac{5}{6} + 2 \frac{1}{2}\right) =\) a) \(1 \frac{1}{12}\) b) \(2 \frac{1}{12}\) c) \(5 \frac{1}{12}\) d) \(6 \frac{1}{12}\)

Evaluate each expression. Pay attention to signs and grouping symbols. a) \(-18+42-(-15)\) b) \(125-(250-75)\) c) \(-15-[-40+(12-22)]\)

Calculate the value of the expression and write the result in simplest form: \(\frac{5}{12} - \left(\frac{1}{4} + \frac{1}{3}\right)\)

Calculate each expression. Write each answer as a fraction in simplest form or as a mixed number. a) \(3 \frac{5}{12}+1 \frac{1}{4}\) b) \(6 \frac{2}{5}-4 \frac{7}{10}\) c) \(2 \frac{3}{4}+0.125\)

Calculate each expression. Write each answer as a mixed number in simplest form. a) \(3 \frac{2}{5}+4 \frac{5}{6}\) b) \(8 \frac{1}{4}-5 \frac{5}{8}\) c) \(10-\left(2 \frac{1}{3}+4 \frac{3}{5}\right)\)

Evaluate the expression efficiently by rearranging and grouping terms. \(5\frac{3}{8} + 4\frac{2}{5} - 2\frac{3}{8} + 1\frac{3}{5}\)

Evaluate the expression and write the result as a decimal: \(\frac{7}{10}-\left(\frac{2}{5}+\frac{1}{2}\right)\)

Find the error in the calculation and give the correct result. \(7\frac{1}{4} - 2.5 = (7 - 2) + (0.25 + 0.5) = 5 + 0.75 = 5.75\)

Evaluate each expression efficiently by choosing a useful fraction or decimal form. a) \(\frac{3}{4} + 0.15\) b) \(0.8 - \frac{1}{5}\) c) \(-\frac{2}{3} + 0.5\) d) \(1.125 - \frac{1}{8}\)

Evaluate each expression efficiently. Decide whether fractions or decimals are more useful. a) \(0.45 + \frac{3}{20}\) b) \(\frac{5}{8} - 0.125\) c) \(-1.2 + \frac{1}{5}\)

Evaluate the sum efficiently, and name the properties you use. \(3.7 + \frac{2}{3} + 1.3 + 1\frac{1}{3}\)

Evaluate each expression. a) \(-4.8-2.35\) b) \(-\frac{5}{6}+\frac{1}{3}\) c) \(0.75+(-1.2)\) d) \(-\left(\frac{1}{4}-\frac{5}{8}\right)\)

Calculate the value of the expression and write the result as a mixed number: \(\left(5 \frac{3}{4}-1 \frac{1}{2}\right)+2 \frac{5}{8}\)

Evaluate and write the result as a fraction in simplest form: \(\frac{2}{5}+\frac{1}{2}-\frac{3}{10}\)

Evaluate each sum or difference of rational numbers. a) \(-8.7+(-13.5)\) b) \(4.2-9.8\) c) \(-\frac{5}{9}+\frac{1}{6}\) d) \(\frac{2}{3}-\frac{3}{4}+\left(-\frac{1}{2}\right)\)

Evaluate each expression. Write the result as either a decimal or a fraction. a) \(\frac{3}{4}-1.25\) b) \(-0.6-\left(-\frac{1}{5}\right)\) c) \(2-\frac{1}{2}-0.75\) d) \(-\frac{1}{8}-0.125\)

The expressions are \(A=x-5.4\) and \(B=-3.2-y\). Evaluate them for \(x=2.1\) and \(y=-1.8\). Which value is greater?

During a winter night, the temperature drops to \(-12\,^\circ\text{C}\). By noon the next day, the temperature has risen to \(7\,^\circ\text{C}\). By how many degrees Celsius did the temperature increase?

Ms. Weber's bank account balance is \(-\$75.20\). She wants the balance to be exactly \(\$120.00\). How much money must she deposit?

Ms. Schneider's checking account balance is \(-\$125.50\). In the morning, she deposits \(\$350.00\). In the afternoon, a \(\$80.00\) bill is withdrawn from the account. Find the end-of-day balance using one expression with rational numbers.

Evaluate \(T(a,b)=a-b\) for each pair of rational numbers. Complete the table using fractions in simplest form or mixed numbers. <table> <tr><td>\(a-b\)</td><td>\(-\frac{2}{3}\)</td><td>\(\frac{5}{6}\)</td></tr> <tr><td>\(-\frac{1}{2}\)</td><td></td><td></td></tr> <tr><td>\(\frac{3}{4}\)</td><td></td><td></td></tr> </table>

Determine whether each result is positive or negative without calculating its exact value. Briefly explain each choice. a) \(-12+(-15)\) b) \(24-(-10)\) c) \(-0.5+0.3\) d) \(\frac{1}{2}-\frac{3}{4}\) e) \(-8-(-5)\)

Choose exactly three different numbers from the list whose sum is \(0\). Find two different solutions. \(0.7,\ -0.3,\ \frac{1}{5},\ -0.4,\ 0.1,\ -0.5\)

Evaluate the expression efficiently by grouping compatible fractions. \(\frac{7}{15} - \frac{3}{4} + \frac{8}{15} - \frac{1}{4}\)

Evaluate the expression efficiently without converting every number to the same form. \(2.7 + \frac{2}{9} - 1.7 + \frac{16}{9}\)

Evaluate each expression by rearranging and grouping terms efficiently. a) \(12.3 - 4.5 - 2.3 + 1.5\) b) \(\frac{3}{8} - 1.4 + \frac{5}{8} - 0.6\)

Evaluate each expression by grouping terms strategically. a) \(34 + 128 - 134\) b) \(12.5 - 6.7 - 2.5 + 1.7\) c) \(-48 + 56 - 52 + 44\)

Rearrange or regroup each expression when helpful, then evaluate it. a) \(15.6 - 7.8 - 2.2\) b) \(-4.9 + 12.5 - 5.1\) c) \(24.3 + 8.7 - 14.3 + 1.3\)

Evaluate the sum efficiently by rearranging and grouping the terms. \(-250 + 68 + 145 - 50 + 32 - 45\)

Find the distance between the numbers in each pair. Which pair is farther apart? Pair A: \(-12\) and \(8\) Pair B: \(-5.5\) and \(-20\)

Evaluate each expression efficiently. a) \(14.7 - 3.9 + 5.3 - 6.1\) b) \(-\frac{3}{8} + 12.5 - 5.5 + 0.375\) c) \(8.4 - (2.4 + 3.9) + 0.9\)

Evaluate the expression: \(\frac{2}{3}-\left(-\frac{1}{4}\right)+\frac{5}{6}-1\)

Evaluate each expression and simplify the result. a) \(45-72\) b) \(-18+(-12)\) c) \(\frac{5}{6}-\frac{1}{6}\) d) \(-\frac{3}{8}-\frac{1}{8}\)

Evaluate each expression. Use common denominators where needed. a) \(\frac{4}{5}+\left(-\frac{1}{2}\right)\) b) \(-\frac{3}{4}-\frac{5}{6}\) c) \(-1.5+\frac{1}{4}\) d) \(\frac{7}{9}-\left(-\frac{2}{3}\right)\)

Ms. Meyer has \(\$150\) in her checking account. A debit of \(\$215\) is then posted for a new desk. Explain why the new balance must be negative, and calculate the balance.

At \(6{:}00\) p.m. on a winter day, the temperature is \(4\,^\circ\text{F}\). By midnight, it drops \(7\,^\circ\text{F}\). During the early morning, it drops another \(2\,^\circ\text{F}\). What is the temperature in the morning?

For each sum, first predict whether the result is positive, negative, or zero. Then calculate mentally. a) \(-14+25\) b) \(18+(-30)\) c) \(-22+(-18)\) d) \(-45+45\)

Find the integer that makes each equation true. a) \(-12+\square=5\) b) \(\square+(-8)=-20\) c) \(15+\square=0\) d) \(\square+10=-3\)

Replace each box with \(<\), \(>\), or \(=\) without calculating the exact sum. Decide only whether the sum is positive, negative, or zero. a) \(-35+40\mathbin{\square}0\) b) \(-12+(-15)\mathbin{\square}0\) c) \(25+(-25)\mathbin{\square}0\) d) \(-50+30\mathbin{\square}0\)

Find each sum. a) \(-38+92\) b) \(54+(-117)\) c) \(-256+(-144)\) d) \(-1025+375\)

Evaluate \(-120+450+(-380)\) by adding step by step.

Mr. Weber's checking account has a balance of \(-\$180\). He deposits \(\$250\) in cash. What is the new account balance?

A research submarine is \(450\,\text{m}\) below sea level. It rises \(185\,\text{m}\) to take a measurement. How far below sea level is the submarine after it rises?

Choose \(+\) or \(-\) for each box to make the equation true. a) \((\mathbin{\square}17)+13=30\) b) \(-24+(\mathbin{\square}16)=-40\) c) \(35+(\mathbin{\square}50)=-15\) d) \((\mathbin{\square}12)+(-28)=-16\)

Choose the missing sign in each equation. a) \(-42+12=\mathbin{\square}30\) b) \(15+(-45)=\mathbin{\square}30\) c) \((\mathbin{\square}60)+(-25)=35\) d) \(-11+(\mathbin{\square}11)=-22\)

First decide whether each sum is positive or negative. Then calculate it. a) \(-415+625\) b) \(-874+(-126)\) c) \(2500+(-3750)\) d) \(-999+1001\)

Evaluate each sum from left to right. a) \(-120+250+(-80)\) b) \(500+(-750)+250\)

A type of plastic loses its flexibility and becomes brittle at \(-35\,^\circ\text{C}\). A new material mixture raises this threshold by \(12\) degrees. At what temperature does the new plastic become brittle?

A hiker begins a climb in a valley where the temperature is \(4\,^\circ\text{F}\). By the time the hiker reaches a mountain shelter, the temperature has dropped a total of \(15\) degrees. What is the temperature at the shelter?

Insert \(+\) or \(-\) in each circle to make the equation true. a) \((\bigcirc 75)+(-25)=-100\) b) \((\bigcirc 120)+(+80)=-40\) c) \((+15)+(\bigcirc 50)=+65\) d) \((\bigcirc 9)+(+21)=+12\)

Find the missing addend in each equation. a) \(15+\square=8\) b) \(15+\square=-2\) c) \(15+\square=0\) d) \(15+\square=16\)

For each equation \(a+x=s\), find \(x\). a) \(-7+x=-15\) b) \(-7+x=4\) c) \(-7+x=-7\) d) \(-7+x=20\)

Find the missing addend. a) What number added to \(10\) gives \(-5\)? b) What number added to \(-20\) gives \(0\)? c) What number added to \(-4\) gives \(-12\)? d) What number added to \(0\) gives \(-8\)?

Evaluate \(154+(-289)+45\).

Decide whether each statement is true or false. Justify with an example or counterexample. a) The sum of two negative numbers is always positive. b) Adding the opposite of \(0\) to any number leaves the number unchanged.

Find the missing addend. a) \(-520+\square=180\) b) \(75+\square=-25\)

Find \(x\). a) \(x+(-150)=-200\) b) \(x+300=50\)

Find \(x\). a) \(-12+x=-12\) b) \(44+x=0\)

For each pair, find \(s=a+b\), then decide whether \(s>a\). a) \(a=12\), \(b=-5\) b) \(a=-6\), \(b=-4\) c) \(a=-9\), \(b=10\)

Rewrite each subtraction as addition of the opposite, and then evaluate. a) \(45-17\) b) \(-32-(-58)\) c) \(12-(-88)\) d) \(-74-26\)

Complete each equation by rewriting subtraction as addition of the opposite. a) \(-120-85=-120+(\square)=\square\) b) \(215-(-45)=215+(\square)=\square\) c) \(-63-(-163)=-63+(\square)=\square\) d) \(19-50=19+(\square)=\square\)

Order the expressions by value. Which expressions have equal values? 1. \(3-8\) 2. \(-2-3\) 3. \(12-4\) 4. \(-2-(-10)\) 5. \(0-5\) 6. \(15-7\)

Insert \(+\) or \(-\) in each box to make the equation true. a) \((\square14)+(-26)=-40\) b) \((-55)-(\square25)=-30\) c) \((+12)+(\square18)=-6\)

A research submarine is \(85\,\text{m}\) below sea level. It descends another \(40\,\text{m}\). Give its new position relative to sea level as an integer.

Evaluate each difference. First rewrite the subtraction as addition of the opposite. a) \((-410)-(+590)\) b) \((+1200)-(-800)\) c) \((-33)-(-33)\) d) \((-75)-(+25)\)

For each value of \(x\), evaluate \((-150)-x\). First rewrite the subtraction as addition. a) \(x=50\) b) \(x=-50\) c) \(x=150\) d) \(x=-200\)

Find each value. a) Find the sum of \(-42\) and \(-18\). b) Find the difference of \(-25\) and \(35\), with \(-25\) as the starting number.

How much less is \(-245\) than \(-112\)?

A number plus \(-67\) equals \(25\). What is the number?

Evaluate \((-45)-(-18)+(-32)\).

Which subtraction expressions have a value of \(-24\)? Write all corresponding letters. A) \(16-40\) B) \(-12-12\) C) \(-30-(-6)\) D) \(0-(-24)\) E) \(-10-14\) F) \(-48-(-24)\)

First rewrite each expression without parentheses using simplified notation. Then evaluate. a) \((+56)+(-14)\) b) \((-33)-(-17)\) c) \((-120)+(-80)\) d) \((+200)-(+45)\)

Rewrite the expression as a sum, and then evaluate efficiently: \(-140+512-(-40)\).

Rewrite the expression as a sum, and then evaluate efficiently: \(385-119+615\).

Evaluate the expressions. Then group the expressions that have equal values. a) \(24-37\) b) \(37-24\) c) \(-(37-24)\) d) \(-24+37\) e) \(-24-(-37)\) f) \(-37+24\)

Rewrite without parentheses using simplified notation, and then evaluate: \((-432)-(-218)\).

Rewrite each expression as a sum by replacing subtraction with addition of the opposite. Then evaluate. a) \(-215-(-45)-30\) b) \(-128-72+100\)

Rewrite each expression using addition only, and then evaluate. a) \(440-600-(-160)\) b) \(-19-(-81)-100\)

Which expressions have equal values? Group expressions with the same value, and give that value. A: \(45-(-5)\) B: \(45+5\) C: \(45+(-5)\) D: \(45-5\) E: \(50-0\) F: \(50-10\)

Evaluate each expression. a) \(-2500+100{,}500\) b) \(-340{,}000-12{,}500\) c) \(50{,}200+(-45{,}200)\) d) \(12{,}300-(-7700)\)

At an Arctic weather station, the outdoor temperature is \(-46\,^\circ\text{C}\) early in the morning. By noon, it has risen to \(-19\,^\circ\text{C}\). By how many degrees Celsius did the temperature increase?

An unmanned research submarine is at \(-780\,\text{m}\) relative to sea level. It must rise to a maintenance station at \(-125\,\text{m}\). How many meters must the submarine rise?

Solve for \(x\). a) \(x+85=42\) b) \(-14+x=36\) c) \(x-55=-19\) d) \(-72+x=-110\)

Evaluate each expression. a) \(72-115+43\) b) \(-56+88-32\) c) \(105-(-45)-200\)

Simplify the operation signs and signs attached to numbers, and then evaluate: \(-12-(-18)+(-25)\).

Imagine moving on a number line. Subtracting a positive number means moving left. Write and evaluate the subtraction for each situation. a) Start at \(20\) and subtract \(55\). b) Start at \(-15\) and subtract \(30\).

Evaluate each expression. a) \((-75)+(-25)\) b) \((-75)-(-25)\) c) \(75+(-25)\) d) \(75-(-25)\)

Evaluate efficiently by using the commutative and associative properties of addition. \(47 - 19 + 53\)

Use sea level as \(0\,\text{m}\). a) A submarine is \(250\,\text{m}\) below sea level. Write its position as an integer. b) A climber is on a peak \(1850\,\text{m}\) above sea level. Write the elevation as an integer. c) A diver is at \(-15\,\text{m}\) and descends another \(10\,\text{m}\). Write the new position as an integer. d) Find the vertical distance between a bird at \(+12\,\text{m}\) and a fish at \(-8\,\text{m}\).

A parking garage labels street level as Level \(0\). Levels below street level are negative, and levels above street level are positive. a) A car is parked on Level \(-3\). Describe its location. b) A visitor parks on Level \(-1\) and takes the elevator up \(4\) levels. On which level does the visitor exit? c) Later, the visitor rides directly from that level to Level \(-2\). Represent the elevator's change in level with a signed number.

A mountain weather station tracks temperature changes during the day. In the morning, the temperature rises by \(x\,^{\circ}\text{C}\). In the afternoon, it falls by \(y\,^{\circ}\text{C}\). a) Write an expression for the net temperature change. b) Find the net change on each day. 1) Day 1: \(x=5.4\), \(y=3.1\) 2) Day 2: \(x=2.8\), \(y=4.5\) c) Explain what the sign of each result means.

A class fund starts the month with some savings. During the month, it earns \(\$e\) from a bake sale and spends \(\$a\) on art supplies. a) Write an expression for the change in the fund balance. b) Find the change when \(e=54\) and \(a=38\). Explain the result. c) Find the change when \(e=25\) and \(a=42\). Compare the ending balance with the starting balance.

A reservoir helps regulate a river. Each hour, \(z\,\text{m}^3\) of water flows into the reservoir, and \(a\,\text{m}^3\) flows out through the gates. a) Write an expression for the change in water volume after one hour. b) What does a value of \(0\) mean in this context? c) What does a negative value mean? d) Find the hourly change when \(z=1250\) and \(a=1310\).

Tim is saving for a skateboard that costs \(\$85\). He has already saved \(\$y\). a) Write an expression for the signed difference “price minus savings.” b) Evaluate the expression for \(y=62\) and for \(y=90\). Explain what each result means.

A hiker is at an elevation of \(h\) feet. The destination lodge is at an elevation of \(4000\) feet. a) Write an expression for the signed elevation difference “destination elevation minus current elevation.” b) Evaluate the difference for \(h=3200\) and for \(h=4500\). Interpret each result as an uphill or downhill change.

A bank account has a current balance of \(\$x\). A bill of \(\$y\) is withdrawn. a) Write an expression for the new account balance. b) Find the balance when \(x=125\) and \(y=40\). c) Find the balance when \(x=50\) and \(y=85\). Explain what a negative result means for the account holder.

Evaluate the expression efficiently by rearranging and grouping the addends. Show your work. \(17.4 + (-5.9) + 2.6 + (-4.1)\) Which property allows you to change the order of the addends?

Find each sum of rational numbers. 1) \((-17)+(+25)+(-13)\) 2) \((+4.8)+(-6.3)+(-2.5)\) 3) \(\left(-\frac{3}{10}\right)+0.75\) 4) \(\left(-2 \frac{1}{4}\right)+\left(-1 \frac{5}{8}\right)\)

A weather station records morning and noon temperatures. Calculate each temperature change as \(\text{noon temperature}-\text{morning temperature}\), and enter a positive number, a negative number, or zero in the table. <table> <thead> <tr> <th>Day</th> <th>Morning temperature</th> <th>Noon temperature</th> <th>Temperature change</th> </tr> </thead> <tbody> <tr> <td>Monday</td> <td>\(+2\,^\circ\text{C}\)</td> <td>\(-3\,^\circ\text{C}\)</td> <td></td> </tr> <tr> <td>Tuesday</td> <td>\(-5\,^\circ\text{C}\)</td> <td>\(+1\,^\circ\text{C}\)</td> <td></td> </tr> <tr> <td>Wednesday</td> <td>\(-4\,^\circ\text{C}\)</td> <td>\(-4\,^\circ\text{C}\)</td> <td></td> </tr> <tr> <td>Thursday</td> <td>\(0\,^\circ\text{C}\)</td> <td>\(-6\,^\circ\text{C}\)</td> <td></td> </tr> </tbody> </table>

Evaluate each expression. 1) \((-18)-(+12)-(-20)\) 2) \((-5.4)-(-2.6)-(+1.2)\) 3) \((+3.7)-(+8.7)-(-5)\)

Evaluate each sum efficiently. 1) \((-34) + 57 + 34\) 2) \(12.4 + (-6.8) + (-3.2)\) 3) \(-2\frac{1}{5} + 8 - 1\frac{4}{5}\)

Calculate \(x-y\) for each pair. a) \(x=-2.4\), \(y=5.6\) b) \(x=\frac{3}{5}\), \(y=-\frac{7}{10}\) c) \(x=-1\frac{1}{2}\), \(y=-2\frac{1}{4}\) d) \(x=-0.75\), \(y=0.75\)

The number lines show integer jumps. Find each number marked with a red question mark.

The number lines show integer jumps. Find the number marked with a red question mark in each part. a) Find the ending value. b) Find the starting value. c) Find the missing intermediate value.

Find the number marked with a red question mark on each number line.

A school snack stand tracks its monthly finances. The bar chart shows the profit (positive values) or loss (negative values), in dollars, for the first six months of the year. a) Find the total profit or loss after the six months. b) Were there more months with a profit or more months with a loss?

Find each ending value on the number lines. Write an addition equation for each jump.

Find each missing value on the number lines.

Find the missing ending value on each number line.

Find the missing ending value for each negative jump.

The number line shows the addition \(-42+65\). Find the missing ending value.

Max’s bank account balance is \(-\$15\). He deposits \(\$40\). What is his new balance?

Calculate the expression and write the result as a fraction in simplest form: \(0.4 + \frac{1}{3} - 15\%\) What problem occurs if you try to calculate this expression exactly using only terminating decimals and no fractions?

Calculate each expression. Write each answer as a fraction in simplest form or as a mixed number. a) \(1 \frac{3}{8} + \frac{7}{8} - \frac{5}{8}\) b) \(\frac{4}{15} - \left(\frac{7}{15} + \frac{12}{15}\right)\) c) \(2 \frac{1}{12} - \frac{5}{12} - \frac{11}{12}\)

Calculate: \(\left(\frac{3}{8} - \frac{5}{6}\right) + \frac{11}{12}\)

Calculate the value of the nested expression: \(\frac{2}{5} - \left(\frac{1}{2} - \left(\frac{3}{10} + \frac{1}{4}\right)\right)\)

Compare the results of calculations \(A\) and \(B\). Insert \(<\), \(>\), or \(=\), and justify your answer with calculations. \(A=5 \frac{1}{3}-2 \frac{1}{2}\) \(B=1 \frac{3}{4}+1 \frac{1}{6}\)

Evaluate the expression using the correct order of operations. Write the answer as a mixed number. \(7 \frac{1}{5}-\left(2 \frac{1}{2}+1 \frac{3}{4}\right)+0.8\)

Evaluate the expression efficiently. Simplify fractions when helpful, and remove the parentheses carefully. \(\left(6\frac{4}{15} + \frac{18}{24}\right) - \left(1\frac{4}{15} - \frac{1}{4}\right)\)

Evaluate the expression efficiently. Briefly explain which properties make your method valid. \(\left(15\frac{5}{6} + 3\frac{1}{4}\right) - \left(2\frac{5}{6} + 1\frac{1}{2} + 1\frac{3}{4}\right)\)

Consider \(\frac{3}{4}+\frac{2}{3}-\frac{1}{2}\). a) Estimate whether the result is greater than or less than \(1\). Briefly justify your estimate. b) Then calculate the exact value as a fraction.

Check the following work for an error: \(\frac{4}{5}-\left(\frac{1}{2}-\frac{1}{10}\right)=\frac{4}{5}-\frac{1}{2}-\frac{1}{10}=\frac{8}{10}-\frac{5}{10}-\frac{1}{10}=\frac{1}{5}\). Explain whether the work is correct. If it is not, identify the error and calculate the correct result.

Evaluate the expression: \(\left(\frac{2}{3}-1.5\right)+\left(-\frac{5}{6}+0.25\right)\)

Evaluate the expression: \((-4.2+1.7)-(0.8-2.3)\)

Evaluate the expression. Write the result as a fraction in simplest form or as a mixed number: \(10-\left(3 \frac{1}{4}+2 \frac{5}{6}\right)-1 \frac{1}{12}\)

A point starts at \(-2.3\) on a number line. It moves \(4.5\) units to the right and then \(1.4\) units to the left. Where does the point end?

Evaluate the expression. Write the answer as a fraction in simplest form or as a mixed number: \(2 \frac{1}{4}-\frac{5}{6}-\frac{3}{8}\)

Find the missing value of \(a\), \(b\), or \(a+b\) in each part. a) \(a=-4.5\), \(b=2.1\), \(a+b=\square\) b) \(a=\square\), \(b=-7.8\), \(a+b=-3.2\) c) \(a=\frac{3}{4}\), \(b=\square\), \(a+b=-\frac{1}{8}\)

Complete the subtraction table and find \(x\) and \(y\). Each entry is the value at the left of its row minus the value at the top of its column. <table> <tr><td>\(-\)</td><td>\(1.2\)</td><td>\(y\)</td><td>\(-3.5\)</td></tr> <tr><td>\(4.5\)</td><td>\(3.3\)</td><td>\(7.2\)</td><td></td></tr> <tr><td>\(-2.8\)</td><td></td><td>\(-0.1\)</td><td>\(0.7\)</td></tr> <tr><td>\(x\)</td><td>\(-5.5\)</td><td></td><td>\(-0.8\)</td></tr> </table>

Insert \(<\), \(>\), or \(=\) to make each statement true. Justify each choice using rules for rational numbers without fully evaluating the expressions. a) \(-4.5+4.5\;\dots\;0\) b) \(-123-(-122)\;\dots\;0\) c) \(-\frac{2}{3}+\left(-\frac{1}{3}\right)\;\dots\;0\) d) \(0.01-0.1\;\dots\;0\)

For each pair, decide which expression has the greater value. Explain without finding the exact final values. a) \((-15)+(-20)\) or \((-15)-(-20)\) b) \(0.4-0.6\) or \(-0.4+0.6\) c) \(-\frac{1}{8}-\frac{1}{4}\) or \(-\frac{1}{8}+\frac{1}{4}\)

Choose exactly four numbers from the list. Place a plus or minus sign between consecutive chosen numbers so that the result is \(0.5\). \(1.2,\ -0.5,\ \frac{1}{4},\ -0.8,\ 0.1,\ -0.2\)

Two students evaluate \(-0.5 + \frac{3}{4} - 0.25 + \frac{1}{2}\) in different ways. Mia works from left to right. Lucas groups values that combine easily. a) Evaluate the expression using Mia’s method. b) Show an efficient grouping Lucas could use. c) Compare the original expression with \(-0.5 + \left(\frac{3}{4} - 0.25\right) + \frac{1}{2}\). Do the parentheses change the value? Explain.

Evaluate each expression efficiently by grouping compatible terms. a) \(-\frac{3}{7} + \frac{5}{8} - \frac{4}{7} + \frac{3}{8}\) b) \(1\frac{2}{5} - 3\frac{1}{4} + \frac{3}{5} + \frac{1}{4}\) c) \(\frac{7}{10} - 0.45 + \frac{3}{10} - 0.55\)

Lina and Tim evaluate \(12.5 - 8.3 + 7.5 - 1.7\) in different ways. Lina groups the positive terms and the amounts being subtracted: \((12.5 + 7.5) - (8.3 + 1.7)\). Tim groups consecutive pairs: \((12.5 - 8.3) + (7.5 - 1.7)\). a) Evaluate the expression using both methods. b) Explain why Lina’s method is especially efficient here.

Evaluate each expression efficiently using properties of rational-number addition. a) \(\frac{5}{9} - \frac{1}{3} + \frac{4}{9}\) b) \(\frac{3}{4} - 2.5 - \frac{7}{4} + 1.5\) c) \(-\frac{2}{7} + \frac{5}{6} + \frac{2}{7} - \frac{1}{6}\)

Use all four number cards \(-4\), \(-2\), \(6\), and \(8\), along with addition and subtraction signs, to write an expression with a value of \(0\). You may use parentheses. Then write a different expression using the same four cards that has a value of \(12\).

Insert an addition or subtraction sign in each blank to make the equation true. a) \(-7\;\square\;(-3)\;\square\;5=-9\) b) \(-7\;\square\;((-3)\;\square\;5)=1\)

A point is at \(-3.4\) on a number line. A second point is exactly \(7.2\) units away. What are the two possible positions of the second point?

Find the distance between each pair. Give each answer as a decimal or a fraction in simplest form. a) \(-\frac{3}{4}\) and \(0.2\) b) \(1\frac{1}{2}\) and \(-\frac{2}{5}\)

Evaluate each expression efficiently using properties of operations. a) \(17.4 - (5.9 + 17.4) + 0.9\) b) \(-\frac{2}{5} + (3.7 + 0.4) - 2.7\)

A weather station starts the day at \(45.5\,{}^\circ\text{F}\). The temperature then changes by \(-3.4\,{}^\circ\text{F}\), \(+8.8\,{}^\circ\text{F}\), \(-2.2\,{}^\circ\text{F}\), \(-5.7\,{}^\circ\text{F}\), and \(+6.1\,{}^\circ\text{F}\), in that order. a) What is the final temperature? b) What is the highest temperature reached during the day? c) What is the lowest temperature reached during the day?

A rain barrel holds \(50\) gallons. It starts the week with \(30.75\) gallons of water. During the week, the amount changes in this order: - Rain: \(+8.50\) gallons - Watering: \(-13.20\) gallons - Rain: \(+3.85\) gallons - Watering: \(-22.40\) gallons a) How much water is in the barrel at the end of the week? b) When the barrel reached its highest amount during the week, how many gallons of empty capacity remained?

A checking account starts with a balance of \(\$250.00\). These transactions occur in order: - Withdrawal: \(\$315.50\) - Deposit: \(\$120.00\) - Withdrawal: \(\$85.25\) a) What is the lowest balance reached during the sequence? b) What is the balance after the final transaction? c) How much must be deposited after the final transaction to bring the balance to exactly \(\$100.00\)?

Find the rational number that belongs in each blank. a) \(\frac{2}{3}+\square=-\frac{1}{6}\) b) \(\square-\frac{3}{5}=-1\) c) \(-\frac{1}{2}-\square=\frac{1}{8}\)

A weather station in Colorado records these temperature changes from one reading to the next. At midnight, the temperature is \(27.5\,{}^\circ\text{F}\). <table> <tr><td>6:00 a.m.</td><td>\(+7.2\,{}^\circ\text{F}\)</td></tr> <tr><td>9:00 a.m.</td><td>\(+6.8\,{}^\circ\text{F}\)</td></tr> <tr><td>12:00 p.m.</td><td>\(+4.4\,{}^\circ\text{F}\)</td></tr> <tr><td>3:00 p.m.</td><td>\(-2.5\,{}^\circ\text{F}\)</td></tr> <tr><td>6:00 p.m.</td><td>\(-8.6\,{}^\circ\text{F}\)</td></tr> <tr><td>9:00 p.m.</td><td>\(-4.3\,{}^\circ\text{F}\)</td></tr> </table> a) Write one expression for the temperature at 9:00 p.m. and calculate it. b) Find the highest and lowest temperatures at the listed reading times, including midnight.

Lucas tracks his allowance account. At the beginning of April, the balance is \(\$28.50\). These transactions occur during the month: <table> <tr><td>Apr. 4</td><td>Movie and popcorn</td><td>\(-\$14.20\)</td></tr> <tr><td>Apr. 10</td><td>Gift from Grandma</td><td>\(+\$20.00\)</td></tr> <tr><td>Apr. 15</td><td>New video game</td><td>\(-\$35.00\)</td></tr> <tr><td>Apr. 22</td><td>Mowing a neighbor's lawn</td><td>\(+\$12.50\)</td></tr> <tr><td>Apr. 28</td><td>Pizza with friends</td><td>\(-\$6.80\)</td></tr> </table> a) Write an expression and find the account balance at the end of April. b) Determine whether the account balance was ever negative during April. If so, give the lowest balance.

A bulk-food store tracks changes in its oatmeal inventory in pounds. On Monday morning, the store has \(34.0\) pounds. During the week, these amounts are sold (negative) or delivered (positive): <table> <tr><td>Monday</td><td>\(-7.0\) lb</td></tr> <tr><td>Tuesday</td><td>\(-10.0\) lb</td></tr> <tr><td>Wednesday</td><td>\(+44.0\) lb (delivery)</td></tr> <tr><td>Thursday</td><td>\(-16.5\) lb</td></tr> <tr><td>Friday</td><td>\(-20.5\) lb</td></tr> </table> a) How many pounds of oatmeal remain on Friday evening? Write an expression. b) What was the greatest amount of oatmeal in the store at one time during the week?

A research submersible is at \(-120\,\text{m}\), where sea level is \(0\,\text{m}\). It descends another \(150\,\text{m}\) to take a measurement, then rises \(40\,\text{m}\). What is the submersible's final position relative to sea level?

Compare the values of Expressions A and B. Which is greater? Expression A: \(-1500+850\) Expression B: \(2100+(-2800)\)

Choose signs for \(20\) and \(45\) to make each equation true. Write the completed equation. a) \((\mathbin{\square}20)+(\mathbin{\square}45)=65\) b) \((\mathbin{\square}20)+(\mathbin{\square}45)=-25\) c) \((\mathbin{\square}20)+(\mathbin{\square}45)=25\) d) \((\mathbin{\square}20)+(\mathbin{\square}45)=-65\)

Evaluate both sides and replace each box with \(<\), \(>\), or \(=\). a) \(-45+20\mathbin{\square}-30+5\) b) \(100+(-150)\mathbin{\square}-80+20\) c) \(-12+(-13)\mathbin{\square}5+(-30)\)

Find the integer \(z\) that makes each equation true. a) \(50+z=-10\) b) \(z+(-120)=-200\) c) \(-15+25+z=0\)

A frozen-food warehouse has several storage zones. Zone A is kept at \(-18\,^\circ\text{C}\). Zone B is \(7\) degrees colder than Zone A. Zone C is \(12\) degrees warmer than Zone B. What are the temperatures in Zones B and C?

Insert either \(+\) or \(-\) in each box to make the equation true. a) \((-18)\mathbin{\square}(-7)=-11\) b) \((+25)\mathbin{\square}(-5)=+30\) c) \((-40)\mathbin{\square}(+10)=-50\) d) \((+12)\mathbin{\square}(-12)=0\)

Insert the missing signs so that each equation is true. a) \((\bigcirc100)+(\bigcirc40)+(-20)=-80\) b) \((+50)+(\bigcirc30)+(\bigcirc10)=+10\)

Evaluate \(-72+[148+(-205)]\).

Evaluate \(-120+55+(-80)+145\).

Maya claims, “The sum of two negative integers is always less than either addend.” Test the claim using \(-7+(-3)\), and then explain whether it is always true.

Let \(a=-8\) in \(a+b=s\). Give one integer value of \(b\) for each condition. a) \(s<a\) b) \(s=a\) c) \(s>a\)

Give one pair of integers with sum \(-32\) for each condition. a) Both addends are negative. b) The first addend is positive, and the second is negative. c) The first addend is negative, and the second is positive.

A submarine’s total change in depth is \(-80\,\text{m}\). Give one addition equation for each situation. a) The submarine descends during both stages. b) The submarine rises during the first stage and descends during the second stage.

Complete each equation so the sum is \(-50\). a) \(25+\square=-50\) b) \(-70+\square=-50\) c) \(\square+\square=-50\), using two identical addends.

Evaluate this claim: “Subtracting the absolute value of an integer from the integer always gives \(0\).” Decide whether the claim is true or false and justify your answer with examples.

On a winter afternoon, the temperature drops by \(9\,^\circ\text{F}\). That evening, the thermometer reads \(-5\,^\circ\text{F}\). What was the temperature before the drop?

Mr. Weber checks his banking app. A credit of \(\$125\) has been added, and his current balance is \(-\$240\). What was his balance immediately before the credit?

A remotely operated underwater vehicle descends \(150\,\text{m}\) from its initial position. It ends at \(-620\,\text{m}\), where sea level is \(0\,\text{m}\). What was the vehicle's position before it descended?

Rewrite each expression as a sum, evaluate it, and decide which value is greater. Expression A: \(-240-160\) Expression B: \(-240-(-160)\)

Evaluate both sides and replace each box with \(<\), \(>\), or \(=\). a) \(-8-2\mathbin{\square}-8-(-2)\) b) \(5-5\mathbin{\square}-3-(-3)\) c) \(-12-4\mathbin{\square}-10-10\)

Evaluate both sides and replace each box with \(<\), \(>\), or \(=\). a) \(-58-22\mathbin{\square}-90+10\) b) \(72+(-84)\mathbin{\square}-5-(-7)\) c) \(-200+150\mathbin{\square}-10-45\)

Complete the calculation chain \(-120\xrightarrow{+45}\square\xrightarrow{-30}\square\xrightarrow{-(-60)}\square\).

Each equation is missing both a sign attached to a number and an operation sign. Insert \(+\) or \(-\) to make each equation true. Find all possibilities. a) \((\square8)\mathbin{\bigcirc}(-12)=+20\) b) \((-25)\mathbin{\bigcirc}(\square15)=-10\) c) \((\square40)\mathbin{\bigcirc}(+60)=-20\)

Complete the subtraction table. Each entry is the row value minus the column value. <table> <tr> <th colspan="2" rowspan="2"></th> <th colspan="4">Number being subtracted</th> </tr> <tr> <th>\(15\)</th> <th>\(-10\)</th> <th>\(-35\)</th> <th>\(60\)</th> </tr> <tr> <th rowspan="3">Starting number</th> <th>\(-20\)</th> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <th>\(45\)</th> <td></td> <td></td> <td></td> <td></td> </tr> <tr> <th>\(-80\)</th> <td></td> <td></td> <td></td> <td></td> </tr> </table>

Ms. Meyer's checking account balance was \(-\$45\) yesterday. Today, two more debits were posted: a \(\$30\) bill and a \(\$25\) shipping charge. What is her current balance?

Decide whether each statement is true or false. a) The sum of \(-15\) and \(15\) is \(0\). b) The difference of \(-40\) and \(-10\) is \(-50\). c) The sum of \(-9\) and \(-11\) is \(-20\).

On a cold January day, temperatures are recorded at two locations in the mountains. At noon, the mountain station is \(-11\,^\circ\text{F}\), and at night it is \(-24\,^\circ\text{F}\). In the valley, the temperature is \(4\,^\circ\text{F}\) at noon and \(-6\,^\circ\text{F}\) at night. a) For each location, by how many degrees Fahrenheit did the temperature decrease from noon to night? b) Find the temperature difference between the mountain station and the valley at noon and at night.

A laboratory uses several cooling areas. The room temperature is \(22\,^\circ\text{C}\), a refrigerator is \(4\,^\circ\text{C}\), a freezer is \(-18\,^\circ\text{C}\), and a dry-ice chamber is \(-78\,^\circ\text{C}\). a) Find the temperature difference between the room and the freezer. b) How many degrees colder is the dry-ice chamber than the refrigerator? c) Compare the temperature difference from the refrigerator to the freezer with the difference from the freezer to the dry-ice chamber. Which difference is greater?

Evaluate each difference, and then insert \(<\), \(>\), or \(=\) to make a true statement. a) \((-12)-8\mathbin{\square}-12\) b) \((-12)-(-8)\mathbin{\square}-12\) c) \(15-15\mathbin{\square}15\) d) \(15-(-15)\mathbin{\square}15\)

Consider the two expressions. Expression \(A\): \((-40)-25\) Expression \(B\): \((-40)-(-25)\) Without calculating exact values, explain which expression is greater. Use what you know about subtracting integers and compare each result with \(-40\).

Evaluate each expression with three numbers. First rewrite it without parentheses using simplified notation. a) \((-15)+(+25)-(-10)\) b) \((+40)-(+60)+(-20)\) c) \((-100)-(-30)-(+70)\)

Rewrite the expression as a sum, and then evaluate efficiently: \(-2650+1433-350+567\).

Compare the values and insert \(<\), \(>\), or \(=\) in each box. a) \(18-30\mathbin{\square}-18+30\) b) \(-50-(-20)\mathbin{\square}-50+20\) c) \(45-(10+50)\mathbin{\square}45-10-50\) d) \(-(25-5)\mathbin{\square}-25-5\)

Rewrite each expression as a sum, and then evaluate. a) \(25{,}000-60{,}000\) b) \(-10^4-5000\) c) \(8800-(-1200)\) d) \(-10^6-(-10^5)\)

Rewrite without parentheses using simplified notation, and then evaluate: \((+675)+(-280)-(+145)\).

Rewrite without parentheses using simplified notation, and then evaluate: \(1000-(-450)+(-1250)-(+200)\).

A research team measures the elevations of several locations relative to sea level. <table> <tr><td>Location</td><td>Elevation</td></tr> <tr><td>A (peak)</td><td>\(+340\,\text{m}\)</td></tr> <tr><td>B (meadow)</td><td>\(+115\,\text{m}\)</td></tr> <tr><td>C (village)</td><td>\(-25\,\text{m}\)</td></tr> <tr><td>D (lakeshore)</td><td>\(-142\,\text{m}\)</td></tr> <tr><td>E (cave floor)</td><td>\(-205\,\text{m}\)</td></tr> </table> a) Find the elevation difference between the peak (A) and the village (C). b) How many vertical meters separate the lakeshore (D) and the cave floor (E)? c) Find the total elevation difference between the highest location (A) and the lowest location (E).

Ms. Berger records her checking account balance at the end of each weekday. <table> <tr><td>Monday</td><td>\(+\$12\)</td></tr> <tr><td>Tuesday</td><td>\(-\$4\)</td></tr> <tr><td>Wednesday</td><td>\(-\$18\)</td></tr> <tr><td>Thursday</td><td>\(-\$9\)</td></tr> <tr><td>Friday</td><td>\(+\$22\)</td></tr> </table> a) By how much did the balance change from Monday to Tuesday? State whether it increased or decreased. b) On which day was the balance lowest, and what was the difference between that balance and Friday's balance? c) Between which two consecutive days did the greatest change occur?

Which tasks have equal values? Sort the letters into the groups with values \(-25\) and \(-55\). (A) \(-40+15\) (B) \(-40-(-15)\) (C) Subtract \(15\) from \(-40\). (D) Add \(-15\) to \(-40\). (E) \(-40-15\) (F) Add \(15\) to \(-40\). (G) Subtract \(-15\) from \(-40\).

Evaluate each expression. a) \(-12{,}450+5670\) b) \(34{,}200-(-8950)\) c) \(-7300-12{,}800\) d) \(10^4-100{,}000\)

Insert \(<\), \(>\), or \(=\) to make each statement true. a) \(-3500+1200\mathbin{\square}-3500-1200\) b) \(-800-450\mathbin{\square}-800-(-450)\) c) \(15{,}000-25{,}000\mathbin{\square}-5000-6000\) d) \(-10^3+1\mathbin{\square}0\)

Leon claims, “When I subtract a negative number from another negative number, the result is always negative.” Disprove his claim with two examples: 1. One example with a positive result. 2. One example with a result of \(0\). Evaluate both differences.

Consider \((-14)-(-20)\). a) Evaluate the difference. b) Explain why the result is positive even though both numbers in the expression are negative.

Use the numbers \(-6\) and \(-10\). 1. Evaluate \((-6)-(-10)\). 2. Evaluate \((-10)-(-6)\). Compare the results. What do you notice about their signs?

A diving robot begins at \(-45\,\text{m}\) relative to sea level and descends \(15\,\text{m}\) each minute. After how many whole minutes will it first be below \(-110\,\text{m}\)?

Evaluate the four expressions, and then order their values from least to greatest. a) \(-110+(-40)\) b) \(-110-(-40)\) c) \(110+(-110)\) d) \(0-110\)

Find the missing value in each addition equation. a) \(-18+30=\square\) b) \(\square+(-12)=-20\) c) \(-45+\square=-15\)

An elevator uses Level \(0\) for street level, positive numbers for levels above street level, and negative numbers for levels below street level. a) The elevator starts on Level \(2\), travels down \(5\) levels, and then travels up \(2\) levels. Where does it stop? b) The elevator is on Level \(-1\) and travels down \(3\) more levels. Where does it stop? c) The elevator is on Level \(-2\) and must travel to Level \(3\). How many levels must it travel upward?

For each movement on a number line, find the missing value and write the corresponding addition equation. a) Start at \(-5\) and move \(8\) units right. b) Start at \(3.5\) and move \(6\) units left. c) You end at \(-2\) after moving \(4\) units left from an unknown starting point. Find the starting point.

Analyze sums on a number line. a) Which sum lies farther left: \((-12)+7\) or \((-3)+(-3)\)? Calculate and compare. b) A point is at \(-4.8\). What number \(x\) must be added to move it to \(0\)? c) A point at \(-2.4\) is moved to its opposite by adding a number \(y\). Find \(y\) and write the complete equation.

Complete the table by finding each missing value of \(x\), \(y\), or \(x+y\). <table> <thead> <tr> <th>Item</th> <th>1</th> <th>2</th> <th>3</th> <th>4</th> <th>5</th> </tr> </thead> <tbody> <tr> <td>\(x\)</td> <td>\(-7.2\)</td> <td>\(3 \frac{1}{4}\)</td> <td>\(-0.8\)</td> <td>\(-\frac{5}{6}\)</td> <td>\(-4.15\)</td> </tr> <tr> <td>\(y\)</td> <td>\(4.5\)</td> <td>\(-5 \frac{1}{2}\)</td> <td>\(\dots\)</td> <td>\(\frac{1}{3}\)</td> <td>\(4.15\)</td> </tr> <tr> <td>\(x+y\)</td> <td>\(\dots\)</td> <td>\(\dots\)</td> <td>\(-2\)</td> <td>\(\dots\)</td> <td>\(\dots\)</td> </tr> </tbody> </table>

Evaluate each expression, then order the results from least to greatest. a) \(-12.5+7.8\) b) \(-\frac{3}{5}-\frac{1}{2}\) c) \(4 \frac{1}{3}+\left(-2 \frac{5}{6}\right)\) d) \(-0.75-(-1.2)\)

Evaluate each sum efficiently using the commutative and associative properties of addition. 1) \((-24) + 15 + (-16) + 35\) 2) \(6.7 + (-3.2) + 1.3 + (-1.8)\) 3) \(-\frac{3}{4} + 2\frac{1}{5} - 0.25 + 0.8\)

Evaluate each sum efficiently. 1) \(0.375 - 5\frac{1}{2} + \frac{5}{8} + 4.5\) 2) \(-8.1 + 2\frac{3}{7} + 1.1 + 5\frac{4}{7}\) 3) \(11\frac{1}{9} - 4.9 - 2\frac{1}{9} - 5.1\)

For each pair of values, find \(c\) so that \(a+b+c=0\). a) \(a=-8.5\), \(b=3\frac{1}{4}\) b) \(a=\frac{2}{3}\), \(b=-\frac{1}{6}\) c) \(a=15.7\), \(b=-20\)

At \(6{:}00\) a.m. on a winter day, the temperature is \(-6\,^\circ\text{F}\). a) By noon, the temperature rises \(11\,^\circ\text{F}\). What is the noon temperature? b) By late evening, the temperature drops \(8\,^\circ\text{F}\) from the noon value. What is the evening temperature? c) Find the difference between the highest and lowest of the morning, noon, and evening temperatures.

Find each requested value. a) Evaluate \((+7)-(-15)\). b) What number must be subtracted from \(-3.8\) to get \(-10\)? c) Subtract \(+1 \frac{3}{4}\) from \(-2 \frac{1}{2}\).

Explore how changing the order affects subtraction. Let \(x=-6.2\) and \(y=-3.4\). a) Find \(x-y\). b) Find \(y-x\). c) Compare your answers from a) and b). What do you notice? d) A student claims, “When you subtract one negative number from another negative number, the result is always positive.” Give a counterexample to show that the claim is false.

Evaluate each expression. Write each result as a simplified fraction or mixed number. 1) \(\left(-\frac{7}{8}\right)-\left(+\frac{1}{8}\right)-(-3)\) 2) \(\left(+\frac{2}{5}\right)-\left(-\frac{1}{2}\right)-\left(+\frac{9}{10}\right)\) 3) \(\left(-2 \frac{1}{4}\right)-\left(-\frac{3}{4}\right)-(+1)\)

Let \(a\) and \(b\) be positive rational numbers. a) What numbers must be added to the positive rational numbers so that \(a-b\) is always included, no matter which positive rational numbers are chosen? b) State the condition on \(a\) and \(b\) that makes \(a-b\): 1. equal to \(0\). 2. negative. 3. positive. c) Give one subtraction example with fractions or decimals for each case in part b).

A weather station recorded these temperatures at midnight during one week: Monday: \(-4\,^\circ\text{C}\), Tuesday: \(-1\,^\circ\text{C}\), Wednesday: \(3\,^\circ\text{C}\), Thursday: \(5\,^\circ\text{C}\), Friday: \(-2\,^\circ\text{C}\), Saturday: \(-6\,^\circ\text{C}\), Sunday: \(0\,^\circ\text{C}\). a) Find the highest and lowest temperatures. b) Find the difference between the warmest and coldest temperatures. c) List the days from coldest to warmest.

Operations with decimals can be shown clearly on a number line. Each arrow shows the direction and size of a jump. Find the numbers represented by the red question marks on the number lines.

The number lines show subtraction as jumps to the left. Find the value represented by the question mark in each diagram. a) Where does the jump end? b) Where did the jump begin? c) What is the missing middle value?

A hiking group is planning a route through the mountains. The bar graph shows the elevation of each stop in feet. a) Read the elevations of the six stops from the graph. b) Find the elevation change between each pair of consecutive stops. Use a negative sign for a descent. c) Find the sum of all the elevation changes from part b). d) A hiker says, “The finish is only \(300\,\text{ft}\) above the start, so we climb only \(300\,\text{ft}\) in all.” Explain why this statement is incorrect.

Find each missing starting number for the subtraction shown on the number line.

What starting value belongs in the box? Use the number line to solve \(\square+(-50)=-12\).

Complete the number line for \(-15+25+(-40)\). Find the missing intermediate and ending values.

The temperature is \(-8\,^\circ\text{F}\) in the morning. It rises \(15\,^\circ\text{F}\) by noon and then falls \(4\,^\circ\text{F}\) by evening. What is the evening temperature?

A student writes \(6 \frac{1}{4}-2 \frac{2}{3}=(6-2)+\left(\frac{2}{3}-\frac{1}{4}\right)=4+\left(\frac{8}{12}-\frac{3}{12}\right)=4 \frac{5}{12}\). Explain the error, then calculate the correct result.

Divide the six number cards into two groups of three so that the sums of the groups are equal. \(1.2,\ \frac{3}{10},\ -1.5,\ 0.8,\ -0.2,\ -\frac{3}{5}\)

Write one subtraction expression with a value of \(-35\) for each condition. a) Both numbers are positive integers. b) The starting number is a negative integer, and the number being subtracted is a positive integer. c) Both numbers are negative integers.

Simon claims, “When I subtract one integer from another integer, the result is always less than the first integer.” Is Simon correct? Use at least two integer examples to justify your answer.

Complete each chain of jumps on the number line. Find every value marked with a question mark.