Free Math Worksheets

- You can write the whole number as a fraction with denominator \(1\). - Look for a common factor between the whole number and the denominator before multiplying.

1. For a), simplify \(18\div6=3\). Then \(\frac{5}{6}\times18=5\times3=15\). 2. For b), simplify \(24\div8=3\). Then \(24\times\frac{3}{8}=3\times3=9\). 3. For c), simplify \(35\div7=5\). Then \(\frac{2}{7}\times35=2\times5=10\).

a) \(15\) b) \(9\) c) \(10\)

- Convert to the requested smaller unit before calculating. - Divide by the denominator and multiply by the numerator. - Finding one unit fraction first can make the calculation easier.

1. For a), \(240\div8=30\), and \(30\times3=90\). The result is \(90\,\text{kg}\). 2. For b), \(4\,\text{km}=4000\,\text{m}\). Then \(4000\div20=200\), and \(200\times7=1400\). The result is \(1400\,\text{m}\). 3. For c), \(2\,\text{h}=120\,\text{min}\). Then \(120\div12=10\), and \(10\times11=110\). The result is \(110\,\text{min}\).

a) \(90\,\text{kg}\) b) \(1400\,\text{m}\) c) \(110\,\text{min}\)

- Think about which number you divide by to find one-half, one-third, or another unit fraction. - What does the denominator tell you to do? - You may be able to work with \(6\) first and then use the two zeros.

1. \(\frac{1}{2} \times 600 = 300\). 2. \(\frac{1}{3} \times 600 = 200\). 3. \(\frac{1}{4} \times 600 = 150\). 4. \(\frac{1}{5} \times 600 = 120\). 5. \(\frac{1}{6} \times 600 = 100\).

a) \(300\) b) \(200\) c) \(150\) d) \(120\) e) \(100\)

- What happens to the result when the denominator doubles? - If the denominator doubles, try halving a result you already know. - Think about division as the inverse of multiplication.

1. Find each fraction by dividing \(240\) by its denominator. 2. a) \(240 \div 2 = 120\), \(240 \div 4 = 60\), and \(240 \div 8 = 30\). 3. b) \(240 \div 3 = 80\), \(240 \div 6 = 40\), and \(240 \div 12 = 20\).

a) \(\frac{1}{2}\) is \(120\), \(\frac{1}{4}\) is \(60\), and \(\frac{1}{8}\) is \(30\). b) \(\frac{1}{3}\) is \(80\), \(\frac{1}{6}\) is \(40\), and \(\frac{1}{12}\) is \(20\).

- Imagine dividing the same pizza into \(4\) equal slices and then into \(5\) equal slices. Which slices are larger? - Work one division at a time. - Look for a pattern as the denominator increases.

1. a) \(1000 \div 5 = 200\), \(1000 \div 10 = 100\), and \(1000 \div 20 = 50\). 2. b) \(1000 \div 4 = 250\), and \(1000 \div 8 = 125\). 3. c) Since \(200 < 250\), \(\frac{1}{5}\) of the number is less than \(\frac{1}{4}\) of the number. 4. When the same whole is divided into more equal parts, each part is smaller.

a) \(\frac{1}{5}\) is \(200\), \(\frac{1}{10}\) is \(100\), and \(\frac{1}{20}\) is \(50\). b) \(\frac{1}{4}\) is \(250\), and \(\frac{1}{8}\) is \(125\). c) \(\frac{1}{5}\) is less than \(\frac{1}{4}\) because dividing the same whole into more equal parts makes each part smaller.

- First find the value of one equal part, such as one-tenth. - Think about how the whole number is divided into equal groups. - After finding one part, how can you find several parts?

1. a) Find one-tenth: \(4000 \div 10 = 400\). Then find three-tenths: \(3 \times 400 = 1200\). 2. b) Find one-fifth: \(1500 \div 5 = 300\). Then find four-fifths: \(4 \times 300 = 1200\).

a) \(1200\) b) \(1200\)

- Find the value of each expression separately. - Use the denominator to decide what division to perform. - Compare the three calculated values at the end.

1. Find A: \(150 \div 3 = 50\). 2. Find B: \(200 \div 5 = 40\). 3. Find C: \(180 \div 4 = 45\). 4. Order the results: \(40 < 45 < 50\). 5. Match the letters to the values: B, C, A.

The correct order is B, C, A because \(40 < 45 < 50\).

- Use the denominator to think about how many equal groups make the whole. - What fraction completes two-thirds to make one whole?

1. Find one-third of the dots: \(54 \div 3 = 18\). 2. The fraction not shaded is the part that completes \(\frac{2}{3}\) to one whole, so it is \(\frac{1}{3}\). 3. Therefore, \(18\) dots are unshaded.

\(18\) dots are unshaded, and the unshaded fraction is \(\frac{1}{3}\).

- Find the numerical value of each fractional amount. - Divide by the denominator, then multiply by the numerator. - Compare the two final measurements.

1. For Value A, \(420\div6=70\), and \(70\times5=350\). Thus, Value A is \(350\,\text{m}\). 2. For Value B, \(400\div8=50\), and \(50\times7=350\). Thus, Value B is \(350\,\text{m}\). 3. The values are equal.

The values are equal; both are \(350\,\text{m}\).

- Find the two values separately. - Record the intermediate results so you can compare the final values. - Use multiplication facts to help with the division.

1. Find Calculation A: \(3200 \div 8 = 400\), and \(5 \times 400 = 2000\). 2. Find Calculation B: \(2700 \div 3 = 900\), and \(2 \times 900 = 1800\). 3. Since \(2000 > 1800\), Calculation A has the greater result.

Calculation A, \(2000\), is greater than Calculation B, \(1800\).

- Find the value on the left side and then the value on the right side. - To find a fraction such as two-fifths, divide by the denominator and multiply by the numerator. - Compare the two final values in each part.

1. a) \(\frac{2}{5} \times 200 = 80\), and \(\frac{1}{2} \times 180 = 90\). Therefore, \(80 < 90\). 2. b) \(\frac{3}{4} \times 120 = 90\), and \(\frac{2}{3} \times 150 = 100\). Therefore, \(90 < 100\). 3. c) \(\frac{5}{10} \times 400 = 200\), and \(\frac{1}{4} \times 800 = 200\). Therefore, \(200 = 200\).

a) \(<\) b) \(<\) c) \(=\)

- How many squares are in the grid altogether? - What does one-half mean for the total number of squares? - Count how many squares are already shaded.

1. Find the total number of squares: \(4 \times 5 = 20\). 2. Find one-half of the squares: \(\frac{1}{2} \times 20 = 10\). 3. Subtract the squares already shaded: \(10 - 6 = 4\).

\(4\) more squares must be shaded.