Free Math Worksheets

- Look closely at the hundredths digits. - Which pairs add to a whole number? - You do not need to add the four numbers in the order given.

1. Pair numbers that add to whole numbers: \(0.85 + 3.15\) and \(2.14 + 1.86\). 2. Evaluate the first pair: \(0.85 + 3.15 = 4.00\). 3. Evaluate the second pair: \(2.14 + 1.86 = 4.00\). 4. Add the pair sums: \(4.00\,\text{kg} + 4.00\,\text{kg} = 8.00\,\text{kg}\).

The total mass is \(8.00\,\text{kg}\). One efficient grouping is \((0.85 + 3.15) + (2.14 + 1.86) = 4.00 + 4.00 = 8.00\).

- Look for decimal parts that combine to make whole numbers. - Several subtractions can be rewritten as subtracting the sum of the amounts. - In b), find two numbers with the same tenths digit and two numbers whose decimal parts make a whole.

1. For a), group numbers that add to whole numbers: \((12.35 + 7.65) + (7.8 + 2.2) = 20 + 10 = 30\). 2. For b), rewrite the subtractions as subtracting a total and group conveniently: \((24.7 - 4.7) - (3.9 + 6.1) = 20 - 10 = 10\).

a) \(30\) b) \(10\)

- Look for decimal parts that combine or cancel to make whole numbers. - Rewrite repeated subtraction as subtracting a sum before regrouping. - Keep the signs attached to the terms when you rearrange.

1. Group the terms to create easy differences and sums: \((12.4 - 2.4) - (5.8 + 1.2)\). 2. Evaluate the groups: \(12.4 - 2.4 = 10\) and \(5.8 + 1.2 = 7\). 3. Subtract: \(10 - 7 = 3\).

\(3\)

- Decide whether fractions or decimals will be easier to use. - Subtract when water is consumed and add when water is refilled. - For the capacity, identify the greatest amount in the bottle at any time.

1. Convert \(\frac{3}{8}\) to a decimal: \(\frac{3}{8}=0.375\). 2. The final amount is \(1.5-0.375+0.5-0.4=1.225\) liters. 3. After the first drink, the bottle contains \(1.5-0.375=1.125\) liters. After refilling, it contains \(1.125+0.5=1.625\) liters. This is the greatest amount in the bottle. 4. Therefore, the minimum capacity is \(1.625\) liters.

a) \(1.225\) liters b) At least \(1.625\) liters

- Determine the value of one small interval between consecutive tenths. - Count hundredths from the nearest labeled tenth. - Subtract the smaller coordinate from the larger one.

1. Each tenth is divided into \(10\) equal intervals, so each small interval represents \(0.01\). 2. Point \(A\) is four intervals right of \(5.2\), so \(A=5.24\). 3. Point \(B\) is seven intervals right of \(5.4\), so \(B=5.47\). 4. The distance is \(5.47-5.24=0.23\).

\(A=5.24\), \(B=5.47\), and the distance is \(0.23\).