Add/Subtract Decimals

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Answer Key & Explanations

Add/Subtract Decimals · Grade 4 · Worksheet 2

1. 15.75 - 8.29 = ? Answer: 7.46 Solution: Write the numbers vertically with decimal points aligned: 15.75 - 8.29 Subtract the hundredths place: 5 - 9 (can't do, so regroup) Borrow 1 from the tenths place: 15 hundredths - 9 hundredths = 6 hundredths Now subtract the tenths place: 6 (after regrouping) - 2 = 4 tenths Subtract the ones…
   Full step-by-step solution

   Step 1: Write the numbers vertically with decimal points aligned: 15.75 - 8.29 Step 2: Subtract the hundredths place: 5 - 9 (can't do, so regroup) Borrow 1 from the tenths place: 15 hundredths - 9 hundredths = 6 hundredths Step 3: Now subtract the tenths place: 6 (after regrouping) - 2 = 4 tenths Step 4: Subtract the ones place: 15 - 8 = 7 ones Step 5: Bring down the decimal point Step 6: The result is 7.46 The answer is 7.46.

2. 15.67 - 8.29 = ? Answer: 7.38 Solution: Write the problem vertically with decimal points aligned: 15.67 - 8.29 Subtract the hundredths place: 7 - 9. Since 7 is less than 9, regroup from the tenths place. The 6 becomes 5, and the 7 becomes 17.
   Full step-by-step solution

   Step 1: Write the problem vertically with decimal points aligned: 15.67 - 8.29 Step 2: Subtract the hundredths place: 7 - 9. Since 7 is less than 9, regroup from the tenths place. The 6 becomes 5, and the 7 becomes 17. 17 - 9 = 8 Step 3: Subtract the tenths place: 5 - 2 = 3 Step 4: Subtract the ones place: 15 - 8 = 7 Step 5: Bring down the decimal point. The final answer is 7.38.

3. A rectangular swimming pool is drawn on a blueprint with a length of 15.25 meters and a width of 8.75 meters. A safety rope needs to be placed around the entire outer edge of the pool. What is the total length of rope needed in meters? Answer: 48 Solution: Recall the formula for the perimeter of a rectangle: Perimeter = 2 × (length + width) Substitute the given values into the formula: Perimeter = 2 × (15.25 + 8.75) Add the length and width: 15.25 + 8.75 = 24.00 Multiply the sum by 2: 2 × 24.00 = 48.00 State the final answer: The total length of…
   Full step-by-step solution

   Step 1: Recall the formula for the perimeter of a rectangle: Perimeter = 2 × (length + width) Step 2: Substitute the given values into the formula: Perimeter = 2 × (15.25 + 8.75) Step 3: Add the length and width: 15.25 + 8.75 = 24.00 Step 4: Multiply the sum by 2: 2 × 24.00 = 48.00 Step 5: State the final answer: The total length of rope needed is 48 meters.

4. Emma is training for a 5K race. On Monday, she ran 3.25 kilometers. On Wednesday, she ran 2.75 kilometers. How many total kilometers did Emma run during these two training sessions? Answer: 6.00 Solution: Monday: 3.25 kilometers Wednesday: 2.75 kilometers 3 + 2 = 5 0.25 + 0.75 = 1.00 5 + 1.00 = 6.00 Emma ran 6.00 kilometers total during these two training sessions.
   Full step-by-step solution

   Step 1: Write down the distances Emma ran each day Monday: 3.25 kilometers Wednesday: 2.75 kilometers Step 2: Add the whole number parts 3 + 2 = 5 Step 3: Add the decimal parts 0.25 + 0.75 = 1.00 Step 4: Combine the results 5 + 1.00 = 6.00 Emma ran 6.00 kilometers total during these two training sessions.

5. A farmer harvested 125.75 kilograms of apples from one orchard and 89.25 kilograms from another. How many total kilograms of apples did the farmer harvest? Answer: 215.00 Solution: Write down the two weights to be added. After carrying, tenths place: We already accounted for 0.75 + 0.25 = 1.00, so tenths are 0, and we carried 1 to the units column.
   Full step-by-step solution

   Let's add the two amounts of apples step by step. Step 1: Write down the two weights to be added. First weight: 125.75 kg Second weight: 89.25 kg Step 2: Align them by decimal point for addition: 125.75 + 89.25 Step 3: Add the hundredths place (digits after the decimal): 0.75 + 0.25 = 1.00 So, we write 0 in the hundredths place and carry over 1 to the units place. Step 4: Add the tenths place: After carrying, tenths place: We already accounted for 0.75 + 0.25 = 1.00, so tenths are 0, and we carried 1 to the units column. Step 5: Add the units place: 5 (from 125.75) + 9 (from 89.25) = 14, plus the carried 1 = 15. Write 5 in the units place, carry 1 to the tens place. Step 6: Add the tens place: 2 (from 125.75) + 8 (from 89.25) = 10, plus the carried 1 = 11. Write 1 in the tens place, carry 1 to the hundreds place. Step 7: Add the hundreds place: 1 (from 125.75) + 0 (from 89.25) = 1, plus the carried 1 = 2. Write 2 in the hundreds place. Step 8: Combine the result: Hundreds: 2, Tens: 1, Units: 5, Decimal: .00 So we get 215.00 Final answer: The farmer harvested 215.00 kilograms of apples in total.

6. A rectangular swimming pool is drawn with a length of 15.25 meters and a width of 9.5 meters. A decorative tile border is installed around the entire edge of the pool. What is the total length of the tile border in meters? Answer: 49.5 Solution: Recall the formula for the perimeter of a rectangle. Perimeter = 2 × (length + width) Substitute the given values into the formula. Perimeter = 2 × (15.25 + 9.5) Add the length and width.
   Full step-by-step solution

   Step 1: Recall the formula for the perimeter of a rectangle. Perimeter = 2 × (length + width) Step 2: Substitute the given values into the formula. Perimeter = 2 × (15.25 + 9.5) Step 3: Add the length and width. 15.25 + 9.5 = 24.75 Step 4: Multiply by 2. 2 × 24.75 = 49.5 Step 5: State the final answer. The total length of the tile border is 49.5 meters.