Add/Subtract Decimals

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Answer Key & Explanations

Add/Subtract Decimals · Grade 4 · Worksheet 1

1. Noah is building a bookshelf and needs to cut two pieces of wood. The first piece needs to be 2.45 meters long and the second piece needs to be 1.85 meters long. How many meters of wood does Noah need in total? Answer: 4.30 Solution: Identify the two lengths Noah needs: 2.45 meters and 1.85 meters Add the two lengths together: 2.45 + 1.85 Add the hundredths place: 5 hundredths + 5 hundredths = 10 hundredths = 1 tenth and 0 hundredths Add the tenths place: 4 tenths + 8 tenths = 12 tenths, plus the 1 tenth from step 3 = 13…
   Full step-by-step solution

   Step 1: Identify the two lengths Noah needs: 2.45 meters and 1.85 meters Step 2: Add the two lengths together: 2.45 + 1.85 Step 3: Add the hundredths place: 5 hundredths + 5 hundredths = 10 hundredths = 1 tenth and 0 hundredths Step 4: Add the tenths place: 4 tenths + 8 tenths = 12 tenths, plus the 1 tenth from step 3 = 13 tenths = 1 one and 3 tenths Step 5: Add the ones place: 2 ones + 1 one = 3 ones, plus the 1 one from step 4 = 4 ones Step 6: Combine all parts: 4 ones, 3 tenths, and 0 hundredths = 4.30 meters Noah needs 4.30 meters of wood in total.

2. Liam is measuring fabric for a school project. He needs 2.75 meters of blue fabric and 1.5 meters of red fabric. How many meters of fabric does Liam need in total? Answer: 4.25 Solution: Write down the amounts of fabric. Blue fabric: 2.75 meters Red fabric: 1.5 meters Align the numbers by their decimal points to add them. 2.75 + 1.50 Add the hundredths place (rightmost digits).
   Full step-by-step solution

   Let's add the two lengths of fabric together step by step. Step 1: Write down the amounts of fabric. Blue fabric: 2.75 meters Red fabric: 1.5 meters Step 2: Align the numbers by their decimal points to add them. 2.75 + 1.50 -------- Step 3: Add the hundredths place (rightmost digits). 5 hundredths + 0 hundredths = 5 hundredths. Write ._ _ 5 Step 4: Add the tenths place. 7 tenths + 5 tenths = 12 tenths. 12 tenths = 1 whole and 2 tenths. Write ._ 2 in the tenths place and carry 1 to the ones place. Step 5: Add the ones place. 2 ones + 1 one = 3 ones, plus the carried 1 makes 4 ones. Write 4 in the ones place. Step 6: Combine the results. 4 ones + 2 tenths + 5 hundredths = 4.25 So, Liam needs 4.25 meters of fabric in total.

3. 15.60 - 8.45 = ? Answer: 7.15 Solution: Write the problem vertically with decimal points aligned: 15.60 - 8.45 Subtract the hundredths place: 0 - 5 (we need to borrow) Borrow from the tenths place: 6 becomes 5, and 0 becomes 10 10 - 5 = 5 hundredths Subtract the tenths place: 5 - 4 = 1 tenth Subtract the ones place: 15 - 8 = 7 ones…
   Full step-by-step solution

   Step 1: Write the problem vertically with decimal points aligned: 15.60 - 8.45 Step 2: Subtract the hundredths place: 0 - 5 (we need to borrow) Borrow from the tenths place: 6 becomes 5, and 0 becomes 10 10 - 5 = 5 hundredths Step 3: Subtract the tenths place: 5 - 4 = 1 tenth Step 4: Subtract the ones place: 15 - 8 = 7 ones Step 5: Bring down the decimal point Step 6: The result is 7.15 The answer is 7.15.

4. Noah is drawing a rectangle on a grid to represent a garden. The length of the rectangle is 15.6 meters and the width is 8.1 meters. He wants to draw a fence along the entire outside edge of the rectangle. What is the total length of the fence in meters? Answer: 47.4 Solution: Identify the side lengths. The rectangle has two sides of length 15.6 meters and two sides of length 8.1 meters. Add the two different side lengths together: 15.6 + 8.1 = 23.7 meters.
   Full step-by-step solution

   Step 1: Identify the side lengths. The rectangle has two sides of length 15.6 meters and two sides of length 8.1 meters. Step 2: Add the two different side lengths together: 15.6 + 8.1 = 23.7 meters. Step 3: Since there are two of each side, multiply the sum by 2: 2 x 23.7 = 47.4 meters. Step 4: The total length of the fence is 47.4 meters.

5. A rectangular school playground is drawn with a length of 125.75 meters and a width of 89.5 meters. A running track is marked along the entire outer edge of the playground. What is the total length of the running track in meters? Answer: 430.5 Solution: Recall the formula for the perimeter of a rectangle. Perimeter = 2 × (length + width) Substitute the given values into the formula. Perimeter = 2 × (125.75 + 89.5) 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 × (125.75 + 89.5) Step 3: Add the length and width. 125.75 + 89.5 = 215.25 Step 4: Multiply by 2. 2 × 215.25 = 430.5 Step 5: State the final answer. The total length of the running track is 430.5 meters.

6. Liam is measuring fabric for a school project. He needs 2.75 meters of blue fabric and 1.25 meters of red fabric. How many meters of fabric does Liam need in total? Answer: 4.00 Solution: Identify the amounts of fabric needed. Blue fabric: 2.75 meters Red fabric: 1.25 meters Set up the addition. Total fabric = 2.75 + 1.25 Add the numbers.
   Full step-by-step solution

   Let's solve this step by step. Step 1: Identify the amounts of fabric needed. Blue fabric: 2.75 meters Red fabric: 1.25 meters Step 2: Set up the addition. Total fabric = 2.75 + 1.25 Step 3: Add the numbers. First, add the hundredths place: 0.75 + 0.25 0.75 + 0.25 = 1.00 Step 4: Add the whole numbers: 2 + 1 = 3 Step 5: Combine the results: 3 + 1.00 = 4.00 Step 6: Final answer: Liam needs 4.00 meters of fabric in total.

7. 12.75 + 8.50 = ? Answer: 21.25 Solution: Write the numbers one under the other, aligning the decimal points. 12.75 + 8.50 Start adding from the rightmost column (hundredths place). 5 hundredths + 0 hundredths = 5 hundredths.
   Full step-by-step solution

   Let's add 12.75 and 8.50 step-by-step. Step 1: Write the numbers one under the other, aligning the decimal points. 12.75 + 8.50 -------- Step 2: Start adding from the rightmost column (hundredths place). 5 hundredths + 0 hundredths = 5 hundredths. Write 5 in the hundredths place. 12.75 + 8.50 -------- .05 Step 3: Move left to the tenths place. 7 tenths + 5 tenths = 12 tenths. 12 tenths is the same as 1 whole and 2 tenths. Write 2 in the tenths place and carry over 1 to the ones place. 12.75 + 8.50 -------- .25 (with 1 carried to ones) Step 4: Add the ones place, including the carry. Ones: 2 + 8 + 1 (carry) = 11 ones. 11 ones means 1 ten and 1 one. Write 1 in the ones place and carry over 1 to the tens place. 12.75 + 8.50 -------- 1.25 (with 1 carried to tens) Step 5: Add the tens place, including the carry. Tens: 1 + 1 (carry) = 2 tens. Write 2 in the tens place. 12.75 + 8.50 -------- 21.25 Step 6: Write the final answer with the decimal point in the correct position. ANSWER: 21.25