Decimal Operations

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Answer Key & Explanations

Decimal Operations · Grade 5 · Worksheet 3

1. 2.75 + 1.35 = ? Answer: 4.10 Solution: 2.75 + 1.35 Add the hundredths place: 5 + 5 = 10. Write 0 in the hundredths place and carry over 1 to the tenths place. Add the tenths place: 7 + 3 + 1 (carried over) = 11.
   Full step-by-step solution

   Step 1: Write the numbers with aligned decimal points: 2.75 + 1.35 Step 2: Add the hundredths place: 5 + 5 = 10. Write 0 in the hundredths place and carry over 1 to the tenths place. Step 3: Add the tenths place: 7 + 3 + 1 (carried over) = 11. Write 1 in the tenths place and carry over 1 to the ones place. Step 4: Add the ones place: 2 + 1 + 1 (carried over) = 4. Write 4 in the ones place. Step 5: The result is 4.10, which can also be written as 4.1. The answer is 4.10.

2. 0.65 × 1.8 = ? Answer: 1.17 Solution: Multiply 0.65 × 1.8 as if they were whole numbers: 65 × 18 65 × 10 = 650 65 × 8 = 520 650 + 520 = 1170 Count the decimal places: 0.65 has 2 decimal places, 1.8 has 1 decimal place, so total is 3 decimal places Place the decimal point in 1170 to get 3 decimal places: 1.170 Remove the trailing…
   Full step-by-step solution

   Step 1: Multiply 0.65 × 1.8 as if they were whole numbers: 65 × 18 Step 2: 65 × 10 = 650 Step 3: 65 × 8 = 520 Step 4: 650 + 520 = 1170 Step 5: Count the decimal places: 0.65 has 2 decimal places, 1.8 has 1 decimal place, so total is 3 decimal places Step 6: Place the decimal point in 1170 to get 3 decimal places: 1.170 Step 7: Remove the trailing zero: 1.17 The answer is 1.17.

3. Liam is comparing the weights of his pet hamster and his pet turtle. His hamster weighs 0.625 kilograms and his turtle weighs 0.58 kilograms. Which pet is heavier, and by how many kilograms? Answer: The hamster is heavier by 0.045 kilograms Solution: Identify the weights of each pet. Hamster weight = 0.625 kg Turtle weight = 0.580 kg Compare the two weights. - Both have 0 in the ones place.
   Full step-by-step solution

   Step 1: Identify the weights of each pet. Hamster weight = 0.625 kg Turtle weight = 0.580 kg Step 2: Compare the two weights. Look at each decimal place from left to right: - Both have 0 in the ones place. - Tenths place: Hamster has 6, Turtle has 5. Since 6 > 5, the hamster is heavier. Step 3: Find the difference in their weights. Subtract the turtle's weight from the hamster's weight: 0.625 - 0.580 Step 4: Perform the subtraction. Align the decimals: 0.625 - 0.580 ________ Start from the rightmost digit: Thousandths place: 5 - 0 = 5 Hundredths place: 2 - 8 (can't do, borrow from tenths) After borrowing: 12 - 8 = 4 Tenths place: 5 (after borrowing) - 5 = 0 Ones place: 0 - 0 = 0 So the result is 0.045 kg. Step 5: State the conclusion. The hamster is heavier by 0.045 kilograms.

4. 0.875 × 2.4 = ? Answer: 2.1 Solution: Multiply 0.875 × 2.4 as if they were whole numbers: 875 × 24 875 × 20 = 17,500 875 × 4 = 3,500 Add the partial products: 17,500 + 3,500 = 21,000 Count the decimal places: 0.875 has 3 decimal places, 2.4 has 1 decimal place, so total is 4 decimal places Place the decimal point in 21,000 to get 4…
   Full step-by-step solution

   Step 1: Multiply 0.875 × 2.4 as if they were whole numbers: 875 × 24 Step 2: 875 × 20 = 17,500 Step 3: 875 × 4 = 3,500 Step 4: Add the partial products: 17,500 + 3,500 = 21,000 Step 5: Count the decimal places: 0.875 has 3 decimal places, 2.4 has 1 decimal place, so total is 4 decimal places Step 6: Place the decimal point in 21,000 to get 4 decimal places: 2.1000 Step 7: Simplify: 2.1000 = 2.1 The answer is 2.1.

5. Hana is comparing the lengths of three hiking trails at a national park. The Tui Trail is 4.806 kilometers long, the Kea Trail is 4.860 kilometers long, and the Kiwi Trail is 4.680 kilometers long. Which hiking trail is the longest? Answer: 4.860 Solution: Write all three trail lengths with three decimal places for easy comparison: Tui Trail = 4.806, Kea Trail = 4.860, Kiwi Trail = 4.680. Compare the whole number part (ones place): All have 4, so move to the tenths place.
   Full step-by-step solution

   Step 1: Write all three trail lengths with three decimal places for easy comparison: Tui Trail = 4.806, Kea Trail = 4.860, Kiwi Trail = 4.680. Step 2: Compare the whole number part (ones place): All have 4, so move to the tenths place. Step 3: Compare the tenths place: Tui has 8, Kea has 8, Kiwi has 6. Since 6 is smaller than 8, Kiwi Trail is the shortest. Step 4: Compare the hundredths place for Tui and Kea: Tui has 0, Kea has 6. Since 6 is greater than 0, Kea Trail is longer than Tui Trail. Step 5: Therefore, Kea Trail at 4.860 kilometers is the longest. The answer is 4.860.

6. Mere is recording the rainfall amounts in her garden for three days. On Monday, 4.038 centimeters of rain fell. On Tuesday, 4.083 centimeters fell. On Wednesday, 4.38 centimeters fell. Write the rainfall amounts in order from least to greatest. Answer: 4.038, 4.083, 4.38 Solution: Write all three numbers with the same number of decimal places to make comparison easier: Monday: 4.038, Tuesday: 4.083, Wednesday: 4.380. Compare the whole number parts: all are 4, so they are the same.
   Full step-by-step solution

   Step 1: Write all three numbers with the same number of decimal places to make comparison easier: Monday: 4.038, Tuesday: 4.083, Wednesday: 4.380. Step 2: Compare the whole number parts: all are 4, so they are the same. Step 3: Compare the tenths place: Monday has 0, Tuesday has 0, Wednesday has 3. Since 0 < 3, Wednesday is the greatest so far, and Monday and Tuesday are smaller. Step 4: Compare Monday and Tuesday. They both have 0 tenths, so move to the hundredths place. Monday has 3 hundredths, Tuesday has 8 hundredths. Since 3 < 8, Monday is smaller than Tuesday. Step 5: So from least to greatest: Monday (4.038), Tuesday (4.083), Wednesday (4.38). The answer is 4.038, 4.083, 4.38.

7. 2.75 + 1.483 = ? Answer: 4.233 Solution: Write the numbers vertically, aligning the decimal points. 2.750 + 1.483 Add the thousandths place: 0 + 3 = 3 Add the hundredths place: 5 + 8 = 13. Write down 3 and carry over 1 to the tenths place.
   Full step-by-step solution

   Step 1: Write the numbers vertically, aligning the decimal points. 2.750 + 1.483 -------- Step 2: Add the thousandths place: 0 + 3 = 3 Step 3: Add the hundredths place: 5 + 8 = 13. Write down 3 and carry over 1 to the tenths place. Step 4: Add the tenths place: 7 + 4 + 1 (carried over) = 12. Write down 2 and carry over 1 to the ones place. Step 5: Add the ones place: 2 + 1 + 1 (carried over) = 4 Step 6: Bring down the decimal point. The final answer is 4.233.

8. A rectangular garden is drawn on a coordinate plane with corners at (2.5, 1.5), (8.5, 1.5), (8.5, 4.5), and (2.5, 4.5). What is the area of this garden in square units? Answer: 18 Solution: Identify the length by finding the difference in x-coordinates between two points on the same horizontal line. Points (2.5, 1.5) and (8.5, 1.5) have the same y-coordinate.
   Full step-by-step solution

   Step 1: Identify the length by finding the difference in x-coordinates between two points on the same horizontal line. Points (2.5, 1.5) and (8.5, 1.5) have the same y-coordinate. Length = 8.5 - 2.5 = 6 units Step 2: Identify the width by finding the difference in y-coordinates between two points on the same vertical line. Points (2.5, 1.5) and (2.5, 4.5) have the same x-coordinate. Width = 4.5 - 1.5 = 3 units Step 3: Calculate the area using the formula: Area = length × width Area = 6 × 3 = 18 square units The area of the garden is 18 square units.

9. 0.625 + 0.375 = ? Answer: 1.000 Solution: Write the problem vertically, aligning the decimal points. 0.625 + 0.375 Add the thousandths place: 5 + 5 = 10. Write down the 0 in the thousandths place and carry over the 1 to the hundredths place.
   Full step-by-step solution

   Step 1: Write the problem vertically, aligning the decimal points. 0.625 + 0.375 -------- Step 2: Add the thousandths place: 5 + 5 = 10. Write down the 0 in the thousandths place and carry over the 1 to the hundredths place. Step 3: Add the hundredths place, including the carry-over: 1 (carried) + 2 + 7 = 10. Write down the 0 in the hundredths place and carry over the 1 to the tenths place. Step 4: Add the tenths place, including the carry-over: 1 (carried) + 6 + 3 = 10. Write down the 0 in the tenths place and carry over the 1 to the ones place. Step 5: Add the ones place, including the carry-over: 1 (carried) + 0 + 0 = 1. Write down the 1 in the ones place. Step 6: Place the decimal point in the answer. The final answer is 1.000.