Q1: What is 2.3 + 1.9? (a) 3.2 (b) 4.2 (c) 4.12 (d) 3.12
Solution:
Ans: (b) Explanation: When adding \(2.3 + 1.9\), we add the tenths place: \(3 + 9 = 12\) tenths. This means we regroup 10 tenths as 1 whole. So \(2 + 1 = 3\) wholes, plus the regrouped 1 whole equals 4 wholes, and 2 tenths remain. The answer is \(4.2\).
Q2: When you add 0.8 + 0.7, how many tenths do you have before regrouping? (a) 1 tenth (b) 5 tenths (c) 15 tenths (d) 10 tenths
Solution:
Ans: (c) Explanation: Adding \(0.8 + 0.7\) gives us \(8\) tenths \(+ 7\) tenths \(= 15\) tenths. Since we have more than 10 tenths, we need to regroup 10 tenths into 1 whole, leaving 5 tenths, which equals \(1.5\).
Q3: What is 5.6 - 2.8? (a) 3.8 (b) 2.8 (c) 3.2 (d) 2.2
Solution:
Ans: (b) Explanation: In \(5.6 - 2.8\), we cannot subtract 8 tenths from 6 tenths. We regroup 1 whole from the 5, making it 4 wholes and 16 tenths. Now \(16 - 8 = 8\) tenths, and \(4 - 2 = 2\) wholes. The answer is \(2.8\).
Ans: (c) Explanation: In \(2.8 + 1.5\), we add the tenths: \(8 + 5 = 13\) tenths. Since 13 tenths is more than 10 tenths, we need to regroup 10 tenths as 1 whole. The other options have tenths that add to 10 or less, so no regrouping is needed.
Q5: What is 4.1 - 1.7? (a) 2.4 (b) 3.4 (c) 2.6 (d) 3.6
Solution:
Ans: (a) Explanation: In \(4.1 - 1.7\), we cannot subtract 7 tenths from 1 tenth. We regroup 1 whole from 4, making it 3 wholes and 11 tenths. Now \(11 - 7 = 4\) tenths, and \(3 - 1 = 2\) wholes. The answer is \(2.4\).
Q6: When adding 1.6 + 2.7, what is the sum? (a) 3.13 (b) 4.3 (c) 3.3 (d) 4.13
Solution:
Ans: (b) Explanation: Adding the tenths: \(6 + 7 = 13\) tenths. We regroup 10 tenths as 1 whole, leaving 3 tenths. Adding the wholes: \(1 + 2 + 1 = 4\) wholes. The answer is \(4.3\).
Q7: What decimal subtraction problem is shown? "I have 3 wholes and 2 tenths. I regroup to get 2 wholes and 12 tenths." (a) 3.2 - 0.5 (b) 3.2 - 1.8 (c) 3.2 - 2.1 (d) 3.2 - 0.2
Solution:
Ans: (b) Explanation: We need to regroup when we cannot subtract the tenths. In \(3.2 - 1.8\), we cannot subtract 8 tenths from 2 tenths, so we regroup 1 whole from 3, giving us 2 wholes and 12 tenths. This matches the description.
Q8: What is 6.0 - 3.5? (a) 2.5 (b) 3.5 (c) 3.0 (d) 2.0
Solution:
Ans: (a) Explanation: In \(6.0 - 3.5\), we have 0 tenths but need to subtract 5 tenths. We regroup 1 whole from 6, making it 5 wholes and 10 tenths. Now \(10 - 5 = 5\) tenths, and \(5 - 3 = 2\) wholes. The answer is \(2.5\).
Section B: Fill in the Blanks
Q9: When adding decimals, if the sum of the tenths is 10 or more, we need to __________ into the ones place.
Solution:
Ans: regroup Explanation: When the sum of tenths reaches 10 or more, we regroup 10 tenths as 1 whole and add it to the ones place.
Q10: In the problem 5.3 - 2.9, we regroup 1 whole from the ones place to get __________ tenths.
Solution:
Ans: 10 Explanation: When we regroup 1 whole, it equals 10 tenths. We add these 10 tenths to the existing tenths to have enough to subtract.
Q11: The sum of 0.9 + 0.8 equals __________.
Solution:
Ans: 1.7 Explanation: Adding \(9 + 8 = 17\) tenths. We regroup 10 tenths as 1 whole, leaving 7 tenths. So the answer is \(1.7\).
Q12: When we regroup 1 whole as tenths, we get __________ tenths.
Solution:
Ans: 10 Explanation: One whole is equal to 10 tenths. This is the foundation of regrouping in decimal subtraction when we need more tenths.
Q13: In 7.2 - 4.6, after regrouping, the 7 wholes become 6 wholes and __________ tenths.
Solution:
Ans: 12 Explanation: We regroup 1 whole from 7 to get 6 wholes and 10 tenths. Adding the original 2 tenths gives us \(10 + 2 = 12\) tenths total.
Q14: If you have 13 tenths after adding, this equals 1 whole and __________ tenths.
Solution:
Ans: 3 Explanation: We regroup 10 tenths as 1 whole. From 13 tenths, after taking away 10 tenths (1 whole), we have 3 tenths remaining.
Section C: Word Problems
Q15: Emma ran 2.7 miles on Monday and 3.6 miles on Tuesday. How many miles did she run in total?
Solution:
Ans: Step 1: Add the tenths: \(7 + 6 = 13\) tenths Step 2: Regroup 10 tenths as 1 whole, leaving 3 tenths Step 3: Add the wholes: \(2 + 3 + 1 = 6\) wholes Final Answer: 6.3 miles
Q16: A water bottle holds 1.5 liters. After drinking some water, there are 0.8 liters left. How much water was drunk?
Solution:
Ans: Step 1: Subtract: \(1.5 - 0.8\) Step 2: Regroup 1 whole from 1 to get 0 wholes and 15 tenths Step 3: Subtract the tenths: \(15 - 8 = 7\) tenths Final Answer: 0.7 liters
Q17: Jason has 5.0 pounds of apples. He uses 2.4 pounds to make a pie. How many pounds of apples does he have left?
Solution:
Ans: Step 1: Subtract: \(5.0 - 2.4\) Step 2: Regroup 1 whole from 5 to get 4 wholes and 10 tenths Step 3: Subtract tenths: \(10 - 4 = 6\) tenths Step 4: Subtract wholes: \(4 - 2 = 2\) wholes Final Answer: 2.6 pounds
Q18: A ribbon is 4.3 meters long. Maria cuts off 1.8 meters. What is the length of the remaining ribbon?
Solution:
Ans: Step 1: Subtract: \(4.3 - 1.8\) Step 2: Regroup 1 whole from 4 to get 3 wholes and 13 tenths Step 3: Subtract tenths: \(13 - 8 = 5\) tenths Step 4: Subtract wholes: \(3 - 1 = 2\) wholes Final Answer: 2.5 meters
Q19: Sophie walked 1.9 kilometers in the morning and 2.6 kilometers in the afternoon. What is the total distance she walked?
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