Q1: What is \(5.8 - 2.3\)? (a) 3.5 (b) 3.4 (c) 4.5 (d) 8.1
Solution:
Ans: (a) Explanation: To subtract decimals, we line up the decimal points. Starting from the tenths place: \(8 - 3 = 5\). In the ones place: \(5 - 2 = 3\). So the answer is \(3.5\). Option (b) is incorrect because the subtraction was not done correctly. Option (c) is wrong because it doesn't follow proper decimal subtraction. Option (d) is the result of addition, not subtraction.
Q2: A ribbon is \(9.7\) meters long. If \(4.2\) meters are cut off, how much ribbon is left? (a) 5.5 meters (b) 5.9 meters (c) 6.5 meters (d) 13.9 meters
Solution:
Ans: (a) Explanation: We need to subtract: \(9.7 - 4.2\). Aligning the decimal points, we get \(7 - 2 = 5\) in the tenths place and \(9 - 4 = 5\) in the ones place. The answer is \(5.5\) meters. Option (b) results from incorrect borrowing. Option (c) has an error in the ones place. Option (d) is the sum instead of the difference.
Q3: Which of the following shows the correct way to set up \(7.6 - 3.4\)? (a) Align the ones digits only (b) Align the decimal points (c) Place the smaller number on top (d) Ignore the decimal point
Solution:
Ans: (b) Explanation: When subtracting decimals, we must align the decimal points to ensure that we subtract tenths from tenths and ones from ones. Option (a) is incorrect because aligning only ones digits ignores the decimal structure. Option (c) is wrong because the larger number should be on top. Option (d) is incorrect as ignoring decimals would give a wrong answer.
Q4: What is \(8.0 - 3.7\)? (a) 4.3 (b) 5.3 (c) 4.7 (d) 11.7
Solution:
Ans: (a) Explanation: We need to borrow from the ones place. Rewrite \(8.0\) as \(7.10\). Now subtract: \(10 - 7 = 3\) in the tenths place and \(7 - 3 = 4\) in the ones place. The answer is \(4.3\). Option (b) results from not borrowing correctly. Option (c) is incorrect due to improper subtraction. Option (d) is the sum instead.
Q5: Mia had \(6.5\) liters of juice. She drank \(2.8\) liters. How much juice does she have left? (a) 3.7 liters (b) 4.3 liters (c) 3.3 liters (d) 9.3 liters
Solution:
Ans: (a) Explanation: Subtract \(6.5 - 2.8\). We need to borrow from the ones place: rewrite \(6.5\) as \(5.15\). Now \(15 - 8 = 7\) in the tenths place and \(5 - 2 = 3\) in the ones place. The answer is \(3.7\) liters. Option (b) is incorrect due to a borrowing error. Option (c) results from incorrect subtraction. Option (d) is the sum.
Q6: What is the difference between \(10.0\) and \(4.6\)? (a) 5.4 (b) 6.4 (c) 6.6 (d) 14.6
Solution:
Ans: (a) Explanation: Subtract \(10.0 - 4.6\). Rewrite \(10.0\) as \(9.10\) after borrowing. Now \(10 - 6 = 4\) in the tenths place and \(9 - 4 = 5\) in the ones place, giving \(5.4\). Option (b) is incorrect due to improper borrowing. Option (c) results from calculation errors. Option (d) is the sum.
Q7: If you subtract \(1.9\) from \(5.2\), what is the result? (a) 3.3 (b) 4.3 (c) 3.7 (d) 7.1
Solution:
Ans: (a) Explanation: Calculate \(5.2 - 1.9\). Borrow from the ones place: \(5.2\) becomes \(4.12\). Now \(12 - 9 = 3\) in the tenths place and \(4 - 1 = 3\) in the ones place. The answer is \(3.3\). Option (b) results from not borrowing. Option (c) has a calculation error. Option (d) is the sum.
Ans: (c) Explanation:Borrowing is needed when the digit in the minuend (top number) is smaller than the digit in the subtrahend (bottom number) in any place. In option (c), \(6.3 - 4.7\), the tenths place has \(3 - 7\), which requires borrowing from the ones place. Options (a), (b), and (d) do not require borrowing as each digit in the top number is greater than or equal to the corresponding digit in the bottom number.
Section B: Fill in the Blanks
Q9:When subtracting decimals, you must always align the __________.
Solution:
Ans: decimal points Explanation: Aligning the decimal points ensures that we subtract digits in the same place value positions (tenths from tenths, ones from ones, etc.).
Q10:In the problem \(9.4 - 3.6\), we need to __________ from the ones place to subtract in the tenths place.
Solution:
Ans: borrow Explanation: Since \(4\) is less than \(6\) in the tenths place, we must borrow one from the ones place, changing \(9.4\) to \(8.14\).
Q11:The answer to a subtraction problem is called the __________.
Solution:
Ans: difference Explanation: The difference is the result when one number is subtracted from another.
Q12:\(12.5 - 7.8 = \) __________
Solution:
Ans: 4.7 Explanation: After borrowing, \(12.5\) becomes \(11.15\). Then \(15 - 8 = 7\) in the tenths place and \(11 - 7 = 4\) in the ones place, giving \(4.7\).
Q13:If you have \(8.0\) and subtract \(2.5\), the result is __________.
Solution:
Ans: 5.5 Explanation: Subtracting \(8.0 - 2.5\): In the tenths place, \(0 - 5\) requires borrowing. \(8.0\) becomes \(7.10\). Then \(10 - 5 = 5\) and \(7 - 2 = 5\), giving \(5.5\).
Q14:When the tenths digit of the number being subtracted is larger than the tenths digit of the number you're subtracting from, you need to __________ from the ones place.
Solution:
Ans: borrow (or regroup) Explanation:Borrowing (also called regrouping) allows us to subtract when a digit in the minuend is smaller than the corresponding digit in the subtrahend.
Section C: Word Problems
Q15:Sarah walked \(4.7\) kilometers on Saturday and \(2.9\) kilometers on Sunday. How much farther did she walk on Saturday than on Sunday?
Solution:
Ans: Step 1: Subtract the distances: \(4.7 - 2.9\) Step 2: Borrow from the ones place: \(4.7\) becomes \(3.17\) Step 3: \(17 - 9 = 8\) in the tenths place Step 4: \(3 - 2 = 1\) in the ones place Final Answer: 1.8 kilometers
Q16:A water tank contained \(15.6\) liters of water. After using some water, \(9.8\) liters remained. How much water was used?
Solution:
Ans: Step 1: Subtract to find the amount used: \(15.6 - 9.8\) Step 2: Borrow from the ones place: \(15.6\) becomes \(14.16\) Step 3: \(16 - 8 = 8\) in the tenths place Step 4: \(14 - 9 = 5\) in the ones place Final Answer: 5.8 liters
Q17:Jason has a rope that is \(7.3\) meters long. He cuts off a piece that is \(3.6\) meters long. What is the length of the rope that remains?
Solution:
Ans: Step 1: Subtract the lengths: \(7.3 - 3.6\) Step 2: Borrow from the ones place: \(7.3\) becomes \(6.13\) Step 3: \(13 - 6 = 7\) in the tenths place Step 4: \(6 - 3 = 3\) in the ones place Final Answer: 3.7 meters
Q18:A basket of apples weighs \(11.2\) kilograms. If \(4.5\) kilograms of apples are removed, what is the weight of the remaining apples?
Solution:
Ans: Step 1: Subtract the weights: \(11.2 - 4.5\) Step 2: Borrow from the ones place: \(11.2\) becomes \(10.12\) Step 3: \(12 - 5 = 7\) in the tenths place Step 4: \(10 - 4 = 6\) in the ones place Final Answer: 6.7 kilograms
Q19:Emma had \(20.0\) dollars. She spent \(12.7\) dollars on a book. How much money does she have left?
Solution:
Ans: Step 1: Subtract the amounts: \(20.0 - 12.7\) Step 2: Borrow from the tens place: \(20.0\) becomes \(19.10\) Step 3: \(10 - 7 = 3\) in the tenths place Step 4: \(19 - 12 = 7\) in the ones place Final Answer: 7.3 dollars
Q20:A garden hose is \(13.5\) meters long. If a \(6.9\) meter section is damaged and removed, how long is the hose now?
Solution:
Ans: Step 1: Subtract the lengths: \(13.5 - 6.9\) Step 2: Borrow from the ones place: \(13.5\) becomes \(12.15\) Step 3: \(15 - 9 = 6\) in the tenths place Step 4: \(12 - 6 = 6\) in the ones place Final Answer: 6.6 meters
The document Worksheet (with Solutions): Subtracting Decimals (Tenths) is a part of the Grade 5 Course Math Grade 5.
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