Q1: What is \(3.45 + 2.31\)? (a) 5.76 (b) 6.76 (c) 5.67 (d) 4.76
Solution:
Ans: (a) Explanation: To add decimals, align the decimal points vertically. Adding \(3.45 + 2.31\): Hundredths place: \(5 + 1 = 6\) Tenths place: \(4 + 3 = 7\) Ones place: \(3 + 2 = 5\) The answer is \(5.76\).
Q2: Which number sentence shows the commutative property of addition with decimals? (a) \(1.25 + 3.40 = 3.40 + 1.25\) (b) \(1.25 + 0 = 1.25\) (c) \(1.25 + 3.40 = 4.65\) (d) \(1.25 + (3.40 + 2.10) = (1.25 + 3.40) + 2.10\)
Solution:
Ans: (a) Explanation: The commutative property states that changing the order of addends does not change the sum. Option (a) shows \(1.25 + 3.40 = 3.40 + 1.25\), which demonstrates this property. Option (b) shows the identity property, option (c) shows a simple addition, and option (d) shows the associative property.
Q3: Sarah added \(4.67 + 3.28\) and got 7.85. What mistake did she make? (a) She forgot to align the decimal points (b) She did not regroup correctly from the hundredths place (c) She added the whole numbers incorrectly (d) She placed the decimal point in the wrong position
Solution:
Ans: (b) Explanation: The correct answer is \(4.67 + 3.28 = 7.95\). Sarah got 7.85 instead. Hundredths place: \(7 + 8 = 15\), write 5 and regroup 1 tenth. Tenths place: \(6 + 2 + 1 = 9\). Sarah did not regroup the 10 hundredths as 1 tenth correctly, so she wrote 8 instead of 9 in the tenths place.
Q4: What is the sum of \(12.08 + 5.92\)? (a) 17.00 (b) 18.00 (c) 17.10 (d) 17.90
Q5: Estimate the sum of \(6.47 + 3.82\) by rounding to the nearest whole number. (a) 9 (b) 10 (c) 11 (d) 12
Solution:
Ans: (b) Explanation: To estimate, round each number to the nearest whole number first. \(6.47\) rounds to \(6\) (since 0.47 is less than 0.5). \(3.82\) rounds to \(4\) (since 0.82 is greater than 0.5). Then add: \(6 + 4 = 10\).
Q6: Which sum is greater: \(7.35 + 2.48\) or \(8.19 + 1.67\)? (a) \(7.35 + 2.48\) (b) \(8.19 + 1.67\) (c) They are equal (d) Cannot be determined
Solution:
Ans: (a) Explanation: Calculate both sums: \(7.35 + 2.48 = 9.83\) \(8.19 + 1.67 = 9.86\) Comparing the two sums: \(9.86 > 9.83\). Therefore, \(8.19 + 1.67\) is greater. The correct answer is (b). Note: There was an error in the initial answer selection. The correct answer is (b).
Q7: What is \(0.56 + 0.44\)? (a) 0.90 (b) 0.10 (c) 1.00 (d) 1.10
Solution:
Ans: (c) Explanation: Adding \(0.56 + 0.44\): Hundredths place: \(6 + 4 = 10\), write 0 and regroup 1 tenth. Tenths place: \(5 + 4 + 1 = 10\), write 0 and regroup 1 one. Ones place: \(0 + 0 + 1 = 1\). The answer is \(1.00\) or \(1\).
Q8: When adding \(15.37 + 9.28\), what is the digit in the tenths place of the sum? (a) 2 (b) 4 (c) 5 (d) 6
Solution:
Ans: (d) Explanation: Calculate \(15.37 + 9.28\): Hundredths place: \(7 + 8 = 15\), write 5 and regroup 1 tenth. Tenths place: \(3 + 2 + 1 = 6\). Ones place: \(5 + 9 = 14\), write 4 and regroup 1 ten. Tens place: \(1 + 0 + 1 = 2\). The sum is \(24.65\), and the digit in the tenths place is \(6\).
Section B: Fill in the Blanks
Q9: When adding decimals, you must always align the __________ before adding.
Solution:
Ans: decimal points Explanation: Aligning the decimal points ensures that digits with the same place value (ones, tenths, hundredths) are added together correctly.
Q10: The sum of \(8.45\) and \(1.55\) is __________.
Q11: In the number \(43.78\), the digit 7 is in the __________ place.
Solution:
Ans: tenths Explanation: In decimal numbers, the first digit after the decimal point represents the tenths place. In \(43.78\), the digit 7 is in the tenths place and 8 is in the hundredths place.
Q12: When you add 10 hundredths together, you get __________ tenth.
Solution:
Ans: 1 Explanation: There are 10 hundredths in 1 tenth. This is the basis for regrouping when adding decimals: \(10 \times 0.01 = 0.10\).
Q13: \(5.30 + 2.70 = \) __________
Solution:
Ans: 8.00 (or 8) Explanation: Adding \(5.30 + 2.70\): Hundredths: \(0 + 0 = 0\). Tenths: \(3 + 7 = 10\), write 0 and regroup 1 one. Ones: \(5 + 2 + 1 = 8\). The sum is \(8.00\).
Q14: The commutative property of addition states that changing the __________ of the addends does not change the sum.
Solution:
Ans: order Explanation: The commutative property means that \(a + b = b + a\). For example, \(3.25 + 4.10 = 4.10 + 3.25\). Changing the order of addends does not affect the sum.
Section C: Word Problems
Q15: Maria bought a notebook for $3.45 and a pen for $1.28. How much did she spend in total?
Solution:
Ans: Step 1: Identify the amounts: notebook = $3.45, pen = $1.28 Step 2: Add the two amounts by aligning decimal points: \[3.45 + 1.28\] Hundredths: \(5 + 8 = 13\), write 3 and regroup 1 tenth. Tenths: \(4 + 2 + 1 = 7\). Ones: \(3 + 1 = 4\). Final Answer: $4.73
Q16: A rectangular garden has one side measuring 12.75 meters and another side measuring 8.50 meters. What is the perimeter of the garden?
Solution:
Ans: Step 1: Recall that the perimeter of a rectangle is the sum of all four sides: \(P = 2 \times (\text{length} + \text{width})\). Step 2: Add the two different sides: \(12.75 + 8.50 = 21.25\) meters. Step 3: Multiply by 2: \(2 \times 21.25 = 42.50\) meters. Final Answer: 42.50 meters
Q17: Tom ran 3.68 kilometers on Monday and 4.57 kilometers on Tuesday. How many kilometers did he run in total over the two days?
Solution:
Ans: Step 1: Identify distances: Monday = 3.68 km, Tuesday = 4.57 km. Step 2: Add the distances: \[3.68 + 4.57\] Hundredths: \(8 + 7 = 15\), write 5 and regroup 1 tenth. Tenths: \(6 + 5 + 1 = 12\), write 2 and regroup 1 one. Ones: \(3 + 4 + 1 = 8\). Final Answer: 8.25 kilometers
Q18: A recipe calls for 2.35 cups of flour and 1.80 cups of sugar. How many cups of dry ingredients are needed in total?
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