This answer key shows the full solution to each of the 10 decimal problems, including how the decimal point is placed. Estimates and checks are included so students can confirm that each answer is reasonable.
Problem 1: Add decimals
Line up the decimal points: \(4.75 + 12.60\). Hundredths: 5. Tenths: \(7 + 6 = 13\), write 3 and carry 1. Ones: \(4 + 2 + 1 = 7\). Tens: 1.
17.35
Problem 2: Subtract decimals
Write \(20.30 – 7.84\). Subtract hundredths: \(10 – 4 = 6\). Tenths: \(2 – 8\) needs a borrow, \(12 – 8 = 4\). Ones: \(9 – 7 = 2\). Tens: 1.
Check: \(12.46 + 7.84 = 20.30\).
12.46
Problem 3: Add three numbers
Write each number with three decimal places: \(3.500 + 0.275 + 12.000\). \(3.500 + 0.275 = 3.775\). \(3.775 + 12 = 15.775\).
15.775
Problem 4: Multiply by a whole number
Multiply \(83 \times 4 = 332\). The factor 8.3 has 1 decimal place and 4 has none, so the product has 1 decimal place.
Estimate: \(8 \times 4 = 32\), close to 33.2.
33.2
Problem 5: Multiply two decimals
Multiply \(48 \times 325 = 15{,}600\). The factors have \(1 + 2 = 3\) decimal places, so the product is \(15.600 = 15.6\).
Estimate: \(5 \times 3 = 15\), close to 15.6.
15.6
Problem 6: Divide by a whole number
The divisor 12 is a whole number. Divide 468 by 12: 12 into 46 is 3 (36), remainder 10. Bring down 8 to get 108: \(9 \times 12 = 108\). Place the decimal point above the point in the dividend.
Check: \(12 \times 3.9 = 46.8\).
3.9
Problem 7: Divide by a decimal
The divisor 0.36 has 2 decimal places. Multiply both numbers by 100: \(792 : 36\). 36 into 79 is 2 (72), remainder 7. Bring down 2 to get 72: \(2 \times 36 = 72\).
Check: \(0.36 \times 22 = 7.92\).
22
Problem 8: School store purchase
Notebooks: \(3 \times \$2.35 = \$7.05\). Total: \(\$7.05 + \$18.99 = \$26.04\). Change: \(\$30.00 – \$26.04 = \$3.96\).
Total \$26.04; change \$3.96.
Problem 9: Ribbon pieces
Divide \(14.4 : 0.45\). Multiply both by 100: \(1{,}440 : 45\). 45 into 144 is 3 (135), remainder 9. Bring down 0 to get 90: \(2 \times 45 = 90\). Quotient 32.
Check: \(0.45 \times 32 = 14.4\).
32 pieces
Problem 10: Weekly training miles
Weekdays: \(5 \times 3.75 = 18.75\) miles. Add Saturday: \(18.75 + 6.4 = 25.15\) miles per week.
Four weeks: \(4 \times 25.15 = 100.6\) miles. Since \(100.6 \ge 100\), he reaches the goal.
25.15 miles in one week; yes, 100.6 miles in 4 weeks.
See every chapter on the Grade 6 math page.