Multi-Digit and Decimal Operations: practice solutions, Grade 6 – download the PDF

1 Multiplying whole numbers ★★★

(a) \(52 \times 6 = 312\) and \(52 \times 30 = 1{,}560\); \(312 + 1{,}560 = 1{,}872\).

(b) \(407 \times 3 = 1{,}221\) and \(407 \times 20 = 8{,}140\); \(1{,}221 + 8{,}140 = 9{,}361\).

Answers: 1,872 and 9,361.

2 Exact long division ★★★

(a) 12 goes into 93 seven times (84), remainder 9; bring down 6: 96 = 12 × 8. The answer is 78.

(b) 25 goes into 127 five times (125), remainder 2; bring down 5: 25 = 25 × 1. The answer is 51.

(c) 42 goes into 201 four times (168), remainder 33; bring down 6: 336 = 42 × 8. The answer is 48.

3 Adding decimals ★★★

(a) \(6.45 + 3.80 = 10.25\).

(b) \(12.07 + 0.93 = 13.00 = 13\).

(c) \(0.506 + 2.740 = 3.246\).

4 Subtracting decimals ★★★

(a) \(9.50 - 4.27 = 5.23\).

(b) \(15.00 - 6.08 = 8.92\).

(c) \(3.004 - 1.750 = 1.254\).

5 Products with decimals ★★★

(a) \(6 \times 7 = 42\) with 2 decimal places: \(0.42\). The grid below shows 42 of 100 squares shaded in orange.

(b) \(4 \times 35 = 140\) with 2 decimal places: \(1.40 = 1.4\).

(c) \(15 \times 2 = 30\) with 2 decimal places: \(0.30 = 0.3\).

6 Dividing decimals by whole numbers ★★★

(a) \(84 \div 4 = 21\), so \(8.4 \div 4 = 2.1\).

(b) \(36 \div 6 = 6\) hundredths, so \(0.36 \div 6 = 0.06\).

(c) \(75 \div 5 = 15\), so \(7.5 \div 5 = 1.5\).

7 Quick estimate of a sum ★★★

Estimate: \(5 + 8 + 3 = 16\).

Exact: \(4.90 + 8.10 + 2.95 = 15.95\), which is very close to 16.

8 Long division with a remainder ★★★

23 goes into 48 twice (46), remainder 2; bring down 1: 21, which is less than 23, so write 0; bring down 7: 217 and \(23 \times 9 = 207\), remainder 10.

The quotient is 209 and the remainder is 10.

Check: \(23 \times 209 = 4{,}807\) and \(4{,}807 + 10 = 4{,}817\).

9 Seats in a theater ★★★

\(38 \times 46 = 38 \times 40 + 38 \times 6 = 1{,}520 + 228 = 1{,}748\).

The theater has 1,748 seats.

10 Products of two decimals ★★★

(a) \(34 \times 26 = 884\), 2 decimal places: \(8.84\).

(b) \(75 \times 12 = 900\), 3 decimal places: \(0.900 = 0.9\).

(c) \(508 \times 4 = 2{,}032\), 3 decimal places: \(2.032\).

11 Dividing by a decimal ★★★

(a) Move one place: \(63 \div 9 = 7\).

(b) Move two places: \(456 \div 12 = 38\).

(c) Move one place: \(17 \div 5 = 3.4\).

12 True or false? ★★★

(a) False. Dividing by 0.1 is the same as multiplying by 10, so \(9.8 \div 0.1 = 98\).

(b) True. \(4 \times 5 = 20\) with 2 decimal places gives \(0.20 = 0.2\).

(c) True. \(7.20 + 0.35 = 7.55\).

(d) False. Multiplying by 0.1 gives one tenth of the number, so it gets smaller (for any positive number).

13 Trading card shopping ★★★

Cards: \(3 \times 4.75 = 14.25\). Total: \(14.25 + 6.30 = 20.55\).

Change: \(25 - 20.55 = 4.45\).

Mia gets 4.45 dollars back.

14 Find the error ★★★

Estimate: \(2 \times 1.5 = 3\), and 2.4 is a bit more than 2, so the product should be a little above 3, not 0.36.

Correct: \(24 \times 15 = 360\), with 2 decimal places: \(3.60 = 3.6\). The student put too many decimal places in the answer.

15 Dividing with decimals in the quotient ★★★

(a) \(147 \div 6 = 24.5\).

(b) \(520 \div 8 = 65\).

(c) \(3.000 \div 8 = 0.375\).

16 Bakery flour ★★★

Flour needed: \(18 \times 0.35 = 6.30\) kg.

Bags: \(6.3 \div 2.5 = 2.52\). She cannot buy part of a bag, so she rounds up.

She must buy 3 bags.

17 Training for a race ★★★

Monday to Saturday: \(6 \times 1.35 = 8.10\) miles. Add Sunday: \(8.10 + 2.80 = 10.90\) miles.

Remaining: \(12 - 10.9 = 1.1\).

Omar needs 1.1 more miles.

18 Best unit price ★★★

12-pack: \(8.40 \div 12 = 0.70\) dollars per can.

18-pack: \(12.06 \div 18 = 0.67\) dollars per can.

The 18-can pack is cheaper per can (0.67 dollars versus 0.70 dollars).

19 Estimate, then compute ★★★

Estimate: \(40 \times 5 = 200\).

Exact: \(38.7 \times 5 = 193.5\) and \(38.7 \times 0.12 = 4.644\), so the product is \(193.5 + 4.644 = 198.144\).

The estimate 200 is very close to 198.144.

20 School fundraiser ★★★

Boxes: \(126 \times 14 = 1{,}764\).

Money collected: \(1{,}764 \times 3.25 = 5{,}733\) dollars.

Cost: \(1{,}764 \times 1.80 = 3{,}175.20\) dollars.

Profit: \(5{,}733 - 3{,}175.20 = 2{,}557.80\) dollars.

21 Mystery numbers ★★★

(a) Undo the multiplication: \(6.5 \div 0.25 = 26\).

(b) Undo the division: \(12.5 \times 0.4 = 5\).

(c) Undo the addition: \(5.1 - 2.35 = 2.75\).

Check (a): \(26 \times 0.25 = 6.5\). Check (c): \(2.75 + 2.35 = 5.10\).