Unit 5: Multiplication and Division

Meet Alvina, an entomologist studying caterpillars. If she counts 32 caterpillars on one plant and there are 15 plants in all, she needs 32 x 15 to find the total. This unit gives you the tools - multiply, divide, estimate and use the order of operations.

Pick any 2 digit cards from 0-9 and multiply them. Notice how the same product can come from different pairs - 12 is 2 x 6, 3 x 4, or 1 x 12. A product is a multiple of each of its factors.

Multiplying by 10, 100 or 1,000 shifts every digit one, two or three places to the left. Dividing does the opposite. So 7,781 x 100 = 778,100 and 778,100 ÷ 10 = 77,810.

Round each factor to the nearest 10, then multiply. 58 x 32 approx 60 x 30 = 1,800. For division, find a near pair you can divide easily: 94 ÷ 28 approx 90 ÷ 30 = 3. Use estimates to check if an answer is reasonable.

Ms. Hawwa buys 17 bags of apples, each with 24 apples. Multiply 24 x 17 in three steps:

Ms. Hawwa buys 408 apples.

Multiply 324 x 46 using the column method: 6 x 324 = 1,944 and 40 x 324 = 12,960. Add: 1,944 + 12,960 = 14,904. The grid model gives the same answer - split each number by place value and add all the boxes.

Column and grid aren't the only ways. You can also try the line (Japanese) method, lattice method and others. Whichever method is easiest for you is the right one - just be careful and stay neat.

Split 1,350 = 1,000 + 300 + 50 and 12 = 10 + 2. Fill the grid:

Totals: 12,000 + 3,600 + 600 = 16,200.

2,465 people buy tickets for a carnival. Each ticket costs MVR 48. Total spent = 2,465 x 48. Multiply step by step: 8 x 2,465 = 19,720; 40 x 2,465 = 98,600. Add: 19,720 + 98,600 = 118,320.

Office chairs cost MVR 999 each. A company buys 38 chairs. Total = 999 x 38. Using the grid: 30 x 900 = 27,000, 30 x 90 = 2,700, 30 x 9 = 270; 8 x 900 = 7,200, 8 x 90 = 720, 8 x 9 = 72. Add: 37,962.

Multiplying by powers of 10 is the easiest case - just tack on zeros.

No carrying needed.

Fill the grid for 154 x 36. Split 154 = 100 + 50 + 4 and 36 = 30 + 6. Multiply each cell and add. 30 x 100 = 3,000, 30 x 50 = 1,500, 30 x 4 = 120, 6 x 100 = 600, 6 x 50 = 300, 6 x 4 = 24. Total = 5,544.

Play in groups of 6. Spin two wheels - one with numbers like 29, 60, 100, the other with 7, 76, 243, 507, 952, 1000. Multiply the two numbers the arrows point to. For example, 29 x 1,000 = 29,000. Most correct answers wins.

Division undoes multiplication. A teacher shares 138 papers among 3 classes. 138 ÷ 3 = 46, so each class gets 46 papers.

Math language: dividend ÷ divisor = quotient (remainder).

Long division uses 4 repeating steps - Divide, Multiply, Subtract, Bring down.

So 866 ÷ 27 = 32 R2.

74 ÷ 21: 21 goes into 74 three times (21 x 3 = 63). 74 - 63 = 11. So 74 ÷ 21 = 3 R11.

264 ÷ 22: 22 into 26 -> 1 (x22=22). 26-22=4, bring down 4 -> 44. 22 into 44 -> 2 (x22=44). Remainder 0. So 264 ÷ 22 = 12.

2,032 ÷ 16: 16 into 20 = 1 (x16=16), 20-16=4, bring 3 -> 43. 16 into 43 = 2 (x16=32), 43-32=11, bring 2 -> 112. 16 into 112 = 7 (x16=112), remainder 0. So 2,032 ÷ 16 = 127.

Practise the four-step routine on bigger numbers:

Check by multiplying quotient x divisor and seeing if you get the dividend.

Read carefully and decide what is being shared equally.

Aaish reads 'an ox could plow 4,840 sq yards in a day -> 1,766,600 in a year'. Is that reasonable? Round each factor to its greatest place: 365 approx 400, 4,840 approx 5,000. 400 x 5,000 = 2,000,000 - close to 1,766,600.

Compatible numbers are easy to divide mentally. 895 students need buses with 25 seats. 895 ÷ 25 approx 900 ÷ 30 = 30 buses. We changed BOTH numbers to make the division easy.

The squiggly equals sign approx means is approximately equal to. Use it whenever you have rounded:

27,056 ÷ 893 approx 30 because 900 x 30 = 27,000.

When two products share a common factor, you don't have to multiply - just compare the other factor.

Volunteers set up seating for a dharus on Naifaru. Section A: 44 rows of 16 seats. Section B: 25 rows of 14 seats. Estimate each: 44x16 approx 40x20 = 800 seats, 25x14 approx 30x10 = 300 seats. Total approx 1,100 seats.

When an expression has more than one operation, we need a rule to know what to do first. Salma has 15 pencils in 2 boxes and 19 pencils in 3 more boxes. Total = 2 x 15 + 3 x 19 = 30 + 57 = 87 pencils. She multiplied FIRST, then added.

BODMAS is the order:

Example: (2+3) x 4 = 5 x 4 = 20 biscuits. Without brackets, 2 + 3 x 4 = 14 - a different answer!

3 + 7 x 1 - 4 ÷ 2:

(56 ÷ 8) - 2 + (5 + 6) x 3 = 7 - 2 + 11 x 3 = 7 - 2 + 33 = 5 + 33 = 38.

19 + 21 ÷ 7 x 8 - 13 = 19 + 3 x 8 - 13 = 19 + 24 - 13 = 43 - 13 = 30.

Aroosha had 48 stamps. She gave 15 to Amjad, then bought 9 more. The expression that matches the story is 48 - 15 + 9. Reading order matters: 'gave' is subtract, 'bought' is add.

Two students multiplied 1,920 x 43.

Aishath packs 315 muffins into boxes of 12. 315 ÷ 12 = 26 R3 -> she needs 27 boxes (you can't ignore the extras). If boxes hold 15 instead: 315 ÷ 15 = 21 boxes exactly. Decisions like 'round up' matter in real life.

Use digit cards 9, 4, 5, 3, 8 to build a 3-digit and a 2-digit number whose product is greatest. Tip: put the biggest digits in the highest places of the multiplier. For example, 458 x 39 = 17,862 - but is that really the biggest? Try other arrangements like 853 x 94 or 943 x 85.

Try these for yourself:

Use column or grid - whichever you prefer.

(3 + 5) x (12 ÷ 4) = 8 x 3 = 24.

(9 + 6) ÷ (9 - 6) = 15 ÷ 3 = 5.

6 x 8 + 30 ÷ 5 - 4 x 9 = 48 + 6 - 36 = 18.

375 tickets x 15 shows = 5,625 tickets. 14 L x 8 minutes = 112 L of blood pumped.

Look back over the unit: