POP

G1.2 Multiplication and Division of Whole Numbers

Image · 914 × 270

01 — Explanation

How do I multiply a large number by a single digit?

Use the column method: line up the numbers by place value, then multiply each digit of the top number by the single digit, starting from the units and carrying any tens into the next column, exactly like column addition.

Example: $32 \times 3$ . Units: $3\times2=6$ . Tens: $3\times3=9$ . Answer: $96$ .

02 — Explanation

How do I multiply two two-digit numbers together?

Multiply the top number by each digit of the bottom number separately, then add the results — but you must shift the second row one place to the left (or add a placeholder zero) because that digit represents tens, not units.

Example: $46 \times 25$ .

Multiply by the units digit (5): $46 \times 5 = 230$ .
Multiply by the tens digit (2): $46 \times 2 = 92$ , and since this "2" is actually 20, write it as $920$ (a zero placeholder in the units column).
Add the two partial products: $230 + 920 = 1150$ .

Common Mistake

Forgetting the placeholder zero when multiplying by the tens digit. Without it, you'd add $230 + 92 = 322$ , which is wrong by a factor of ten — always write that trailing zero before you start the second row.

03 — Explanation

How do I divide a number by a single digit (short division)?

Short division, sometimes called the "bus stop method," works left to right: at each digit, work out how many times the divisor fits, write that above the digit, and carry the remainder to combine with the next digit.

Example: $156 \div 4$ .

$4$ doesn't go into $1$ , so look at $15$ : $4 \times 3 = 12$ , remainder $3$ . Write $3$ above the $5$ .
Carry the remainder $3$ to make $36$ with the next digit.
$4 \times 9 = 36$ exactly, remainder $0$ . Write $9$ above the $6$ .
The answer is $39$ .

Exam Tip

If there's a remainder left at the very end, don't just drop it — the question will tell you whether to round the quotient, give a remainder (e.g. "39 r 2"), or continue into decimal places by adding a decimal point and zeros to the dividend.

04 — Explanation

How do I know which operation a worded question actually wants?

Look for the structural clue in the wording: "share equally," "how many groups of," or "split between" all signal division; "total," "altogether," or "lots of" signal multiplication. Writing the calculation out in full before computing (e.g. " $156 \div 4$ " rather than jumping straight to column working) protects you from picking the wrong operation under time pressure.

05 — Worked example

Worked Exam-Style Question

A coach company has 184 passengers to transport using minibuses that each seat 8 people. How many minibuses are needed?

This is division: $184 \div 8$ .
$8$ doesn't go into $1$ , so use $18$ : $8 \times 2 = 16$ , remainder $2$ . Write $2$ above the $8$ .
Carry the remainder $2$ to make $24$ with the next digit.
$8 \times 3 = 24$ exactly, remainder $0$ . Write $3$ above the $4$ .
The quotient is $23$ , so exactly 23 minibuses are needed.

Exam Tip

Watch for questions where the division doesn't come out exactly and you must round up rather than down — e.g. if 184 had been 185 passengers, $185 \div 8 = 23$ remainder $1$ , but you'd still need 24 minibuses, because one person can't be left behind. Always re-read what the remainder means in context.