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G1.1 Addition and Subtraction of Whole Numbers

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01 — Explanation

How do I add numbers with more than one digit?

Line the numbers up by place value — units under units, tens under tens — then add each column starting from the right (the units column). If a column totals 10 or more, write down the units digit and carry the tens digit into the next column to the left.

Example: $68 + 25$ . Units: $8+5=13$ , write $3$ , carry $1$ . Tens: $1+6+2=9$ . Answer: $93$ .

Exam Tip

Always add from the right. Adding from the left is where almost every carrying mistake comes from, because you haven't yet seen whether the column to the right needs to carry anything into the one you've just written.

02 — Explanation

How do I subtract numbers with more than one digit?

Align by place value exactly as with addition, and subtract from the units column first. If the top digit in a column is smaller than the digit below it, you must borrow 1 from the column to its left: that column's digit drops by 1, and 10 is added to the digit you're subtracting from.

Example: $64 - 27$ . You can't do $4-7$ , so borrow from the tens: the $6$ becomes $5$ , and the $4$ becomes $14$ . Units: $14-7=7$ . Tens: $5-2=3$ . Answer: $37$ .

Common Mistake

Subtracting the smaller digit from the larger one regardless of which is on top (e.g. doing $7-4$ instead of borrowing for $4-7$ ). This gives a digit-reversal error that's easy to miss — always check your answer makes sense by estimating first (here, $64-27$ should be a bit more than $64-30=34$ , so $37$ is sensible).

03 — Explanation

How do I check that carrying and borrowing haven't gone wrong?

Estimate first by rounding both numbers to the nearest 10, and compare. For $68+25$ , round to $70+30=100$ , so an answer of $93$ is reasonable. For $64-27$ , round to $60-30=30$ , so $37$ is reasonable. If your worked answer is wildly different from the estimate, you've likely made a carrying or borrowing slip and should redo the column arithmetic.

04 — Worked example

Worked Exam-Style Question

A school hall holds 346 chairs for an assembly. 178 students and teachers are already seated. How many empty chairs are left?

This is a subtraction: $346 - 178$ .
Units column: $6 - 8$ isn't possible, so borrow from the tens. The tens digit $4$ becomes $3$ , and the units digit becomes $16$ . Now $16 - 8 = 8$ .
Tens column: we now have $3 - 7$ , which still isn't possible, so borrow from the hundreds. The hundreds digit $3$ becomes $2$ , and the tens digit becomes $13$ . Now $13 - 7 = 6$ .
Hundreds column: $2 - 1 = 1$ .
Reading the columns gives $346 - 178 = 168$ empty chairs.

Exam Tip

When a subtraction needs borrowing twice in a row like this, write the "new" digit small above the one you're changing at every step rather than trying to track it in your head — this is the single biggest source of lost marks in multi-digit column subtraction.