1.2 The four operations — Learn

Prerequisites: place value and ordering (section 1.1).

By the end of this section you can: add, subtract, multiply and divide integers and decimals using written methods; and check an answer with an inverse operation.

1. Addition and subtraction

Line up the digits by place value — ones under ones, tenths under tenths. Then work column by column.

Example 1. Work out $78 + 14.8$.

So $78 + 14.8 = 92.80$.

Watch out. If you line up the final digits, you may put the $8$ in $14.8$ under the $8$ ones in $78$. That treats eight tenths as eight ones. Align the decimal points instead: $78.00 + 14.80 = 92.80$.

2. Multiplication

Short multiplication multiplies by a single digit. Long multiplication multiplies by a number with more than one digit, working one digit at a time and adding the partial products.

Example 2. Work out $120 \times 0.65$.

First work out $120 \times 65 = 7\,800$. Then place the decimal point: $0.65$ has two decimal places, so the answer also has two:

So the drinks cost £78.00.

Example 3. Work out $8 \times 1.85$.

$8 \times 185 = 1\,480$, and $1.85$ has two decimal places, so the answer has two: $8 \times 1.85 = 14.80$. So the cakes cost £14.80.

3. Division

Division is the inverse of multiplication. Use short division for a single-digit divisor.

Example 4. Work out $132 \div 6$.

Example 5. Work out $95 \times 1.20$ to find the drinks revenue.

$95 \times 120 = 11\,400$, and $1.20$ has two decimal places, so $95 \times 1.20 = 114$. The drinks revenue is £114.00.

Where a division does not come out exactly, either give the remainder ($29 \div 4 = 7$ remainder $1$) or continue past the decimal point ($29 \div 4 = 7.25$).

4. Checking with inverse operations

Every operation has an inverse that undoes it:

Example 6. You work out $78 + 14.8 = 92.8$. Check it: $92.8 - 14.8 = 78$. ✓

Estimation gives a second, independent check: $120 \times 0.65$ is about $120 \times 0.7 = 84$, and $78$ is reasonable.

Watch out. In long multiplication, forgetting that the second partial product represents tens (not ones) shifts every following column and makes the answer ten times too small.

5. Progress check

Work out the two costs exactly and add them:

The stall spent £92.80 on stock. How does this compare with your estimate from the chapter opener?

You should now be able to

• add and subtract integers and decimals with the digits correctly aligned;
• multiply by one- and two-digit numbers using written methods;
• divide, giving a remainder or a decimal answer as required;
• check any answer with an inverse operation.