Australian Curriculum v9 / ACiQ Year 7 Mathematics - Unit 1 - Integers and rational number operations

Integers and Rational Number Operations | Year 7 Mathematics

Use number lines, signs, fractions and decimals to calculate accurately and explain what each operation means.

Updated 2026-06-15 - 4 min read

Integers are whole numbers and their opposites: $\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots$. Rational numbers are numbers that can be written as a fraction, such as $\frac{3}{4}$, $-2.5$ or $0.6$.

Year 7 number work is not only about getting answers. The stronger skill is knowing what the signs, fractions and decimals mean so you can explain the result.

Integers show direction

Positive and negative numbers often describe opposite directions or changes. A temperature increase of $4^\circ\text{C}$ and a decrease of $4^\circ\text{C}$ have the same size, but different directions.

Adding a positive number moves right on a number line. Adding a negative number moves left.

$-3 + 5 = 2$

This starts at $-3$ and moves 5 places to the right.

$4 + (-7) = -3$

This starts at $4$ and moves 7 places to the left.

Subtracting can mean moving the other way

Subtraction is where many sign errors start. Think of subtracting as removing a movement.

$2 - 5 = -3$

You start at $2$ and move 5 places left.

$2 - (-5) = 7$

Subtracting a negative is different. You are removing a left movement, so the result moves right.

Fractions and decimals still need meaning

Fractions and decimals are both ways to show parts of a whole. Before adding or subtracting fractions, make the parts the same size.

For example:

$\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}$

For decimals, line up place value:

$3.7 + 0.46 = 4.16$

This works because $3.7$ means $3.70$, so the tenths and hundredths line up.

Estimate before you calculate

Estimation is not a separate skill from calculation. It is how you catch unreasonable answers.

If you calculate $-8 + 3.5 - 0.5$, you should expect the answer to stay negative because the positive movement is not large enough to pass zero. If a calculator or written method gives $+5$, the sign should feel suspicious.

For fractions, estimate the size before finding the exact answer. For example, $\frac{2}{3} + \frac{1}{6}$ is a little more than one half plus one sixth, and it should be less than 1. The exact answer $\frac{5}{6}$ fits that expectation.

For decimals, place value helps you avoid lining up digits incorrectly. In $3.7 + 0.46$, the 7 is tenths and the 4 is tenths, so they must line up in the same column.

Worked example

Quick check

  1. Calculate $-4 + 9$.
  2. Calculate $6 - (-2)$.
  3. Calculate $\frac{2}{3} + \frac{1}{6}$.
  4. Explain why $0.4$ is the same as $\frac{4}{10}$.

Answers:

  1. $5$
  2. $8$
  3. $\frac{5}{6}$
  4. $0.4$ means four tenths, so it can be written as $\frac{4}{10}$.

Transfer task

Write a short story problem that matches $-6 + 2.5 - 4$. Then solve it. A good context makes the signs meaningful, such as temperature, elevation, debt, game points or movement.

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