Module 2

Decimals & linear graphs

Quick-reference revision notes for parents.

2.1 Adding and subtracting decimals

Line up the decimal points, not the right-hand digits. Fill blanks with zeros so every number has the same number of decimal places.

Worked example — 3.7 + 12.45

3.70
+12.45
------
16.15

Watch out

Don't right-align — 3.7 + 12.45 with right-aligned digits gives the wrong answer.

2.2 Multiplying and dividing (reminder)

Use long multiplication or short division for whole-number calculations. The decimal versions build on these — make sure the basics are solid first.

2.3 Multiplying decimals

Ignore the decimal points, multiply as whole numbers, then put the decimal point back. Count the total decimal places in the question — the answer has the same number.

Worked example — 0.4 × 0.3

4 × 3 = 12. Two decimal places in the question (one in each), so two in the answer: 0.12.

Worked example — 1.2 × 0.05

12 × 5 = 60. Three decimal places total (one + two), so: 0.060 = 0.06.

Sense check

Multiplying by a number less than 1 makes things smaller. 0.4 × 0.3 = 0.12 — smaller than both, as expected.

2.4 Dividing decimals

Make the divisor (the number you're dividing by) a whole number. Multiply both numbers by 10, 100 or 1000 as needed.

Worked example — 4.8 ÷ 0.6

Multiply both by 10: 48 ÷ 6 = 8.

Worked example — 7.2 ÷ 0.04

Multiply both by 100: 720 ÷ 4 = 180.

2.5 Plotting straight line graphs

Equation form: y = mx + c

Letter	Meaning
m	Gradient — how steep the line is
c	y-intercept — where it crosses the y-axis

Method: build a table

Pick three or four x-values (e.g. −1, 0, 1, 2)
Substitute each into the equation to find y
Plot the (x, y) pairs and join with a ruler

Worked example — y = 2x + 1

x: −1 0 1 2
y: −1 1 3 5

Gradient = 2 (goes up 2 for every 1 right). y-intercept = 1 (crosses y-axis at 1).

Gradient from two points

gradient = (change in y) ÷ (change in x) — "rise over run".

2.6 Real-life graphs

Most common types:

Distance–time

Gradient = speed. Flat line = stopped. Steeper line = faster.

Conversion graph

Convert one unit to another (e.g. £ to $). Read across and down.

Filling/cooling

Shape of curve tells the story (steep then flat = filling fast then slowing).

Quick reference

Adding decimals: line up the decimal points
Multiplying decimals: count total decimal places in the question
Dividing decimals: make the divisor whole first
Straight line: y = mx + c — m is gradient, c is y-intercept
Gradient = rise ÷ run

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