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Number foundations

Simplification: one step at a time

Read expressions correctly, use equal-priority operations from left to right, and spot useful arithmetic shortcuts.

BeginnerAbout 11 min3 worked examples
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01 / THE STARTING POINT

Before you begin

What you need: The four basic arithmetic operations.

  • Apply brackets and powers before other operations
  • Handle multiplication/division and addition/subtraction correctly
  • Use the distributive law to reduce arithmetic
02 / BUILD THE CONCEPT

Understand the idea

Order is part of the meaning

An expression is a set of instructions. Brackets group operations; powers come next; multiplication and division follow; addition and subtraction come last.

Equal priority means left to right

Multiplication does not always come before division. They share a level, so 24 ÷ 6 × 2 is 4 × 2 = 8. Addition and subtraction also share a level.

Rearrange only with valid rules

The distributive law a(b + c) = ab + ac can simplify mental calculation. For example, 19 × 7 = (20 − 1) × 7 = 140 − 7. Subtraction and division cannot be freely reordered.

03 / A DIFFERENT WAY TO SEE IT

Follow the operation ladder

  1. Brackets
  2. Powers
  3. × and ÷ →
  4. ＋ and − →
The arrows remind you to work left to right within each shared-priority level.
04 / FROM IDEA TO ANSWER

A method you can reuse

KEEP THIS HANDY

a × (b + c) = a × b + a × c

Distribution also works with subtraction: a(b − c) = ab − ac.
  1. Simplify the innermost brackets, then evaluate powers.
  2. Do multiplication and division from left to right.
  3. Do addition and subtraction from left to right, and estimate to check.
A useful insight

Multiplying by 25 is the same as multiplying by 100 and dividing by 4. For example, 48 × 25 = 4800 ÷ 4 = 1200.

05 / WATCH THE METHOD WORK

Worked examples

Read the question first. Try a step yourself, then compare your reasoning.

EXAMPLE 01

Bracket first

Simplify 18 + 6 × (5 − 2).

  1. 5 − 2 = 3.
  2. 6 × 3 = 18.
  3. 18 + 18 = 36.
Answer36
EXAMPLE 02

A left-to-right test

Simplify 48 ÷ 6 × 4 + 3.

  1. 48 ÷ 6 = 8.
  2. 8 × 4 = 32.
  3. 32 + 3 = 35.
Answer35
EXAMPLE 03

Mental multiplication

Calculate 99 × 16.

  1. Write 99 as 100 − 1.
  2. Distribute: 100 × 16 − 1 × 16.
  3. 1600 − 16 = 1584.
Answer1584
06 / YOUR TURN

Check your understanding

Quick questions, with explanations. These are for self-study and do not affect your account score.

0 of 3 questions checked

QUESTION 1Evaluate 20 − 8 + 3.

See the explanation

15. Addition and subtraction share priority: 20 − 8 = 12, then 12 + 3 = 15.

QUESTION 2Evaluate 3² + 2 × 5.

See the explanation

19. Square first: 9. Then 2 × 5 = 10. Finally 9 + 10 = 19.

QUESTION 3Evaluate 36 ÷ (3 × 2).

See the explanation

6. The bracket is 6; 36 ÷ 6 = 6. Without brackets the expression would have a different value.

07 / TAKE THE NEXT STEP

Put your understanding to work

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EXPLORE THE NUMBERS

Multiplication Calculator

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Simplification Practice Quiz 1

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Simplification Practice Quiz 2

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Simplification Practice Quiz 3

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Simplification practice

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NEXT LESSONFractions and Decimals
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