Number — Fractions and Percentages — Self-Assessment

Simplifying Fractions (1b.1)

Simplify a fraction by dividing the numerator and denominator by their highest common factor.

Always check if a fraction can be simplified in your final answer.

Simplifying Fractions (1b.1) — Key Knowledge

Simplifying dividing top and bottom by the same number — 6/8 = 3/4
Equivalent fractions fractions that look different but have the same value — 2/4 = 1/2

Comparing and Ordering Fractions (1b.1)

To compare fractions, convert them to the same denominator, then compare the numerators.

A bigger denominator does NOT mean a bigger fraction — 1/8 is smaller than 1/4.

Comparing and Ordering Fractions (1b.1) — Key Knowledge

Common denominator a shared multiple of both denominators
Ordering fractions convert to a common denominator then compare numerators

Adding and Subtracting Fractions (1b.1)

To add or subtract fractions, first find a common denominator. Then add or subtract the numerators only.

The biggest mistake: adding numerators AND denominators (1/2 + 1/3 ≠ 2/5). You must find a common denominator first.

Adding and Subtracting Fractions (1b.1) — Key Knowledge

Common denominator the LCM of both denominators
Adding fractions make denominators the same, then add numerators — 2/3 + 3/4 = 8/12 + 9/12 = 17/12

Multiplying and Dividing Fractions (1b.1)

Multiply: numerator × numerator, denominator × denominator. Divide: Keep Change Flip — keep the first fraction, change ÷ to ×, flip the second fraction.

Keep Change Flip only works for division — never use it for addition or subtraction.

Multiplying and Dividing Fractions (1b.1) — Key Knowledge

Multiplying fractions multiply straight across — 2/3 × 4/5 = 8/15
Keep Change Flip to divide fractions — 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

Mixed Numbers and Improper Fractions (1b.1)

A mixed number has a whole part and a fraction part. An improper fraction has a numerator bigger than its denominator.

Always convert mixed numbers to improper fractions before multiplying or dividing.

Mixed Numbers and Improper Fractions (1b.1) — Key Knowledge

Mixed number e.g. 1 5/12 — a whole number plus a fraction
Improper fraction e.g. 17/12 — numerator larger than denominator
Converting mixed to improper: multiply whole by denominator, add numerator; improper to mixed: divide numerator by denominator

Fraction to Decimal (1b.2)

To convert a fraction to a decimal, divide the numerator by the denominator.

Learn the common fraction-decimal pairs — they come up everywhere and save time.

Fraction to Decimal (1b.2) — Key Knowledge

Fraction to decimal divide top by bottom — 3/8 = 3 ÷ 8 = 0.375
Common equivalences 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/10 = 0.1

Decimal to Percentage and Back (1b.2)

Decimal to percentage: multiply by 100. Percentage to decimal: divide by 100.

Moving between FDP (fractions, decimals, percentages) is a core skill used across all maths topics.

Decimal to Percentage and Back (1b.2) — Key Knowledge

Decimal to percentage × 100 — 0.375 = 37.5%
Percentage to decimal ÷ 100 — 37.5% = 0.375
Fraction-decimal-percentage three ways of writing the same value

Finding a Percentage of an Amount (1b.3)

To find a percentage of an amount, convert the percentage to a decimal and multiply.

"Of" means multiply — 15% of 80 means 0.15 × 80, not 15 + 80.

Finding a Percentage of an Amount (1b.3) — Key Knowledge

Percentage of an amount e.g. 15% of 80 = 0.15 × 80 = 12
Building percentages find 10% by dividing by 10, then combine — 15% = 10% + 5%

Percentage Increase and Decrease (1b.3)

Increase or decrease an amount by a percentage using a multiplier.

The multiplier method is faster and less error-prone than finding the percentage then adding/subtracting.

Percentage Increase and Decrease (1b.3) — Key Knowledge

Percentage increase multiply by 1 + the percentage as a decimal — increase by 20% → × 1.2
Percentage decrease multiply by 1 − the percentage as a decimal — decrease by 15% → × 0.85

Reverse Percentages (1b.3)

Finding the original amount before a percentage change — divide by the multiplier, don't add/subtract the percentage back.

The trap: adding the percentage back on gives the wrong answer. The reduced price IS 85%, so divide by 0.85 to get 100%.

Reverse Percentages (1b.3) — Key Knowledge

Reverse percentage if the sale price is £51 after 15% off, the original was £51 ÷ 0.85 = £60 — NOT £51 × 1.15

Expressing as a Percentage (1b.3)

To express one quantity as a percentage of another, divide the part by the whole and multiply by 100.

Always check which number is the "part" and which is the "whole" — getting them the wrong way round is a common error.

Expressing as a Percentage (1b.3) — Key Knowledge

One as a percentage of another part ÷ whole × 100 — e.g. 15 out of 60 = 15/60 × 100 = 25%

Order of Operations — BIDMAS (1b.4)

BIDMAS tells you the order to do operations: Brackets, Indices, Division/Multiplication (left to right), Addition/Subtraction (left to right).

3 + 4 × 2 = 11 (not 14) because multiplication comes before addition. Brackets override everything.

Order of Operations — BIDMAS (1b.4) — Key Knowledge

BIDMAS Brackets, Indices, Division, Multiplication, Addition, Subtraction
Equal precedence division and multiplication are done left to right — not multiplication first; same for addition and subtraction

Number — Fractions and Percentages

Self-Assessment

Session Complete

Number — Fractions and Percentages