KS3 · Maths

Equivalent fractions and simplifying

Which is bigger: 1/2 or 7/14? The 7 and 14 look bigger — yet on a number line they land on exactly the same spot. Here's why.

Place them, then check

Where does each fraction land?

This line runs from 0 to 2, and each whole is split into 10 equal intervals — tenths. Drag each fraction to where you think it belongs. Think about the equal parts, not how big the digits look. Then check.

What a fraction really says

Fair reading or not?

Sort each reading: is it a fair way to read the drawing as a fraction, or not?

Still to sort

Fair reading (0)

Equal parts, one clear whole.

Where the line is: The denominator only works if every part is the same size, and fractions can only be compared when they are fractions of the same whole.

Not a fair reading (0)

Unequal parts, or two different wholes.

5 of 5 still to sort.

Each card describes a drawing and what someone says it shows. Is the reading fair?

Bigger number, bigger fraction?

Which slice would you rather have?

Two identical pizzas. The first is shared equally between 3 friends, so each gets 1/3. The second is shared equally between 8 friends, so each gets 1/8.

Who gets more pizza: a person with 1/3 of the first pizza, or a person with 1/8 of the second? Pick the idea closest to what you think right now.
How sure are you?

The secret behind equivalent fractions

?

Reason it through

Why can you multiply or divide the top and bottom of a fraction by the same number without changing its value?

Link 1 of 4

First link · your turn

Start with something you already know. What happens to any number when you multiply it by 1?

2
Locked — reveal the link above first
3
Locked — reveal the link above first
4
Locked — reveal the link above first

Your turn to finish the method

Build one up, then break one down

Two jobs. (a) Find the missing number: 3/4 = ?/20. (b) Write 18/24 in its simplest form in one step.

  1. (a) The denominator has gone from 4 to 20. Ask: what did 4 get multiplied by?
  2. missing step
Which line is step 2?

Big numbers: prime factors

Spot the slip

Simplify 140/1260 using prime factors.

Sam's working — which line goes wrong?

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Different-looking fractions, one number — and how to make them and simplify them.

What you need to know

  • The denominator is how many equal parts the whole is split into; the numerator counts how many of those parts you have.
  • Equivalent fractions have the same value, so they sit at the same point on a number line.
  • Multiply the numerator and denominator by the same number to make an equivalent fraction.
  • Divide the numerator and denominator by a common factor to simplify; dividing by the highest common factor (HCF) reaches the simplest form in one step.

The big picture

A fraction is a number, so it has one place on the number line. Fractions that land on the same place are equivalent: they have the same value, just written differently. You make an equivalent fraction by multiplying the numerator and denominator by the same number, and you simplify by dividing both by a common factor. Both work for the same reason: a fraction with the same number on top and bottom, like 4/4 or 6/6, is just 1 in disguise, and multiplying by 1 never changes a value.

Key points

1A fraction only describes a diagram when its parts are equal, and fractions can only be compared as parts of the same whole.
2Any fraction with the same non-zero number on top and bottom, like 5/5 or 11/11, is equal to 1.
3Multiplying by 1 never changes a value, so multiplying top and bottom by the same number gives an equivalent fraction — there are infinitely many of them.
4Simplifying is the inverse: divide top and bottom by a common factor. The common factors form a fraction equal to 1; they don't just vanish.
5For large numbers, write the top and bottom as products of prime factors and use the common ones. If every factor on top is common, the numerator is 1, not 0.
6A bigger denominator means smaller parts, not a bigger fraction.

Worked example

Problem

Are 14/35 and 6/15 equivalent fractions?

⚠ Watch out

Dividing by a number that only goes into the top OR the bottom. In 21/28, 3 goes into 21 but not into 28, so you can't use it. You need a factor of BOTH: 7 goes into each, giving 21/28 = 3/4.

🧠

Memory hook

Same number on top and bottom? That's 1 in disguise. Multiply by 1 and nothing changes — only the look.

✓

Check yourself

Is 45/60 equivalent to 3/4? Decide first, then check: the HCF of 45 and 60 is 15, and 45 ÷ 15 = 3, 60 ÷ 15 = 4. So yes — 45/60 = 3/4.

Flashcards

(14)
What does the denominator of a fraction tell you?
How many equal parts the whole has been divided into.
What does the numerator of a fraction count?
How many of those equal parts the fraction represents.
When can a shaded shape be described with a fraction?
Only when the parts are equal in size. If the parts are unequal, 3 shaded out of 10 is not 3/10.
Why must fraction bars be the same length before you compare them?
Each bar is the whole. The same fraction of different wholes can be different sizes, so only bars of equal length can be compared.
What does it mean for two fractions to be equivalent?
They have the same value — they land on exactly the same point on a number line.
How many fractions are equivalent to 1/2?
Infinitely many: 2/4, 7/14, 50/100 and so on — you can always multiply top and bottom by another number.
What is 11/11 equal to, and why?
1 — any number (except 0) divided by itself is 1.
How do you make a fraction equivalent to 2/3?
Multiply the top and bottom by the same number, e.g. × 11/11 gives 22/33. You're multiplying by 1, so the value stays the same.
7/9 = 70/? — how do you find the missing number?
Find the multiplier: 7 × 10 = 70, so multiply 9 by 10 too. 7/9 = 70/90.
What is the highest common factor (HCF) of two numbers?
The greatest number that is a factor of both.
Why divide by the HCF when simplifying?
It reaches the simplest form in one step. A smaller common factor still works, but takes more steps.
How can prime factors simplify 30/42?
30/42 = (2 × 3 × 5)/(2 × 3 × 7). The common 2 × 3 makes 6/6 = 1, leaving 5/7.
Is 1/8 bigger than 1/3?
No. The same whole is cut into more pieces, so each piece is smaller: 1/3 is bigger.
Where does 17/10 go on a number line?
Split each whole into 10 equal parts and count 17 of them: between 1 and 2, at 1 7/10.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

Learning with Lightbulb is opening soon

You can use this lesson now. Join the waitlist and we'll let you know when the full Lightbulb experience is ready.

Keep me posted

More KS3 Maths topics

See the full KS3 Maths curriculum →

How this lesson was checked. This KS3 Mathslesson was published through Lightbulb Learning's human-designed editorial process — the educational standards, accuracy rules and publication checks it must pass were authored and approved by Philip Halpin. It passed subject-specific assessment, automated educational checks and technical publication verification before going live (publication checks completed 1 October 2026). Published pages are monitored, human spot-checking is ongoing across the lesson library, and anything found wrong is corrected or withdrawn. How our lessons are made and checked. Spotted a mistake? Email hello@lightbulblearning.co and we'll review it.