Mathematics
Intermediate
39 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen

Simplifying Fractions

Learn to simplify fractions by dividing the top and bottom by common factors. Use fraction strips to see that 4/8, 2/4 and ½ all show the same amount, then practise writing fractions in their simplest form.

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    1 - Getting Started ~4 mins

    Here is a fraction: 4/8. What is the simplest way you could write the same amount? Have a think before any hands go up.

    2 - Watch and Notice ~9 mins

    Illustration for Watch and Notice

    4/8 = 1/2

    Four of the eight parts are shaded, and they line up exactly with the single shaded part on the strip of two below. Both strips reach the same length, so they show the same amount. Now look for a number that divides into both 4 and 8: 4 goes into 4 once and into 8 twice, so we divide the top and bottom both by 4 to get ½.

    6/9 = 2/3

    Six of nine parts line up with two of three parts. The amount has not changed, only the number of pieces. Which number divides into both 6 and 9? Not 2, because 9 is not even. But 3 goes into 6 twice and into 9 three times, so we divide the top and bottom both by 3 to get ⅔.

    12/16 = 3/4

    Twelve of sixteen parts line up with three of four parts. Same length again. The biggest number that divides into both 12 and 16 is 4: it goes into 12 three times and into 16 four times, so we divide the top and bottom both by 4 to get ¾.

    3 - Try It Together ~11 mins

    Let's stack 4/8, 2/4 and ½ on the fraction strips and watch where they all reach the same length. The 2/4 strip is a halfway step between 4/8 and ½. After that we will build 4/6 and 10/12 together and decide each one's simplest form as a class.

    Stack them and check

    4 - Work the Divide Step in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, work each simplification by writing the divide-by step underneath. For example: 4/8 ÷4/4 = ½. Underline the simplest form on each one.

    • 4/8
    • 6/9
    • 10/15
    • 12/16

    5 - Class Challenge ~7 mins

    Let's work through four fractions together. Simplify 6/8, then 9/12, then 24/36, and finally decide whether 7/12 is already in its simplest form. Build each one on the strips and check it against its simplest form.

    Simplify and check

    6 - What Did We Notice? ~2 mins

    MATHS TALK

    When we simplified, what was the biggest number we could divide the top and bottom by each time? That biggest number has a name: the greatest common factor — the biggest number that goes into both the top and the bottom. Why is finding it faster than dividing a little at a time?

    7 - What's Next ~3 mins

    What we learned today

    • A fraction is in its simplest form when the top and bottom share no common factor bigger than 1.
    • We simplify by dividing the top and bottom by the same number.
    • Finding the greatest common factor gets us there in one step.

    Coming up

    Coming up

    Next we will compare two fractions to decide which is bigger, using common denominators and benchmarks like one half.

    Pupil practice
    Module 3 · Fractions, Decimals and Percentages Number
    Lesson 33 · Simplifying Fractions
    Download Activity Book page (PDF)
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