Mathematics
Intermediate
40 mins
Teacher/Student led
+80 XP
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IWB/Projector/Large Screen

Comparing and Ordering Fractions with Unlike Denominators

Learn to compare fractions with different denominators by renaming them to a common denominator, then order them from smallest to largest using visual fraction strips.

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    1 - Getting Started ~4 mins

    Here are two fractions: ⅔ and ¾. Hands up: which one do you think is bigger? Be ready to say how you decided. Careful, though, because just looking at the top numbers, or just the bottom numbers, can fool you.

    2 - Watch and Notice ~9 mins

    Illustration for Watch and Notice

    ⅔ against ¾

    Watch the fraction strips. We can only compare fairly when the parts are the same size, so we rename both fractions to twelfths. For ⅔ we multiply top and bottom by 4, so ⅔ = 8/12. For ¾ we multiply top and bottom by 3, so ¾ = 9/12. The 9/12 strip reaches further, so ¾ is the bigger one.

    ⅚ against 7/9

    Now we rename both to eighteenths. For ⅚ we multiply top and bottom by 3, so ⅚ = 15/18. For 7/9 we multiply top and bottom by 2, so 7/9 = 14/18. The longer strip wins, so ⅚ is bigger.

    Four fractions in order

    Here are ½, ⅔, ¾ and ⅚ on strips of the same whole. To put four fractions in order we still rename them all to one common denominator: 12 works for all four. So ½ = 6/12, ⅔ = 8/12, ¾ = 9/12 and ⅚ = 10/12. Now we just read them off by length, smallest first.

    3 - Try It Together ~8 mins

    Today we explore: here are three fractions on their strips. Shade each one, then rename them all to a common denominator so the parts are the same size. Once the parts match, line the shaded strips up by length and put the whole set in order from smallest to largest.

    Rename then order

    4 - Compare the Pairs in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, take each pair of fractions and rewrite them with a common denominator, one above the other. Then place the correct < or > sign between the two original fractions.

    • ⅔ and ¾
    • ⅚ and 7/9
    • ½ and 4/9

    5 - Class Challenge ~11 mins

    Today we work through these sets together: shade and rename each set of four fractions to a common denominator, then put them in order from smallest to largest. Each set is a step trickier than the one before.

    Order each set ascending

    6 - What Did We Notice? ~2 mins

    MATHS TALK

    Why does a bigger denominator usually mean a smaller slice? Think about a pizza cut into 4 pieces against the same pizza cut into 12 pieces — which slice would you rather have?

    7 - What's Next ~3 mins

    What we learned today

    • To compare fractions fairly, we rename them to a common denominator so all the parts are the same size.
    • The fraction with the longer shaded strip is the bigger one — and that is not always the one with the bigger numbers.
    • A bigger denominator usually means a smaller slice, because the whole is shared into more parts.

    Coming up

    Key point

    Next we will add and subtract fractions with unlike denominators — and renaming to a common denominator is exactly the skill we will need.

    Pupil practice
    Module 3 · Fractions, Decimals and Percentages Number
    Lesson 28 · Comparing and Ordering Fractions with Unlike Denominators
    Download Activity Book page (PDF)
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