Math // Fractions

Simplifying Fractions

Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator

Ages
10 to 11
Type
Method
Builds on
3 topics
Leads to
4 topics
Standards
1 code

Quick check

If the learner has the fraction 12/16, can they simplify it to its lowest terms — and explain what they divided the top and bottom by?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Simplify 18/24 to 3/4 by identifying the HCF of 18 and 24
  • Express 2/3 and 5/8 with a common denominator of 24
  • Explain why dividing numerator and denominator by a common factor produces an equivalent fraction

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

3 topics
  • Fraction NotationRequired

    Fractions // Ages 6 to 9

    Simplifying fractions to simplest form requires 'simplest form' and 'common factor' vocabulary

  • Equivalent fractions (age 9+)Required

    Fractions // Ages 9 to 10

    Simplifying fractions extends Y5 equivalent fractions concept

  • Factors, multiples, and primesRequired

    Multiplication & Division // Ages 9 to 11

    Using common factors/multiples requires knowledge of common factors and multiples

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Simplifying Fractions

Ages 10 to 11 // Method

Leads to

4 topics

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Teach simplifying as the equivalence principle run in reverse: dividing numerator and denominator by a common factor regroups the same quantity into fewer, larger pieces without changing its value, just as multiplying both by n does. Simplest form is reached when numerator and denominator share no common factor but 1 (you have divided by the HCF). The same number-theory machinery — finding a common multiple — lets two fractions be rewritten over a shared denominator. Anchor to the Year 5 fact a/b = (n×a)/(n×b), so a/b = (a÷n)/(b÷n), and treat simplification as 'un-grouping' back to the coarsest partition, not a memorised rule.

Common misconceptions

  • Simplifying by SUBTRACTING a common amount from numerator and denominator (6/8 → 4/6 by taking 2 from each) instead of dividing — treats the fraction additively.
  • Stopping before simplest form: dividing 18/24 by 2 to get 9/12 and calling it done, not checking for a remaining common factor.
  • Operating on only one part — dividing the numerator but not the denominator (or renaming only the denominator when finding a common denominator).
  • Believing simplifying changes the fraction's value ('3/4 is bigger than 6/8 because 4 is fewer pieces') rather than renaming the same quantity.
  • When finding a common denominator, changing the denominators to match but forgetting to scale the numerators correspondingly.

Useful representations

  • Fraction wall / bar model where equivalent fractions align to identical length (6/8 sits exactly over 3/4)
  • Area model / grid that can be re-partitioned by merging small cells into larger groups (24 cells shaded 18, re-grouped into 4 columns of which 3 are shaded → 3/4)
  • Factor pairs and HCF listing beside the fraction (18 = 2×3×3, 24 = 2×2×2×3, common = 2×3 = 6)
  • Number line showing 18/24 and 3/4 landing on the identical point
  • Common-multiple ladder for the common-denominator task (thirds and eighths both re-cut into 24ths)

Teaching practices

  • Anchor the procedure to the equivalence principle already learned: show that dividing top and bottom by the same number is the inverse of multiplying by the same number, so the value is unchanged — use a fraction wall or area model where 6/8 and 3/4 occupy identical length.
  • Connect directly to common factors/multiples work: to simplify, divide by a common factor (fastest via the HCF); to find a common denominator, use a common multiple (efficiently the LCM). Make the number theory visible, not incidental.
  • Distinguish 'an equivalent, simpler fraction' from 'simplest form' explicitly — a child who writes 6/8 = 3/4 has simplified; a child who writes 6/8 = ... but stops at a form still sharing a factor has not finished. Ask 'can you go further?' every time.
  • Use dividing-by-HCF as the efficient route but accept repeated division by any common factor (÷2 then ÷2) as valid — the concept, not the shortcut, is the target.
  • Contrast simplifying with the illegal move of adding or subtracting the same number from top and bottom, which does change the value; have children test 6/8 vs (6-2)/(8-2)=4/6 against the wall.

Activities to try

  1. 1

    Un-grouping a bar: 18/24 back to simplest form

    Why it works: Dividing both parts by a common factor regroups the same quantity into fewer, larger equal pieces, leaving the value (length) unchanged; simplest form is reached only when no common factor above 1 remains.

    1. Start with a bar partitioned into 24 cells with 18 shaded, labelled 18/24.
    2. Choose a number to 'group by' (a divisor) and merge the cells into equal groups of that size, watching the fraction label recompute (e.g. grouping in sixes gives 4 fat groups with 3 shaded → 3/4).
    3. Observe that for each valid grouping of the original 24-cell bar the shaded LENGTH does not move while the label takes an equivalent form (grouping by 2 → 9/12, by 3 → 6/8, by 6 → 3/4) — the quantity is unchanged, only the cut is coarser.
    4. Deliberately try a divisor that is NOT a common factor (e.g. 5): notice the cells will not group evenly and leftovers remain, so that divisor is rejected.
    5. Keep going until no grouping beyond 1 is possible, then state the simplest form and name the HCF (6) that would have reached it in one step.
  2. 2

    Common denominator by re-cutting to a shared multiple

    Why it works: Expressing fractions over a common denominator uses a common multiple (efficiently the LCM); when you change a denominator you must scale its numerator by the same factor, or you change the quantity.

    1. Place bars for 2/3 and 5/8 (or thirds and eighths) side by side.
    2. Find a common multiple of 3 and 8 to use as the shared denominator (24 works; 48 also works — find the smallest, the LCM).
    3. Re-cut BOTH bars into 24ths and rewrite each fraction: 2/3 = 16/24 and 5/8 = 15/24, scaling each numerator by the same factor used on its denominator.
    4. Check: 2/3 becomes 16/24 because both parts were multiplied by 8; 5/8 becomes 15/24 because both were multiplied by 3 — the numerator must scale with the denominator.
    5. Compare using 24 versus 48 and explain why 24 is the smallest denominator that works.
  3. 3

    Divide versus subtract: testing the illegal move

    Why it works: Simplifying is division of both parts by a common factor, not subtraction of a common amount; the additive move generally changes the value (it keeps it only in special cases such as fractions equal to 1), so it is not a valid equivalence method.

    1. Take 6/8 and perform the illegal move of subtracting the same amount from both parts: (6−2)/(8−2) = 4/6.
    2. Lay 6/8 and 4/6 on the same fraction wall or bar and compare their lengths.
    3. Observe that the lengths differ, so subtracting the same number from top and bottom DID change the value.
    4. Contrast with dividing both parts by 2: 6/8 → 3/4, whose length matches 6/8 exactly.
    5. State what the test showed: multiplying or dividing both parts by the same non-zero number keeps the value, but subtracting the same amount from both parts generally changes it (as 6/8 → 4/6 did).

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Ma6/2.3a

Math // Fractions

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