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MathidiaMathematics Academy
Exact number and rational reasoning
Lesson 12 of 75
Easy practice

Fractional change

Objective. Model increases and decreases using fractional multipliers.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Fractional change describes increases or decreases expressed as multipliers built from fractions rather than percentages. To increase a quantity by a fraction such as 2/5, multiply the original amount by (1 + 2/5) = 7/5. To decrease by a fraction such as 1/4, multiply by (1 − 1/4) = 3/4. For example, increasing £60 by 1/3 means calculating 60 × 4/3 = 80. This single-multiplier approach avoids calculating the fractional change separately and then adding or subtracting, which reduces arithmetic errors in multi-step problems.

Worked example

A population of 450 increases by 3/10. Find the new population using a fractional multiplier.

3/10
Fraction bar showing 3 out of 10 parts shaded
  1. 1Increasing means the multiplier is 1 + 3/10 = 13/10.
  2. 2Multiply the original amount by this multiplier: 450 × 13/10.
  3. 3450 × 13 = 5850.
  4. 45850 ÷ 10 = 585.

Answer: 585

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Practice

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Common mistake. Pupils often find the fractional amount correctly but then forget to add or subtract it from the original, giving the change itself as the final answer rather than the new total. Always combine the fraction into a single multiplier first.

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