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      Expressing multiplicative relationships as ratios and fractions

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      Lesson details

      Learning outcome

      I can express a multiplicative relationship as a ratio or as a fraction.

      Key learning points

      1. By expressing the multiplicative relationship as a ratio, it can be easier to scale further.
      2. The relationship can be represented using a bar model.
      3. A bar model shows both parts of the ratio as well as the whole.
      4. A multiplicative relationship can be expressed as a fraction.
      5. There are many different ways to express the relationship.

      Keywords

      • Proportionality - means when variables are in proportion if they have a constant multiplicative relationship.

      • Ratio - shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.

      • Fraction - shows us how many equal parts in a whole.

      Common misconception

      Pupils see the bar model and/or fraction as the whole as opposed to the proportion of the whole.

      Emphasise equivalent fractions and equivalent bar models which show different parts to whole, but are the same proportion. e.g 3/5 = 60/100

      Teacher tip

      Using MWB, get pupils to represent the ratio of 2 circles to 1 square in as many different ways. Asking: what are the total shapes, how many circles and/or squares do you have? Emphasising the proportion is the same but totals are different.

      Licence

      This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0
       except where otherwise stated. See Oak's terms & conditions
       (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      Download starter quiz questions (PDF)

      6 Questions

      Q1.
      If two things are proportional then the ratio of part to whole is maintained and the __________ relationship between parts is also maintained.

      subtractive
      additive
      Correct answer: multiplicative
      inverse
      opposite

      Q2.
      The ratio table shows a recipe for a pizza topping sauce. Complete this statement: Pizza sauce $$\times$$ = Puree.

      An image in a quiz
      Correct Answer: 120

      Q3.
      The ratio table shows a recipe for a pizza topping sauce. Complete this statement: Garlic $$\times$$ = Puree.

      An image in a quiz
      Correct Answer: 30, thirty

      Q4.
      A bowl of fruit contains apples and bananas. For every 3 apples, there are 5 bananas. There are 15 apples in the bowl. There are bananas in the bowl.

      Correct Answer: 25, twenty five, twentyfive, twenty-five

      Q5.
      A box of fruit contains apples and bananas. For every 3 apples, there are 5 bananas. There are 80 pieces of fruit in total. How many bananas are there? bananas.

      Correct Answer: 50, fifty

      Q6.
      Which are equivalent ratios to: "For every 3 circles there are 5 squares."

      "For every 9 circles there are 14 squares."
      Correct answer: "For every 9 circles there are 15 squares."
      Correct answer: "For every 36 circles there are 60 squares."
      Correct answer: "For every 1.5 circles there are 2.5 squares."
      "For every 1 circle there are 1.5 squares."

      Assessment exit quiz

      Download exit quiz questions (PDF)

      6 Questions

      Q1.
      Which are equivalent to this ratio?

      An image in a quiz
      Correct answer: For every 1 t-shirt, there is 1 pair of shorts.
      For every 1 t-shirt, there are 2 pairs of shorts.
      Correct answer: Number of pairs of shorts × 1 = Number of t-shirts
      Number of pairs of shorts × 0.5 = Number of t-shirts

      Q2.
      Which are equivalent to this ratio?

      An image in a quiz
      Correct answer: For every cat, there are 4 mice.
      For every 2 cats, there are 9 mice.
      Correct answer: For every 2 cats, there are 8 mice.
      Correct answer: Number of cats × 4 = Number of mice
      Number of cats × 5 = Number of mice

      Q3.
      Which are equivalent to this ratio?

      An image in a quiz
      For every 4 phones, there are 3 houses.
      Correct answer: For every 4 houses, there are 3 phones.
      Correct answer: Number of houses $$\times \frac{3}{4}=$$ Number of phones
      Number of phones $$\times \frac{3}{4}=$$ Number of houses
      Correct answer: Number of phones $$\times \frac{4}{3}=$$ Number of houses

      Q4.
      A quantity is divided into two parts: A and B. Match each ratio with the correct fraction.

      Correct Answer:For every 2 As, there are 3 Bs,Fraction of A is $$\frac{2}{5}$$
      Correct Answer:For every 2 As, there are 5 Bs,Fraction of A is $$\frac{2}{7}$$
      Correct Answer:For every 2 As, there are 2 Bs,Fraction of A is $$\frac{1}{2}$$
      Correct Answer:For every 1 As, there are 2 Bs,Fraction of A is $$\frac{1}{3}$$

      Q5.
      A quantity is divided into two parts: A and B. Match each ratio with the correct formula.

      Correct Answer:For every 2 As, there are 3 Bs.,A $$\times\frac{3}{2} $$ = B
      Correct Answer:For every 2 As, there are 5 Bs.,A $$\times\frac{5}{2}$$ = B
      Correct Answer:For every 2 As, there are 2 Bs.,A $$\times1 $$ = B
      Correct Answer:For every 1 As, there are 2 Bs.,A $$\times2$$ = B

      Q6.
      A quantity is divided into two parts: A and B. Match each fraction with the correct formula to find B.

      Correct Answer:A is $$\frac{2}{3}$$,A $$\times\frac{1}{2} $$ = B
      Correct Answer:A is $$\frac{3}{5}$$,A $$\times\frac{2}{3} $$ = B
      Correct Answer:A is $$\frac{4}{7}$$,A $$\times\frac{3}{4} $$ = B
      Correct Answer:A is $$\frac{1}{3}$$,A $$\times 2 $$ = B

      To help you plan your 7 maths lesson on: Expressing multiplicative relationships as ratios and fractions, download all teaching resources for free and adapt to suit your pupils' needs...