Daniel and Rachel train by running laps of a track. Every morning, Daniel runs 3 laps. And every morning, Rachel runs 2. One day, Rachel counts up. She has run 8 laps. What's the missing number in 3 : 2 = ? : 8?
Daniel has run 12 laps.
Ans: 12
How to solve it
Write the pattern as a ratio: for every 3 laps Daniel runs, Rachel runs 2, so the ratio is 3 to 2.
As the mornings add up the pattern stays the same: after 2 mornings the ratio is 6 to 4, the same comparison.
Divide both numbers by the same number: 6 divided by 2 is 3, and 4 divided by 2 is 2.
For simplest form, divide until no number bigger than 1 divides both. 3 and 2 have no common factor.
To find a missing number, start from the side you can see: 2 became 8, which is times 4, so 3 times 4 is 12.
Multiply both numbers by the same number, or divide both by the same number. The ratio doesn't change.
Practice questions with worked solutions
Question 1 is free to try. The other 11 open in the free trial, each with its full working.
Question 1 of 12 · Basic · free to tryThe bar graph shows the number of pupils in each of the three houses at a…The bar graph shows the number…
The bar graph shows the number of pupils in each of the three houses at a school sports day. Write the ratio of the number of pupils in the Red House to the number of pupils in the Blue House to the number of pupils in the Green House in its simplest form.
Red House : Blue House : Green House = 60 : 40 : 90
highest common factor of 60, 40 and 90 = 10
Red House = 60 ÷ 10 = 6
Blue House = 40 ÷ 10 = 4
Green House = 90 ÷ 10 = 9
Red House : Blue House : Green House = 6 : 4 : 9
Answer: 6 : 4 : 9
For parents
How do you solve equivalent ratios questions in P6?
Equivalent ratios are the same comparison written with different numbers.
What your child learns here
Equivalent ratios are the same comparison written with different numbers. Your child uses this skill in almost every later ratio question, so it pays to make it automatic in Primary 6.
Make an equivalent ratio by multiplying or dividing every term by the same number.
Write a ratio of two or three terms in its simplest form.
Find the missing term in a pair of equivalent ratios, scaling down first when the numbers do not divide neatly.
Does the answer make sense?
When your child matches a ratio to real numbers, the bigger term must go with the bigger amount: if Hafiz's stall is the 7 in 7 : 4, it sold more sets. A ratio in simplest form has no number above 1 that divides every term.
How to practise these questions
Basic questions train scaling a ratio up and down and writing it in simplest form. Intermediate questions add extra conditions on the values. Challenge questions apply equivalent ratios in less direct settings with more steps. If equivalent ratios do not line up, read the written step-by-step solution together.
Questions parents ask
Is simplest form the same as lowest terms for a ratio? Yes, they mean the same thing. The MOE syllabus calls it expressing a ratio in its simplest form: no whole number bigger than 1 divides every term. It works in the same way as simplifying a fraction.
How do I help my child find a missing number in equivalent ratios? Ask 'times what?' Find the term that has a partner on both sides, work out the multiplier, and apply it to the other term. If the numbers do not divide neatly, simplify the ratio first, as the worked example on this page shows.
Can a ratio in simplest form have three numbers? Yes. The Primary 6 syllabus covers a : b : c as well as a : b. A three-term ratio is in simplest form when no number bigger than 1 divides all three terms, even if two of them share a factor, as in 2 : 4 : 5.
