In the lesson (Reading a ratio as times). The bars didn't change. The question did. In the lesson (Reading a ratio as times). The second number tells you how many of the first it takes.
Lesson videos, with the working
Lesson 1
Reading a ratio as times
2 min 37 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
Adam and Grace tip out all the bottle caps collected in their jars. The number of Adam's caps to Grace's is in the ratio 3 : 5. What fraction of all the caps are Adam's?
Fraction of all the caps that are Adam's = 3/8
Ans: {3|8}
Example 1
What fraction of all the caps are Grace's?
Fraction of all the caps that are Grace's = 5/8
Ans: {5|8}
How to solve it
Draw the first quantity as one blue unit and write the names: Box A to Box B, 1 to 2.
Read the second number as copies: Box B is 2 copies of Box A, so Box B is 2 times Box A.
Write Box A's count where Box A is: Box A holds 24 parcels, so 24 goes in.
Work it out: 2 times 24 is 48 parcels.
If the first quantity is itself a calculation, such as 7 units minus 42, it goes in twice: 14 units minus 84.
The second number tells you how many of the first it takes.
Lesson 2
Reading a ratio as times
4 min 28 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
Two boxes at a post office hold parcels. The number of parcels in Box A to the number of parcels in Box B is 1 : 2. Box A holds 24 parcels. How many parcels are in Box B?
Number of parcels in Box B = 2 × 24 = 48
Ans: 48
Example 1
The number of stickers in Album P to the number of stickers in Album Q is 1 : 3. Album P has 15 stickers. How many stickers are in Album Q?
Number of stickers in Album Q = 3 × 15 = 45
Ans: 45
Example 2
The number of tickets at Booth A to the number of tickets at Booth B was in the ratio 7 : 5. After 42 tickets were moved from Booth A to Booth B and 36 newly printed tickets were placed in Booth B, the ratio became 1 : 2. How many tickets were at Booth A at first?
Booth A at first = 7 × 18 = 126 tickets
Ans: 126
How to solve it
Draw the first quantity as one blue unit and write the names: Box A to Box B, 1 to 2.
Read the second number as copies: Box B is 2 copies of Box A, so Box B is 2 times Box A.
Write Box A's count where Box A is: Box A holds 24 parcels, so 24 goes in.
Work it out: 2 times 24 is 48 parcels.
If the first quantity is itself a calculation, such as 7 units minus 42, it goes in twice: 14 units minus 84.
The second number tells you how many of the first it takes.
Practice questions with worked solutions
Question 1 is free to try. The other 6 open in the free trial, each with its full working.
How do you solve fraction and ratio questions in P6?
The same bar model can be read as a ratio between parts or as a fraction of a whole.
What your child learns here
The same bar model can be read as a ratio between parts or as a fraction of a whole. This page teaches your child to move between the two, which many Primary 6 word problems need without saying so.
Write one part as a fraction of the whole by adding all the units to find the whole.
Write one part as a fraction of another part when the question names a different whole.
Read a ratio such as 1 : 3 as 'the second is 3 times the first'.
Use fractions and ratios of three quantities in the same way.
Does the answer make sense?
When your child gives one part as a fraction of everything, it must be less than 1, and its bottom number should match the ratio's units added together, as 3 : 5 gives eighths. Only a part compared with another part, like Syafiq's loans with Wei Ling's, can go above 1.
How to practise these questions
The Basic questions train reading a fraction and a ratio off the same bar, keeping track of which whole each one refers to. Intermediate questions add more steps between the fraction given and the ratio asked. Challenge questions require switching between the two readings several times. When a fraction and a ratio seem to disagree, read the written step-by-step solution.
Questions parents ask
Where is fraction and ratio in the MOE syllabus? It is outcome 1.7 of the Primary 6 Ratio sub-strand: relationship between fraction and ratio. It joins the fractions your child has met in earlier years with the new ratio notation.
Why does 3 : 5 not mean three fifths? Because a ratio compares two parts, and a fraction compares a part with a whole. With 3 units and 5 units, the whole is 8 units, so the first part is three eighths of the whole. It is three fifths of the second part only.
How can my child tell which whole a question means? Look at the words after 'a fraction of'. If they name everything, add all the units; if they name one person or one kind, that amount is the whole.
