In this one, nothing stayed the same. So we didn't look for something that did. We cut the units small enough for both fractions to be whole numbers of the small units, and counted from there. In the lesson. We cut the units small enough for both fractions to be whole numbers of the small units, and counted from there.
Lesson video, with the working
Nothing stays the same
4 min 19 s
The film teaches 1 question. The question shows first; its working is written as the film explains it.
A florist had roses and tulips. The number of roses to the number of tulips was 3 : 2. 2/9 of the roses and 1/4 of the tulips were then sold. After that, there were 55 more roses than tulips left. How many roses did the florist have at first?
The florist had 198 roses at first.
Ans: 198
How to solve it
Draw roses as 3 units and tulips as 2. Cut every unit into 6, the lowest common multiple of 3 and 2.
Now the roses are 3 times 6, which is 18 small units, and the tulips are 2 times 6, which is 12.
Work out what was sold: two ninths of 18 is 4 units, and one quarter of 12 is 3 units.
What is left: 18 minus 4 is 14 units of roses, and 12 minus 3 is 9 units of tulips.
The gap is 14 minus 9, which is 5 units, and that is 55. So 1 unit is 11.
The roses at first were 18 units: 18 times 11 is 198 roses.
In this one, nothing stayed the same. So we didn't look for something that did. We cut the units small enough for both fractions to be whole numbers of the small units, and counted from there.
Practice questions with worked solutions
Questions 1 and 8 are free to try. The other 6 open in the free trial, each with its full working.
Question 1 of 8 · Basic · free to tryA jar held 4 times as many pebbles as shells. 18 pebbles were then taken out…A jar held 4 times as many…
A jar held 4 times as many pebbles as shells. 18 pebbles were then taken out and 9 more shells were put in. After that, there were equal numbers of pebbles and shells in the jar. How many pebbles and shells were there altogether in the jar at first?
Question 8 of 8 · Challenge · free to tryThe number of tickets at Booth A to the number of tickets at Booth B was in…The number of tickets at Booth A…
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?
Show the working and the answer
Working
Booth A in the end = 7 units − 42
in the end, Booth A : Booth B = 1 : 2
Booth B in the end = 2 × (7 units − 42)
= 14 units − 84
Answer: 126
For parents
How do you solve P6 ratio questions where both quantities change?
These are the most demanding before-and-after ratio questions on this chapter: both quantities change, by different amounts or fractions, so there is no fixed total, difference or quantity to hold on to.
What your child learns here
These are the most demanding before-and-after ratio questions on this chapter: both quantities change, by different amounts or fractions, so there is no fixed total, difference or quantity to hold on to. Your child learns to resize the units so every change can be counted.
Check whether the total, the difference or either quantity stays the same before choosing a method.
When none does, cut every unit into the same number of smaller units, using the lowest common multiple of the denominators.
Work out the change on each side in small units, then use the given number to find 1 small unit.
Applies equivalent ratios and fraction of a quantity in multi-step word problems.
Does the answer make sense?
Every starting amount must be large enough to cover what the story removes, and when a fraction is taken, such as a quarter of the red lanterns, that amount must divide exactly by the bottom number. If your child gets half a lantern or a negative count, the units were not resized.
How to practise these questions
Basic questions train before-and-after ratio questions where every quantity changes, so the units must be drawn carefully. Intermediate questions add rescaling to a common total, and a quantity your child may assume is constant when it is not. Challenge questions add more changes in sequence, or a total that increases. If nothing stays the same and the bars feel slippery, read the written step-by-step solution together.
Questions parents ask
How does my child know nothing stays the same? Check three things: did the total change, did the difference change, did either quantity change? If all three did, none of the shorter methods applies, and the units have to be cut smaller.
Why cut every unit into the same number of pieces? Units in a ratio must all be the same size. Cutting each unit into the same number of smaller pieces keeps them equal, while making each fraction of each bar a whole number of pieces.
Is this beyond the P6 syllabus? No. It uses only Primary 6 outcomes: equivalent ratios and the relationship between fraction and ratio. What makes it demanding is that several steps are chained together.
