True or False? If a ratio question wants a fraction or percentage answer, it is sometimes possible to pick your own value for the total number of items to help (e.g. assume there are 100 pupils in the school).

True. If a ratio question wants a fraction or percentage answer, it is sometimes possible to pick your own value for the total number of items to help (e.g. assume there are 100 pupils in the school).

IGCSEMathsEdexcelMaths A (Modular)Higher Unit 2FlashcardsNumberRatio Problem Solving

Ratio Problem Solving (Edexcel IGCSE Maths A (Modular))

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True or False?
A ratio can be expressed as a fraction.

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Cards in this collection (8)

True or False?
A ratio can be expressed as a fraction.
True.
A ratio can be expressed as a fraction (of the whole).
For example, with a ratio of $2 : 3$ , the first part is $\frac{2}{2 + 3} = \frac{2}{5}$ of the whole, and the other part is $\frac{3}{2 + 3} = \frac{3}{5}$ of the whole.
True or False?
The ratio $1 : 4$ is equivalent to $\frac{1}{4}$ .
False.
A ratio of $1 : 4$ is not equivalent to $\frac{1}{4}$ .
The two parts of that ratio are equivalent to $\frac{1}{1 + 4} = \frac{1}{5}$ of the whole and $\frac{4}{1 + 4} = \frac{4}{5}$ of the whole.
If a ratio is $X : Y$ , write down a formula for the fraction of the whole belonging to $X$ .
If a ratio is $X : Y$ , then the fraction of the whole belonging to $X$ is $\frac{X}{X + Y}$ .
Similarly, the fraction of the whole belonging to $Y$ is $\frac{Y}{X + Y}$ .
A bag contains blue and red marbles in the ratio 3 : 5.
If 20% of blue marbles are cracked, what percentage of the bag of marbles are blue and cracked?
The ratio 3 : 5 can be written as a fraction (there are 3 + 5 = 8 parts).
So $\frac{3}{8}$ of the bag are blue marbles.
20% of blue marbles are cracked, so find 20% of $\frac{3}{8}$ , for example $\frac{20}{100} \times \frac{3}{8}$ .
This gives $\frac{3}{40} = 0.075$ so 7.5% are blue are cracked.
A bag contains blue and red marbles in the ratio 3 : 5.
If $\frac{4}{25}$ of red marbles are cracked, find the fraction of the bag of marbles that are cracked red marbles.
The ratio 3 : 5 can be written as a fraction (there are 3 + 5 = 8 parts).
So $\frac{5}{8}$ of the bag are red marbles.
$\frac{4}{25}$ of red marbles are cracked, so find $\frac{4}{25}$ of $\frac{5}{8}$ , for example $\frac{4}{25} \times \frac{5}{8}$ .
This gives $\frac{1}{10}$ which is the fraction of the bag of marbles that are red and cracked.
True or False?
If a ratio question wants a fraction or percentage answer, it is sometimes possible to pick your own value for the total number of items to help (e.g. assume there are 100 pupils in the school).
True.
If a ratio question wants a fraction or percentage answer, it is sometimes possible to pick your own value for the total number of items to help (e.g. assume there are 100 pupils in the school).
Given two, two-part ratios that share different amounts of a common quantity, how can they be combined into a single three -part ratio?
E.g. if $x : y = 1 : 3$ and $y : z = 2 : 5$ , what is the combined ratio $x : y : z$ ?
To combine two, two-part ratios into a single three-part ratio:
1. Find equivalent ratios so that the value for $y$ is the same for both.
2. Join the two ratios by their common quantity.
E.g.
$x : y = 1 \times 2 : 3 \times 2 = 2 : 6$
$y : z = 2 \times 3 : 5 \times 3 = 6 : 15$
So, $x : y : z = 2 : 6 : 15$
True or False?
If $x : y = 1 : 3$ and $x : z = 1 : 2$ , then $x : y : z = 1 : 3 : 2$ .
True.
If $x : y = 1 : 3$ and $x : z = 1 : 2$ , then $x : y : z = 1 : 3 : 2$ .
In both original two-part ratios, the quantity $x$ has the same value of 1, so no equivalent ratios need to be found.
The three quantities can be written in the required order as a single three-part ratio.

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