A ratio is a way of comparing one part of a whole to another.

How do you simplify a ratio?

To simplify a ratio, divide both sides of the ratio by the same number.

What does it mean to convert a ratio to a fraction?

To convert a ratio to a fraction means to express one side of the ratio as a fraction of the total.

What does it mean to share an amount in a ratio?

Sharing an amount in a ratio is the process of dividing a given amount proportionally according to a specified ratio.

What is the process for sharing an amount in a ratio?

To share an amount into a ratio: Find the total number of parts Then divide the amount by the total number of parts to find the value of one part. Finally, multiply the value of one part by each ratio number to find the share for each part of the ratio.

True or False? When sharing an amount into a ratio, you first find the value of one part before finding the shares.

True. When sharing an amount into a ratio, you first find the value of one part before finding the shares for each part of the ratio.

True or False? Instead of being given the total amount to share, you might be given the difference between two shares in a ratio problem.

True. Instead of being given the total amount to share, you might be given the difference between two shares in a ratio problem.

What is the process if you are given one part of a ratio, rather than the total amount to be shared?

If you are given one part of a ratio rather than the total amount to be shared: Find the value of one part by dividing the given part by its ratio number Then multiply the value of one part by the other ratio number(s) to find the other part(s)

What is the advantage of showing a ratio problem in a simple diagram?

Showing a ratio problem in a simple diagram can help visualize the parts and shares, making it easier to understand and work through the problem.

Proportion is the relationship between two quantities where multiplying one by a scale factor means the other will be multiplied by the same scale factor.

What is the unitary method?

The unitary method is when the proportion relating to just 1 unit of a quantity is found by dividing the quantities that are in proportion by the same scale factor. This can then be used to find any proportional amount.

What does it mean for quantities to be inversely proportional ?

If two quantities are inversely proportional, then as one increases the other decreases.

True or False? If two quantities are inversely proportional, multiplying one quantity by a scale factor will divide the other quantity by the same scale factor.

True. If two quantities are inversely proportional, multiplying one quantity by a scale factor will divide the other quantity by the same scale factor. E.g. if 200 builders can build a stadium in 12 months, then doubling the number of builders to 400 will halve the time it takes to 6 months.

True or False? When calculating proportional quantities, you may need to round your answer to the nearest whole number.

True. When calculating proportional quantities, you may need to round your answer to the nearest whole number. Exactly how to round will depend on the context of the question.

What should you do if your answer needs to be a whole number when working with proportions?

If your answer needs to be a whole number when working with proportions, you should round your answer to a whole number. This may not always be the nearest whole number. For example if you find you need 2.3 bags of flour for a recipe, you should round that up to 3 bags to make sure you have enough.

State the meaning of scaling up in proportions.

Scaling up in proportions means to increase all the quantities by a certain scale factor while maintaining the same proportional relationship. This means multiplying all the quantities by the same number (with that number being greater than 1).

What does it mean to scale down in proportions?

To scale down in proportions means to decrease all the quantities by a certain scale factor while maintaining the same proportional relationship. This means dividing all the quantities by the same number (with that number being greater than 1).

True or False? In proportion questions like scaling up or scaling down a recipe, if you increase one quantity by a scale factor, you must decrease the other quantities by the same scale factor.

False. In proportion questions like scaling up or scaling down a recipe, if you increase one quantity by a scale factor, you must increase the other quantities by the same scale factor.

IGCSEMaths A: HigherEdexcelFlashcards

Ratio Toolkit (Edexcel IGCSE Maths A)

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What is a ratio?

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Cards in this collection (25)

What is a ratio?
A ratio is a way of comparing one part of a whole to another.
What is an equivalent ratio?
An equivalent ratio is a ratio that represents the same relationship between quantities but with different numbers.
For example, $2 : 3$ and $4 : 6$ are equivalent ratios.
How do you simplify a ratio?
To simplify a ratio, divide both sides of the ratio by the same number.
True or False?
When finding equivalent ratios, you can write down what you are doing to both sides to help check your work.
True.
When finding equivalent ratios, you can write down what you are doing to both sides (for example ' $\times 2$ ' or ' $\div 3$ ') to help check your work.
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.
What does it mean to convert a ratio to a fraction?
To convert a ratio to a fraction means to express one side of the ratio as a fraction of the total.
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.
How do you find the fraction of the whole for a ratio?
To find the fraction of the whole for a ratio, divide one of the numbers in the ratio by the total of all the numbers in the ratio.
For example, in the ratio $3 : 7$ the '3' part is $\frac{3}{3 + 7} = \frac{3}{10}$ 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 $\frac{Y}{X + Y}$ .
What does it mean to share an amount in a ratio?
Sharing an amount in a ratio is the process of dividing a given amount proportionally according to a specified ratio.
What is the process for sharing an amount in a ratio?
To share an amount into a ratio:
1. Find the total number of parts
2. Then divide the amount by the total number of parts to find the value of one part.
3. Finally, multiply the value of one part by each ratio number to find the share for each part of the ratio.
True or False?
When sharing an amount into a ratio, you first find the value of one part before finding the shares.
True.
When sharing an amount into a ratio, you first find the value of one part before finding the shares for each part of the ratio.
True or False?
Instead of being given the total amount to share, you might be given the difference between two shares in a ratio problem.
True.
Instead of being given the total amount to share, you might be given the difference between two shares in a ratio problem.
What is the process if you are given one part of a ratio, rather than the total amount to be shared?
If you are given one part of a ratio rather than the total amount to be shared:
1. Find the value of one part by dividing the given part by its ratio number
2. Then multiply the value of one part by the other ratio number(s) to find the other part(s)
True or False?
Adding labels to ratios is a recommended practice to avoid confusion.
True.
Adding labels to ratios is a recommended practice to avoid confusion and makes the working clearer.
For example, writing ' $yellow : purple = 4 : 7$ ' will help you keep clear which part of the ratio belongs to 'yellow' and which part belongs to 'purple'.
What is the advantage of showing a ratio problem in a simple diagram?
Showing a ratio problem in a simple diagram can help visualize the parts and shares, making it easier to understand and work through the problem.
What is proportion?
Proportion is the relationship between two quantities where multiplying one by a scale factor means the other will be multiplied by the same scale factor.
What is the unitary method?
The unitary method is when the proportion relating to just 1 unit of a quantity is found by dividing the quantities that are in proportion by the same scale factor.
This can then be used to find any proportional amount.
What does it mean for quantities to be inversely proportional?
If two quantities are inversely proportional, then as one increases the other decreases.
True or False?
If two quantities are inversely proportional, multiplying one quantity by a scale factor will divide the other quantity by the same scale factor.
True.
If two quantities are inversely proportional, multiplying one quantity by a scale factor will divide the other quantity by the same scale factor.
E.g. if 200 builders can build a stadium in 12 months, then doubling the number of builders to 400 will halve the time it takes to 6 months.
True or False?
When calculating proportional quantities, you may need to round your answer to the nearest whole number.
True.
When calculating proportional quantities, you may need to round your answer to the nearest whole number.
Exactly how to round will depend on the context of the question.
What should you do if your answer needs to be a whole number when working with proportions?
If your answer needs to be a whole number when working with proportions, you should round your answer to a whole number.
This may not always be the nearest whole number. For example if you find you need 2.3 bags of flour for a recipe, you should round that up to 3 bags to make sure you have enough.
State the meaning of scaling up in proportions.
Scaling up in proportions means to increase all the quantities by a certain scale factor while maintaining the same proportional relationship.
This means multiplying all the quantities by the same number (with that number being greater than 1).
What does it mean to scale down in proportions?
To scale down in proportions means to decrease all the quantities by a certain scale factor while maintaining the same proportional relationship.
This means dividing all the quantities by the same number (with that number being greater than 1).
True or False?
In proportion questions like scaling up or scaling down a recipe, if you increase one quantity by a scale factor, you must decrease the other quantities by the same scale factor.
False.
In proportion questions like scaling up or scaling down a recipe, if you increase one quantity by a scale factor, you must increase the other quantities by the same scale factor.

1. Numbers & the Number System

2. Equations, Formulae & Identities

3. Sequences, Functions & Graphs

4. Geometry & Trigonometry

5. Vectors & Transformation Geometry

6. Statistics & Probability