A ratio compares one part of a whole with another part, and is written with the parts separated by a colon, such as 4 : 3. A ratio may have two or three parts.

A cake recipe mixes flour and butter in the ratio 2 : 1. Which number goes with which ingredient, and why?

Flour goes with the 2 and butter with the 1, because whatever is mentioned first in the question is the first part of the ratio. Writing it the other way round, as 1 : 2, would describe a completely different mixture.

In the ratio 4 : 3, what does the 4 actually count?

It counts parts , not an amount: the first quantity has four parts for every three the second quantity has. Until you know what one part is worth, 4 : 3 could describe 4 and 3, or 40 and 30, or 4 kg and 3 kg.

Define equivalent ratios .

Equivalent ratios are ratios that describe the same proportions, such as 5 : 10 and 20 : 40. The parts differ in size but their relationship to one another is unchanged.

How do you find a ratio equivalent to 2 : 3 : 7?

Multiply, or divide, every part by the same value, for example multiplying each by 4 to give 8 : 12 : 28. Changing only some of the parts alters the proportions and produces a different ratio altogether.

A cake recipe gives flour and butter in the ratio 3 : 2. Why would you scale this up to 300 : 200?

The ratio fixes only the proportions, so 3 g of flour and 2 g of butter would make almost no cake at all. Scaling to 300 g and 200 g keeps the mixture the same while giving amounts that are usable in practice.

When is a ratio in its simplest form ?

A ratio is in its simplest form when every part is a whole number and the parts share no common factor other than 1. So 45 : 30 is not in its simplest form, but 3 : 2 is.

True or False? The ratio 2.5 : 4 is already in its simplest form, because 2.5 and 4 have no common factor.

False. Every part of a ratio in its simplest form has to be a whole number, and 2.5 is not one. Multiplying both parts by 2 gives 5 : 8, which is the simplest form.

Why is it best to divide by the highest common factor when simplifying a ratio?

The highest common factor reaches the simplest form in a single step. A smaller common factor still works but leaves more to do, since dividing 24 : 36 by 4 gives 6 : 9, which then has to be divided by 3 as well.

Write the ratio 30 : 66 : 12 in its simplest form.

The highest common factor of 30, 66 and 12 is 6, so dividing each part by 6 gives 5 : 11 : 2. With three parts the factor has to divide all three of them, not just two.

True or False? Simplifying a ratio produces a ratio equivalent to the one you started with.

True. Simplifying is just scaling a ratio down, so the proportions are untouched and only the numbers written get smaller. That is why 45 : 30 and 3 : 2 describe the very same mixture.

True or False? After sharing an amount in a ratio, adding the shares together should give back the original amount.

True. The shares are simply the whole amount split up, so nothing is created or lost along the way. Sharing £200 in the ratio 5 : 3 gives £125 and £75, and £125 + £75 = £200 as expected.

How does sharing an amount change when the ratio has three parts instead of two?

It does not change at all: all three numbers are added to give the total number of parts, and each quantity then takes its own number of parts. Sharing 90 in the ratio 2 : 3 : 4 gives nine parts of 10, so the three shares are 20, 30 and 40.

What is the process for sharing an amount in a ratio ? E.g. Share 84 in the ratio 2 : 5

To share an amount into a ratio: Find the total number of parts , e.g. 2 + 5 = 7 parts Divide the amount by the total number of parts to find the value of one part , e.g. 84 ÷ 7 = 12 Multiply the value of one part by each ratio number to find the share for each part of the ratio, e.g. 2 × 12 : 5 × 12 = 24 : 60

What is the process to solve a problem if you are given one part of a ratio , rather than the total amount to be shared? E.g. A sum of money is shared between A and B in the ratio 4 : 3, A is given $60, how much is B given?

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, e.g. 60 ÷ 4 = 15 Multiply the value of one part by the other ratio number(s) to find the other part(s) , e.g. 15 × 3 = 45

True or False? A number of chocolates is shared between two people, A and B, in the ratio 5 : 7. Given that B receives 14 more chocolates than A, A must receive 35 chocolates and B receive 49 chocolates.

True. A must receive 35 chocolates and B receive 49 chocolates. When given the difference between two parts : Divide the difference given by the difference in the number of parts to find the value of one part , e.g. 14 ÷ (7 - 5) = 7 Multiply the value of one part by the number of parts for each quantity in the ratio to find the amount for each quantity , e.g. 5 × 7 : 7 × 7 = 35 : 49

What is meant when two quantities are said to be in direct proportion ?

If two quantities are said to be in direct proportion to one another, then as one quantity increases, the other increases by the same scale factor . E.g. Doubling one quantity will double the other.

What does it mean for two quantities to be inversely proportional ?

If two quantities are inversely proportional , then as one increases the other decreases . Both quantities change by the same scale factor .

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? If your answer needs to be a whole number when working with proportions, you should always round to the nearest whole number .

False. If your answer needs to be a whole number when working with proportions, you should round your answer to a whole number . However, 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.

What is the unitary method ?

The unitary method is when the proportion relating to just 1 unit of a quantity is found. You can find this value by dividing the quantities that are in proportion by the same scale factor , e.g. If 9 cakes weigh 10.8 kg, then 1 cake will weigh 10.8 ÷ 9 = 1.2 kg. This can then be used to find any proportional amount, e.g. 14 cakes will weigh 14 × 1.2 = 16.8 kg.

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Ratio & Proportion (Cambridge (CIE) O Level Maths): Flashcards

Exam code: 4024

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FrontIntroduction to Ratios
Define a ratio.

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Cards in this collection (30)

Define a ratio.
A ratio compares one part of a whole with another part, and is written with the parts separated by a colon, such as 4 : 3.
A ratio may have two or three parts.
A cake recipe mixes flour and butter in the ratio 2 : 1. Which number goes with which ingredient, and why?
Flour goes with the 2 and butter with the 1, because whatever is mentioned first in the question is the first part of the ratio.
Writing it the other way round, as 1 : 2, would describe a completely different mixture.
A quantity is divided in the ratio 2 : 5 : 3. Complete the sentence:
The second quantity is made up of five parts, and the whole is made up of $______$ parts, found by $______$ the three numbers together.
The completed sentence is:
The second quantity is made up of five parts, and the whole is made up of ten parts, found by adding the three numbers together.
In the ratio 4 : 3, what does the 4 actually count?
It counts parts, not an amount: the first quantity has four parts for every three the second quantity has.
Until you know what one part is worth, 4 : 3 could describe 4 and 3, or 40 and 30, or 4 kg and 3 kg.
What does a ratio compare, and what does a fraction compare?
A ratio compares one part with another part, while a fraction compares a part with the whole.
A pizza shared 5 slices to 3 gives the ratio 5 : 3, and the first person's share written as a fraction is $\frac{5}{8}$ of the whole pizza.
True or False?
The ratio 1 : 4 means the same thing as the fraction $\frac{1}{4}$ does.
False.
A ratio of 1 : 4 means one part to four parts, so there are five parts altogether and the first quantity is $\frac{1}{5}$ of the whole.
The fraction $\frac{1}{4}$ would instead mean one part out of four.
Define equivalent ratios.
Equivalent ratios are ratios that describe the same proportions, such as 5 : 10 and 20 : 40.
The parts differ in size but their relationship to one another is unchanged.
How do you find a ratio equivalent to 2 : 3 : 7?
Multiply, or divide, every part by the same value, for example multiplying each by 4 to give 8 : 12 : 28.
Changing only some of the parts alters the proportions and produces a different ratio altogether.
Two rabbits eat cabbage leaves in the ratio 7 : 5, and the second rabbit eats 35 leaves. Complete the sentence:
Multiplying each part by $______$ turns 7 : 5 into an equivalent ratio whose second part is 35, and the first part is then $______$ leaves.
The completed sentence is:
Multiplying each part by 7 turns 7 : 5 into an equivalent ratio whose second part is 35, and the first part is then 49 leaves.
A cake recipe gives flour and butter in the ratio 3 : 2. Why would you scale this up to 300 : 200?
The ratio fixes only the proportions, so 3 g of flour and 2 g of butter would make almost no cake at all.
Scaling to 300 g and 200 g keeps the mixture the same while giving amounts that are usable in practice.
When is a ratio in its simplest form?
A ratio is in its simplest form when every part is a whole number and the parts share no common factor other than 1.
So 45 : 30 is not in its simplest form, but 3 : 2 is.
True or False?
The ratio 2.5 : 4 is already in its simplest form, because 2.5 and 4 have no common factor.
False.
Every part of a ratio in its simplest form has to be a whole number, and 2.5 is not one.
Multiplying both parts by 2 gives 5 : 8, which is the simplest form.
Why is it best to divide by the highest common factor when simplifying a ratio?
The highest common factor reaches the simplest form in a single step.
A smaller common factor still works but leaves more to do, since dividing 24 : 36 by 4 gives 6 : 9, which then has to be divided by 3 as well.
Write the ratio 30 : 66 : 12 in its simplest form.
The highest common factor of 30, 66 and 12 is 6, so dividing each part by 6 gives 5 : 11 : 2.
With three parts the factor has to divide all three of them, not just two.
True or False?
Simplifying a ratio produces a ratio equivalent to the one you started with.
True.
Simplifying is just scaling a ratio down, so the proportions are untouched and only the numbers written get smaller.
That is why 45 : 30 and 3 : 2 describe the very same mixture.
£200 is shared between two people in the ratio 5 : 3. Why is the £200 divided by 8 rather than by 2?
The ratio splits the money into equal parts, and there are 5 + 3 = 8 of them, so one part is worth £25 because $200 \div 8 = 25$ exactly.
Dividing by 2 would only be right if the two people received equal shares, which the ratio 5 : 3 says they do not.
True or False?
After sharing an amount in a ratio, adding the shares together should give back the original amount.
True.
The shares are simply the whole amount split up, so nothing is created or lost along the way.
Sharing £200 in the ratio 5 : 3 gives £125 and £75, and £125 + £75 = £200 as expected.
Mark needs 60 litres of pink paint, mixing red and white in the ratio 3 : 2. Complete the working:
There are five parts altogether, so one part is $______$ litres, and Mark needs $______$ litres of red paint.
The completed working is:
There are five parts altogether, so one part is 12 litres, and Mark needs 36 litres of red paint.
The white paint takes the other two parts, which is $2 \times 12 = 24$ litres of paint.
How does sharing an amount change when the ratio has three parts instead of two?
It does not change at all: all three numbers are added to give the total number of parts, and each quantity then takes its own number of parts.
Sharing 90 in the ratio 2 : 3 : 4 gives nine parts of 10, so the three shares are 20, 30 and 40.
£240 is shared in the ratio 5 : 3. What fraction of the £240 does the first share take, and what is it worth?
The first share takes 5 of the 8 parts, which is $\frac{5}{8}$ of the money.
Working with that fraction directly, $\frac{5}{8}$ of £240 is £150, which is the same share that counting parts gives.
What is the process for sharing an amount in a ratio?
E.g. Share 84 in the ratio 2 : 5
To share an amount into a ratio:
1. Find the total number of parts, e.g. 2 + 5 = 7 parts
2. Divide the amount by the total number of parts to find the value of one part, e.g. 84 ÷ 7 = 12
3. Multiply the value of one part by each ratio number to find the share for each part of the ratio, e.g. 2 × 12 : 5 × 12 = 24 : 60
What is the process to solve a problem if you are given one part of a ratio, rather than the total amount to be shared?
E.g. A sum of money is shared between A and B in the ratio 4 : 3, A is given $60, how much is B given?
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,
  e.g. 60 ÷ 4 = 15
2. Multiply the value of one part by the other ratio number(s) to find the other part(s),
  e.g. 15 × 3 = 45
True or False?
A number of chocolates is shared between two people, A and B, in the ratio 5 : 7.
Given that B receives 14 more chocolates than A, A must receive 35 chocolates and B receive 49 chocolates.
True.
A must receive 35 chocolates and B receive 49 chocolates.
When given the difference between two parts:
1. Divide the difference given by the difference in the number of parts to find the value of one part, e.g. 14 ÷ (7 - 5) = 7
2. Multiply the value of one part by the number of parts for each quantity in the ratio to find the amount for each quantity, e.g. 5 × 7 : 7 × 7 = 35 : 49
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.
What is meant when two quantities are said to be in direct proportion?
If two quantities are said to be in direct proportion to one another, then as one quantity increases, the other increases by the same scale factor.
E.g. Doubling one quantity will double the other.
What does it mean for two quantities to be inversely proportional?
If two quantities are inversely proportional, then as one increases the other decreases.
Both quantities change by the same scale factor.
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?
If your answer needs to be a whole number when working with proportions, you should always round to the nearest whole number.
False.
If your answer needs to be a whole number when working with proportions, you should round your answer to a whole number.
However, 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.
What is the unitary method?
The unitary method is when the proportion relating to just 1 unit of a quantity is found.
You can find this value by dividing the quantities that are in proportion by the same scale factor, e.g. If 9 cakes weigh 10.8 kg, then 1 cake will weigh 10.8 ÷ 9 = 1.2 kg.
This can then be used to find any proportional amount, e.g. 14 cakes will weigh 14 × 1.2 = 16.8 kg.

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