How do you share an amount in a given ratio?

Add the parts to find the total number of parts , then divide the amount by that total to find what one part is worth. Finally, multiply that value by each part of the ratio in turn.

GCSEMathsEdexcelFoundationFlashcardsRatio, Proportion & Rates of ChangeIntroduction to Ratios

Introduction to Ratios (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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FrontIntroduction to Ratios
Define a ratio.

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Cards in this collection (18)

Define a ratio.
A ratio is a way of comparing one part of a whole to another part.
It is written using a colon, such as $2 : 5$ or $4 : 2 : 3$ .
Complete the pair of sentences by filling in what each one compares:
A fraction compares a part to the $______$ .
A ratio compares one part to $______$ .
The completed sentences are:
A fraction compares a part to the whole.
A ratio compares one part to another part.
True or False?
The ratio $1 : 4$ means the same as the fraction $\frac{1}{4}$ .
False.
$1 : 4$ means 1 part to 4 parts, so there are 5 parts altogether.
The first quantity is therefore $\frac{1}{5}$ of the whole, not $\frac{1}{4}$ .
True or False?
Writing a ratio as $5 : 3$ instead of $3 : 5$ changes what it means.
True.
Whatever is mentioned first in the question is matched to the first number in the ratio, and so on in order.
So a mixture of flour to butter in the ratio $3 : 5$ is quite different from one in the ratio $5 : 3$ .
What does the ratio $2 : 5 : 3$ tell you?
It compares three quantities rather than two.
The first is made up of $2$ parts, the second of $5$ parts and the third of $3$ parts.
Define equivalent ratios.
Equivalent ratios are ratios that represent the same proportion of a whole.
For example $5 : 10$ and $20 : 40$ are equivalent, because each part keeps the same size relative to the others.
Each part of the ratio $2 : 3 : 7$ has been multiplied by $4$ . Complete the equivalent ratio:
$______:______: 28$
The completed ratio is:
$8 : 12 : 28$
Multiplying $7$ by $4$ gives the $28$ that was already shown.
The ratio of leaves eaten by Alfred to Bob is $7 : 5$ , and Bob eats $35$ . How many does Alfred eat?
Alfred eats $49$ leaves.
Dividing $35$ by Bob's $5$ parts gives a multiplier of $7$ , and $7 \times 7 = 49$ .
True or False?
To find a ratio equivalent to $3 : 4$ , you can add $2$ to each part to get $5 : 6$ .
False.
Equivalent ratios come from multiplying or dividing each part by the same value, never from adding.
$3 : 4$ and $5 : 6$ are not equivalent, because $3$ is three quarters of $4$ but $5$ is not three quarters of $6$ .
When is a ratio in its simplest form?
When all of its values are whole numbers and they share no common factor other than $1$ .
Both conditions have to hold, not just one of them.
How do you simplify the ratio $30 : 66 : 12$ ?
Divide every part by a common factor, ideally the highest common factor so that it is done in one step.
Here the highest common factor is $6$ , and dividing gives $5 : 11 : 2$ .
Amber receives $30$ of $48$ cake pieces and Naomi receives the rest. Write the ratio of Amber to Naomi in its simplest form.
The ratio is $5 : 3$ .
Naomi receives $48 - 30 = 18$ pieces, giving $30 : 18$ , and dividing both parts by $6$ gives $5 : 3$ .
True or False?
The ratio $4.5 : 3$ is in its simplest form.
False.
A ratio in its simplest form contains only whole numbers, so the decimal has to be cleared first.
Multiplying both parts by $2$ gives $9 : 6$ , and then dividing both by $3$ gives $3 : 2$ .
How do you share an amount in a given ratio?
Add the parts to find the total number of parts, then divide the amount by that total to find what one part is worth.
Finally, multiply that value by each part of the ratio in turn.
£200 is shared between A and B in the ratio $5 : 3$ , which is $8$ parts in total. Complete the working:
One part is worth £ $______$ , so A receives £ $______$ .
The completed working is:
One part is worth £ $25$ , so A receives £ $125$ .
$200 \div 8 = 25$ , and A has $5$ parts, so $5 \times 25 = 125$ .
True or False?
If an amount has been shared correctly in a ratio, adding the shares together gives back the original amount.
True.
The shares are simply the whole amount split up, so nothing is created or lost along the way.
Sharing £60 in the ratio $1 : 2$ gives £20 and £40, and $20 + 40 = 60$ .
Pink paint is made from $3$ parts red to $2$ parts white, and $60$ litres are needed. How much red paint is required?
$36$ litres of red paint.
There are $5$ parts in total, so one part is $60 \div 5 = 12$ litres, and red takes $3$ of them: $3 \times 12 = 36$ .
True or False?
To share £200 between two people in the ratio $5 : 3$ , you divide £200 by $2$ because there are two people.
False.
You divide by the total number of parts, which is $5 + 3 = 8$ .
How much each person receives depends on how many parts they have, not on how many people are sharing.

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