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.

True or False? You always start a ratio problem by dividing the total amount by the total number of parts.

False. That only works when the total is the thing you have been given. When you are given one share, or the difference between two shares, you compare that amount with its own number of parts instead.

Define direct proportion .

Two quantities are in direct proportion when increasing or decreasing one by a certain factor changes the other by the same factor . The ratio of the two quantities therefore stays constant.

Define inverse proportion .

Two quantities are in inverse proportion when increasing one by a certain factor decreases the other by that same factor. It works the other way round too: decreasing one increases the other.

True or False? The unitary method can be used for inverse proportion as well as for direct proportion.

True. You still find the value for one unit first, but you use the opposite operation at each step. Where direct proportion divides to reach one unit, inverse proportion multiplies.

True or False? If more robots means less time to build a car, the two quantities are in direct proportion.

False. More robots and less time move in opposite directions, which makes this inverse proportion. Direct proportion would be something like more boxes of cereal giving more cornflakes.

IGCSEMathsCambridge (CIE)CoreFlashcardsNumberRatio & Proportion

Ratio & Proportion (Cambridge (CIE) IGCSE Maths: Core): Flashcards

Exam code: 0580 & 0980

1/32

0Still learning

Know0

FrontIntroduction to Ratios
Define a ratio.

Was this flashcard helpful?

Cards in this collection (32)

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.
Alfred and Bob eat cabbage leaves in the ratio $7 : 3$ , and Alfred eats $12$ more than Bob. How do you find the total eaten?
Use the difference in parts: $7 - 3 = 4$ parts must account for the $12$ extra leaves, so one part is $3$ .
The $10$ parts altogether then give $10 \times 3 = 30$ leaves.
True or False?
You always start a ratio problem by dividing the total amount by the total number of parts.
False.
That only works when the total is the thing you have been given.
When you are given one share, or the difference between two shares, you compare that amount with its own number of parts instead.
Kerry and Kacey share money in the ratio $8 : 5$ and Kacey gets $50$ . How do you find Kerry's share?
Compare the given amount with its own number of parts: Kacey's $50$ is $5$ parts, so one part is worth $10$ .
Kerry has $8$ parts, giving $8 \times 10 = 80$ .
Black socks to striped socks are in the ratio $5 : 2$ , and striped to white are in the ratio $6 : 7$ . Complete the step that lets the two ratios be joined.
$B : S = 5 : 2 =______: 6$
The completed step is:
$B : S = 5 : 2 = 15 : 6$
Multiplying both parts by $3$ makes the striped figure match the $6$ in the other ratio, so the two can then be joined.
If black to striped socks is $15 : 6$ and striped to white is $6 : 7$ , what is the three-part ratio?
It is $B : S : W = 15 : 6 : 7$ .
The striped figure is the same in both ratios, so striped acts as the link that lets them be written as one.
In the ratio $B : S : W = 15 : 6 : 7$ , what percentage is black?
There are $15 + 6 + 7 = 28$ parts in total, so $15$ out of every $28$ are black.
That gives $\frac{15}{28} = 0.5357 \dots$ , which is $53.6 %$ to $3$ significant figures.
Define direct proportion.
Two quantities are in direct proportion when increasing or decreasing one by a certain factor changes the other by the same factor.
The ratio of the two quantities therefore stays constant.
$2$ boxes of cereal contain $800$ g. Complete the working for $6$ boxes:
the factor is $6 \div 2 =______$ , so the mass is $800 \times______= 2400$ g
The completed working is:
the factor is $6 \div 2 = 3$ , so the mass is $800 \times 3 = 2400$ g
The same factor of $3$ applies to both quantities, which is exactly what makes this direct proportion.
$8$ boxes weigh $60$ kg. Use the unitary method to find the weight of $7$ boxes.
$52.5$ kg.
Divide to find the weight of one box, $60 \div 8 = 7.5$ kg, then multiply by $7$ to get $52.5$ kg.
Define inverse proportion.
Two quantities are in inverse proportion when increasing one by a certain factor decreases the other by that same factor.
It works the other way round too: decreasing one increases the other.
$3$ pumps fill a pool in $12$ hours. How long would $9$ pumps take?
$4$ hours.
The number of pumps is multiplied by $9 \div 3 = 3$ , so the time is divided by $3$ , giving $12 \div 3 = 4$ .
$5$ workers take $20$ hours to finish a job. How long would $8$ workers take?
$12.5$ hours.
One worker would take $5 \times 20 = 100$ hours, because fewer workers means more time, and then $100 \div 8 = 12.5$ hours for eight of them.
True or False?
The unitary method can be used for inverse proportion as well as for direct proportion.
True.
You still find the value for one unit first, but you use the opposite operation at each step.
Where direct proportion divides to reach one unit, inverse proportion multiplies.
True or False?
If more robots means less time to build a car, the two quantities are in direct proportion.
False.
More robots and less time move in opposite directions, which makes this inverse proportion.
Direct proportion would be something like more boxes of cereal giving more cornflakes.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:Fractions, Decimals & PercentagesNext:Money Calculations