How can you check your answer after sharing an amount in a ratio?

Add the shares back together: they must come to the amount you started with. It is a genuine check rather than a formality, because it catches the two commonest slips, dividing by the wrong number of parts and multiplying a share by the wrong part.

Define direct proportion .

Direct proportion is a relationship in which multiplying one quantity by a factor multiplies the other by the same factor. Both rise together and both fall together, and the ratio between them stays constant: 2 boxes of cereal hold 800 g, so 4 boxes hold 1600 g.

True or False? The time taken to produce 100 items is in direct proportion to the number of machines in the factory.

False. Adding machines makes the job take less time, so the two quantities move in opposite directions and this cannot be direct proportion. The test to apply is always the same: ask what happens to the second quantity when the first increases.

Define indirect proportion .

Indirect proportion is a relationship in which one quantity increases as the other decreases, and at the same rate. For example, 2 robots take 15 hours to build a car, while 6 robots take only 5 hours.

National 5MathsSQAApplications of MathematicsFlashcardsNumeracy SkillsRatio & Proportion

Ratio & Proportion (SQA National 5 Applications of Mathematics): Flashcards

Exam code: X844 75

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FrontScaling in a Ratio
Define equivalent ratios.

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Cards in this collection (19)

Define equivalent ratios.
Equivalent ratios are ratios that describe the same proportion, so each part is the same size relative to the others.
For example $5 : 10$ and $20 : 40$ are equivalent, because the second quantity is twice the first in both.
True or False?
To find an equivalent ratio you can add the same number to every part.
False.
Every part must be multiplied or divided by the same value, never added to.
Adding 2 to each part of $1 : 2$ gives $3 : 4$ , and the second quantity is no longer twice the first, so the proportion has changed.
Why is a recipe written as a ratio such as $3 : 2$ rather than fixed amounts?
Because a ratio fixes only the relative sizes, so it can be scaled to whatever quantity is actually wanted.
3 g of flour and 2 g of butter would make almost nothing, but the equivalent ratio $300 : 200$ gives a realistic cake using the same proportions.
The ratios $2 : 5$ and $7 : x$ are equivalent. What are the two ways of finding $x$ ?
Either scale between the two ratios: $7 \div 2 = 3.5$ , so $x = 5 \times 3.5 = 17.5$ .
Or scale within one ratio: $5 \div 2 = 2.5$ , so $x = 7 \times 2.5 = 17.5$ .
Both give the same answer, so use whichever division is easier.
Complete the equivalent ratio:
$2 : 3 : 7 = 8 :______:______$
The completed ratio is:
$2 : 3 : 7 = 8 : 12 : 28$
Every part was multiplied by 4, and a ratio with three parts is scaled in exactly the same way as one with two.
The ratio of children to teachers on a trip must be 15 : 2, and 8 teachers are going. How many children can go?
60 children can go.
The teachers went from 2 to 8, which is a scale factor of $8 \div 2 = 4$ .
Applying the same factor to the children gives $15 \times 4 = 60$ .
£200 is shared between A and B in the ratio 5 : 3. What is the first thing you work out?
The total number of parts, found by adding every part of the ratio together.
Here that is $5 + 3 = 8$ , and it matters because the amount being shared has to be split into that many equal parts before anything else can be worked out.
£360 is shared between C and D in the ratio 7 : 2. Complete the working:
$360 \div 9 = 40, so C gets 7 \times 40 =______and D gets 2 \times 40 =______$
The completed working is:
$360 \div 9 = 40, so C gets 7 \times 40 = 280 and D gets 2 \times 40 = 80$
So C receives £280 and D receives £80.
How can you check your answer after sharing an amount in a ratio?
Add the shares back together: they must come to the amount you started with.
It is a genuine check rather than a formality, because it catches the two commonest slips, dividing by the wrong number of parts and multiplying a share by the wrong part.
A and B share money in the ratio 5 : 3, and A receives £90. How much does B receive?
B receives £54.
A's £90 is 5 parts, so one part is worth $90 \div 5 = 18$ pounds.
B has 3 parts, which comes to $3 \times 18 = 54$ pounds.
True or False?
Sharing an amount in the ratio $2 : 3$ is the same as finding $\frac{2}{5}$ and $\frac{3}{5}$ of it.
True.
There are 5 parts altogether, so one share is 2 of those 5 and the other is 3 of them.
The total number of parts is what goes on the bottom of each fraction, which is why the two fractions always add to 1.
Fiona and Gert share sweets in the ratio 4 : 7, with Fiona receiving 24 fewer than Gert. How many sweets does Gert receive?
Gert receives 56 sweets.
A difference is given rather than a share, and the difference is $7 - 4 = 3$ parts, so one part is $24 \div 3 = 8$ sweets.
Gert has 7 parts, which comes to $7 \times 8 = 56$ .
Define direct proportion.
Direct proportion is a relationship in which multiplying one quantity by a factor multiplies the other by the same factor.
Both rise together and both fall together, and the ratio between them stays constant: 2 boxes of cereal hold 800 g, so 4 boxes hold 1600 g.
What is the unitary method?
Finding the value of one unit first, and then scaling that up to however many you need.
If 8 boxes weigh 60 kg then one box weighs $60 \div 8 = 7.5$ kg, so 7 boxes weigh $7.5 \times 7 = 52.5$ kg.
It is useful whenever the jump from the given number to the wanted number is not a tidy one.
True or False?
The time taken to produce 100 items is in direct proportion to the number of machines in the factory.
False.
Adding machines makes the job take less time, so the two quantities move in opposite directions and this cannot be direct proportion.
The test to apply is always the same: ask what happens to the second quantity when the first increases.
A cake decorator can decorate 4 cakes in 74 minutes. How long will 10 cakes take?
It will take 185 minutes.
The number of cakes is multiplied by $10 \div 4 = 2.5$ , and because the two quantities are in direct proportion the time is multiplied by the same factor.
That gives $74 \times 2.5 = 185$ .
Define indirect proportion.
Indirect proportion is a relationship in which one quantity increases as the other decreases, and at the same rate.
For example, 2 robots take 15 hours to build a car, while 6 robots take only 5 hours.
Complete the method for an indirect proportion question:
Find the factor that the first quantity has been multiplied by, then $______$ the second quantity by that factor rather than $______$ it.
The completed method is:
Find the factor that the first quantity has been multiplied by, then divide the second quantity by that factor rather than multiplying it.
This one word is the only difference from a direct proportion question, and it is where nearly all the marks are lost.
5 cleaners take 3.5 hours to clean a building. How long will 7 cleaners take, working at the same rate?
It will take 2.5 hours.
The number of cleaners is multiplied by $7 \div 5 = 1.4$ , so the time is divided by 1.4, giving $3.5 \div 1.4 = 2.5$ .
The answer is less than 3.5 hours, which is the sense check: more cleaners must mean less time.

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