True or False? The order of the numbers in a ratio does not matter.

False. The order that the numbers are in does matter. The order should correspond with the order in which they are listed in words. E.g. A ratio of 3 parts white paint to every 2 parts red paint, should be expressed as, W : R = 3 : 2 A ratio written as W : R = 2 : 3 would indicated 2 parts white paint to every 3 parts red paint.

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 A receives 14 more chocolates than B, 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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Working with Ratios (Cambridge (CIE) IGCSE Maths)

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True or False?
The order of the numbers in a ratio does not matter.

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True or False?
The order of the numbers in a ratio does not matter.
False.
The order that the numbers are in does matter.
The order should correspond with the order in which they are listed in words.
E.g. A ratio of 3 parts white paint to every 2 parts red paint, should be expressed as, W : R = 3 : 2
A ratio written as W : R = 2 : 3 would indicated 2 parts white paint to every 3 parts red paint.
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?
E.g. 12 : 32
To simplify a ratio, divide both sides of the ratio by the same number.
This will find an equivalent ratio with smaller values.
E.g. $12 : 32 \begin{matrix} \div 4 & \div 4 \end{matrix} 3 : 8$
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.
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.
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 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 A receives 14 more chocolates than B, 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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