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Chapter overview
Learning goals
Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
Other graphs
Ratio
Proportion
Rates of change
Shapes
Properties of shapes
Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
Ratios are used to describe how something is divided between two or more categories. You need to know how to read, interpret and simplify ratios, as well as solve problems involving ratios.
A ratio is a piece of information that compares quantities.
A ratio is written using colons (:) to separate and compare numbers. When reading ratios, read the colons as "to". For example, the ratio $2:3$ is read as "two to three".
Ratios are best understood through examples.
It is possible to simplify ratios to their lowest form, much like fractions. However, it is first important to understand how two ratios can be equal.
If all the numbers in a ratio are multiplied or divided by the same number, then the value of the ratio doesn't change.
1. | Find a number that all numbers in the ratio can be divided by. This is called a common factor. |
2. | Divide all the numbers in the ratio by this common factor. |
3. | Keep doing this until the ratio cannot be simplified any further. This is called the simplest form of the ratio. |
Simplify the ratio $10:6:16$ to its simplest form.
$10$, $6$, and $16$ are all even numbers. So, they are all divisible by $2$. Hence, $2$ is a common factor.
Divide all three numbers in the ratio by $2$:
$10\div2=5$
$6\div2=3$
$16\div2=8$
Therefore:
$10:6:16=5:3:8$
The numbers $5$, $3$ and $8$ have no common factors, so this ratio cannot be simplified further. Therefore:
$\underline{10:6:16=5:3:8}$ in its simplest form.
Ratios can be used to calculate how much of a certain quantity is needed in relation to another given quantity.
The ratio of boys to girls in a classroom is $4:3$. If there are $20$ boys in this class, how many girls are there?
Call the number of girls in the class $x$. The $20$ boys and $x$ girls must be in the ratio $4:3$. Therefore:
$4:3=20:x$
Find what number is multiplied by $4$ that gives $20$:
$20\div4=5$
Multiply $3$ by $5$ to get the number of girls in the class:
$4:3=(4\times5):(3\times5)=20:15$
$x=15$
There are $\underline{15}$ girls in the class.
Another common type of ratio question is to divide and share a quantity into a given ratio. With these problems, it's easiest to think of "parts".
$£150$ is split between two friends Carl and Daniel in the ratio $7:3$. How much money does Carl get?
Calculate the total number of parts by adding the numbers in the ratio:
Carl gets $7$ "parts" of the money, and Daniel will get $3$ "parts".
$7$ parts + $3$ parts = $10$ parts in total.
Find the value of $1$ part:
If $10$ parts $=£150$, then $1$ part = $£150\div10=£15$.
Find how much money Carl gets:
If $1$ part = $£15$, and Carl gets $7$ parts, then Carl gets $£15\times7=£105$.
Carl gets $\underline{£105.}$
Ratios are used to describe how something is divided between two or more categories. You need to know how to read, interpret and simplify ratios, as well as solve problems involving ratios.
A ratio is a piece of information that compares quantities.
A ratio is written using colons (:) to separate and compare numbers. When reading ratios, read the colons as "to". For example, the ratio $2:3$ is read as "two to three".
Ratios are best understood through examples.
It is possible to simplify ratios to their lowest form, much like fractions. However, it is first important to understand how two ratios can be equal.
If all the numbers in a ratio are multiplied or divided by the same number, then the value of the ratio doesn't change.
1. | Find a number that all numbers in the ratio can be divided by. This is called a common factor. |
2. | Divide all the numbers in the ratio by this common factor. |
3. | Keep doing this until the ratio cannot be simplified any further. This is called the simplest form of the ratio. |
Simplify the ratio $10:6:16$ to its simplest form.
$10$, $6$, and $16$ are all even numbers. So, they are all divisible by $2$. Hence, $2$ is a common factor.
Divide all three numbers in the ratio by $2$:
$10\div2=5$
$6\div2=3$
$16\div2=8$
Therefore:
$10:6:16=5:3:8$
The numbers $5$, $3$ and $8$ have no common factors, so this ratio cannot be simplified further. Therefore:
$\underline{10:6:16=5:3:8}$ in its simplest form.
Ratios can be used to calculate how much of a certain quantity is needed in relation to another given quantity.
The ratio of boys to girls in a classroom is $4:3$. If there are $20$ boys in this class, how many girls are there?
Call the number of girls in the class $x$. The $20$ boys and $x$ girls must be in the ratio $4:3$. Therefore:
$4:3=20:x$
Find what number is multiplied by $4$ that gives $20$:
$20\div4=5$
Multiply $3$ by $5$ to get the number of girls in the class:
$4:3=(4\times5):(3\times5)=20:15$
$x=15$
There are $\underline{15}$ girls in the class.
Another common type of ratio question is to divide and share a quantity into a given ratio. With these problems, it's easiest to think of "parts".
$£150$ is split between two friends Carl and Daniel in the ratio $7:3$. How much money does Carl get?
Calculate the total number of parts by adding the numbers in the ratio:
Carl gets $7$ "parts" of the money, and Daniel will get $3$ "parts".
$7$ parts + $3$ parts = $10$ parts in total.
Find the value of $1$ part:
If $10$ parts $=£150$, then $1$ part = $£150\div10=£15$.
Find how much money Carl gets:
If $1$ part = $£15$, and Carl gets $7$ parts, then Carl gets $£15\times7=£105$.
Carl gets $\underline{£105.}$
FAQs
Question: How do you simplify ratios?
Answer: First, find a common factor that divides all the numbers. Then, divide all the numbers in the ratio by this common factor. Repeat until you cannot simplify the ratio any further.
Question: How do you read and write ratios?
Answer: Separate numbers with a colon, the colon is read as "to".
Question: What is a ratio?
Answer: A ratio is a piece of information that compares quantities.
Theory
Exercises
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