A ratio is a mathematical statement that expresses the relative sizes of two quantities.

As an example, let's look at the triangles and circles below.

We can express the ratio of the number of circles to the number of triangles as follows:

{\color{blue}{\textrm{number of circles}}} : {\color{red}{\textrm{number of triangles}}}

To find this ratio, we start by counting the number of occurrences of each shape:

  • First, we count the number of circles. There are \color{blue}5 circles.

  • Next, we count the number of triangles. There are \color{red}2 triangles.

Therefore, the ratio of circles to triangles is {\color{blue}5}:{\color{red}2}.

We can describe this ratio in words as follows:

The ratio of circles to triangles is {\color{blue}5}:{\color{red}2} because there are {\color{blue}5} circles for every {\color{red}{2}} triangles.

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Example: Finding a Ratio

What ratio describes the number of pentagons to the total number of shapes?

EXPLANATION

We can express the ratio of the number of pentagons to the total number of shapes as follows:

\textrm{number of pentagons} : \textrm{total number of shapes}

To find this ratio, we start by counting the number of occurrences of each shape:

  • First, we count the number of pentagons. There are 3 pentagons.

  • Next, we count the total number of shapes. There are 6 shapes.

Therefore, the ratio of pentagons to total shapes is 3:6.

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Practice: Finding a Ratio

What ratio describes the number of triangles to squares?

a
$4:1$
b
$4:5$
c
$1:4$
d
$4:3$
e
$3:4$
Practice: Finding a Ratio

In the diagram above, the ratio of circles to the total number of shapes is

a
b
c
d
e
Example: Word Problems

A merchant has 8 black crates and 5 green crates. What ratio describes the number of green crates to the total number of crates?

EXPLANATION

We can express the ratio of the number of green crates to the total number of crates as follows:

\textrm{number of green crates} : \textrm{total number of crates}

We compute our ratio as follows:

  • First, we count the number of green crates. There are 5 green crates.

  • Next, we count the total number of crates. There are 8+5 = 13 crates.

Therefore, the ratio of green crates to total crates is 5:13.

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Practice: Word Problems

To organize a field trip, there must be $1$ adult for every $10$ students. What ratio describes the number of students to the number of adults?

a
b
c
d
e
Practice: Word Problems

A bag contains $6$ green and $5$ red marbles. What ratio describes the number of red marbles to the total number of marbles?

a
$11:5$
b
$5:11$
c
$6:11$
d
$5:6$
e
$6:5$

The ratio of red marbles to blue marbles in a bag is 7:8. What is the meaning of this ratio?

EXPLANATION

If the ratio of red marbles to blue marbles is {\color{red}{7}}:{\color{blue}{8}}, it means that there are {\color{red}{7}} red marbles for every {\color{blue}{8}} blue marbles.

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From left to right, what are the missing numbers in the statement below?

The ratio of octagons to rectangles is $\fbox{$\phantom{0}$}:2\,$ because there are $\,\fbox{$\phantom{0}$}\,$ rectangles for every $4$ octagons.

a
$2$ and $2$
b
$3$ and $4$
c
$4$ and $2$
d
$2$ and $4$
e
$4$ and $3$

The ratio of male to the female members of a chess club is $2:3.$ What is the meaning of this ratio?

a
There are $3$ male members for every $2$ female members
b
There are $2$ male members for every $5$ female members
c
There are exactly $3$ male members and exactly $2$ female members
d
There are $2$ male members for every $3$ female members
e
There are exactly $2$ male members and exactly $3$ female members
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