Informative line

# Representation of Ratios

Ratio

• Ratio is the comparison between two quantities.
• It can be represented in the following ways:

(1) By using the word 'to' -

We can represent a ratio by using the word 'to'.

For example: (a) $$4$$ blue balls to $$5$$ red balls

(b) $$10$$ boys to $$15$$ girls

(2) By using a colon (:) -

We can represent a ratio using a colon.

For example: $$\begin {array} {c} 4:5\\ 10:15 \end {array}$$

(3) In the form of fraction-

We can represent a ratio in fraction form.

For example: $$\dfrac{4}{5},\;\dfrac{10}{15}$$

• Ratio is a multiplicative comparison of two numbers.

Example: Mr. Jones has $$3$$ pens and $$2$$ pencils.

It means he has as many as $$\dfrac{3}{2}$$ pens as he has pencils.

Important note:

• A ratio is an ordered pair of positive numbers.
• While writing a ratio, the order is very important.

For example$$\begin {array} {c} 1:7\neq7:1\\ \end {array}$$

As $$\dfrac{1}{7}\neq\dfrac{7}{1}$$

Since $$\dfrac{1}{7}$$ is not equal to $$7,$$ thus the order of a ratio cannot be changed.

#### In a zoo, there are $$16$$ cats and $$9$$ dogs. Which one of the following DOES NOT represent the ratio of number of cats to number of dogs?

A $$16:9$$

B $$16$$ to $$9$$

C $$16.9$$

D $$\dfrac{16}{9}$$

×

Given:

Number of cats $$=16$$

Number of dogs $$=9$$

A ratio can be represented by using the word "to", a "colon", or a "fraction bar".

In option (C), $$16.9$$ does not represent a ratio.

Thus, option (C) is correct.

### In a zoo, there are $$16$$ cats and $$9$$ dogs. Which one of the following DOES NOT represent the ratio of number of cats to number of dogs?

A

$$16:9$$

.

B

$$16$$ to $$9$$

C

$$16.9$$

D

$$\dfrac{16}{9}$$

Option C is Correct

# Concept of Ratio

Ratio

• Ratio is a relationship between quantities.
• It states that a quantity is in comparison with another.
• The quantities whose ratios are to be written, can be anything, like pens, fruits, bikes, books, shirts, etc or two groups of things.

For example: A recipe for pancakes requires $$3$$ cups of flour and $$2$$ cups of milk.

Here, $$3$$ cups of flour is compared to $$2$$ cups of milk, which means, for every $$2$$ cups of milk there are $$3$$ cups of flour.

#### Which one of the following is a ratio?

A A recipe for hummingbird food calls for one part water to four parts sugar.

B There are seven blue balls in a bag.

C He has six shirts.

D Marc has five candies.

×

We know that ratio is the comparison between two quantities.

In option (A), there is a comparison between amount of water and sugar.

Hence, option (A) is correct.

In options (B), (C) and (D), there is no comparison between the given quantities. They are simply statements.

Thus, options (B), (C) and (D) are incorrect.

### Which one of the following is a ratio?

A

A recipe for hummingbird food calls for one part water to four parts sugar.

.

B

There are seven blue balls in a bag.

C

He has six shirts.

D

Marc has five candies.

Option A is Correct

# Part to Part Ratio

Ratio

• Ratio is the comparison between two quantities.

Types of ratio

There are three types of ratio:

1. Part to part ratio
2. Part to whole ratio
3. Whole to part ratio

Here, we will learn about the part to part ratio.

## Part to part ratio

• The part to part ratio represents the comparison between two parts.

For example: Consider a hexagonal plate as shown in the figure.

• The hexagonal plate is divided into six equal parts out of which two are shaded.
• Thus, we will write the part to part ratio, i.e. the ratio of shaded part to unshaded part for the hexagonal plate as:

Number of shaded parts $$=2$$

Number of unshaded parts $$=4$$

Thus, the ratio of shaded parts to unshaded parts $$=\dfrac{\text{Number of shaded parts}}{\text{Number of unshaded parts}}$$

$$=\dfrac{2}{4}$$

$$=2:4$$

• Thus, the ratio of shaded part to unshaded part is a part to part ratio.
• The part to part ratio is not considered to be a fraction because a fraction is always a ratio of part to whole.

#### In a bag, there are $$3$$ yellow balls for every $$5$$ black balls. Which one of the following represents the ratio of yellow balls to black balls?

A $$3:8$$

B $$3:5$$

C $$5:3$$

D $$5:8$$

×

Given:

Number of yellow balls $$=3$$

Number of black balls $$=5$$

Ratio of yellow balls to black balls $$=\dfrac{\text{Number of yellow balls}}{\text{Number of black balls}}$$

$$=\dfrac{3}{5}$$

$$=3:5$$

Hence, option (B) is correct.

### In a bag, there are $$3$$ yellow balls for every $$5$$ black balls. Which one of the following represents the ratio of yellow balls to black balls?

A

$$3:8$$

.

B

$$3:5$$

C

$$5:3$$

D

$$5:8$$

Option B is Correct

# Part to Whole Ratio

Ratio

• Ratio is the comparison between two quantities.

Types of ratio

There are three types of ratio:

1. Part to part ratio
2. Part to whole ratio
3. Whole to part ratio

Here, we will learn about the part to whole ratio.

## Part to whole ratio

• In the part to whole ratio, we compare a part with the whole.
• For example: Consider a hexagonal plate as shown in the figure.
• The hexagonal plate is divided into six equal parts out of which two are shaded.
• We will write the part to whole ratio, i.e. the ratio of shaded parts to the total number of parts for the hexagonal plate as:

Number of shaded parts $$=2$$

Total number of parts $$=6$$

Thus, the ratio of shaded parts to the total number of parts

$$=\dfrac{\text{Number of shaded parts}}{\text{Total number of parts}}$$

$$=\dfrac{2}{6}$$

$$=2:6$$

• Hence, the ratio of shaded parts to the total number of parts is a part to whole ratio.

#### A painter is mixing colors to get the right shade of green color. He has used $$4$$ parts of blue color for every $$5$$ parts of yellow color. What is the ratio of blue to the entire mixture?

A $$4:5$$

B $$5:4$$

C $$9:4$$

D $$4:9$$

×

Number of parts of blue color $$=4$$

Number of parts of yellow color $$=5$$

Total number of parts in the entire mixture

$$=4+5$$

$$=9$$

Ratio of blue color to entire mixture

$$=\dfrac{\text{Number of parts of blue color}}{\text{Total number of parts in the entire mixture}}$$

$$=\dfrac{4}{9}$$

$$=4:9$$

Hence, option (D) is correct.

### A painter is mixing colors to get the right shade of green color. He has used $$4$$ parts of blue color for every $$5$$ parts of yellow color. What is the ratio of blue to the entire mixture?

A

$$4:5$$

.

B

$$5:4$$

C

$$9:4$$

D

$$4:9$$

Option D is Correct

# Statement Form of Ratio

• A ratio can be written in the form of statements.

For example: In a restaurant, there are chairs and tables. The ratio of chairs to tables is $$19:12$$.

Number of chairs $$=19$$

Number of tables $$=12$$

The given ratio in statement form can be written as-

There are $$19$$ chairs for every $$12$$ tables in the restaurant.

or

For every $$12$$ tables in the restaurant, there are $$19$$ chairs.

or

There are $$19$$ chairs to $$12$$ tables in the restaurant.

#### In a basket, there are mangoes and apples. The ratio of mangoes to apples is $$5:4$$. Which statement is true?

A There are $$5$$ mangoes for every $$4$$ apples in the basket.

B There are $$2$$ mangoes for every $$12$$ apples in the basket.

C There are $$4$$ mangoes for every $$5$$ apples in the basket.

D There are $$3$$ mangoes for every $$8$$ apples in the basket.

×

In the basket, the ratio of mangoes to apples is $$5:4$$.

Mangoes $$=5$$

Apples $$=4$$

Total fruits $$=5+4=9$$

This ratio represents that there are $$5$$ mangoes for every $$4$$ apples in the basket.

Thus, option (A) is true.

### In a basket, there are mangoes and apples. The ratio of mangoes to apples is $$5:4$$. Which statement is true?

A

There are $$5$$ mangoes for every $$4$$ apples in the basket.

.

B

There are $$2$$ mangoes for every $$12$$ apples in the basket.

C

There are $$4$$ mangoes for every $$5$$ apples in the basket.

D

There are $$3$$ mangoes for every $$8$$ apples in the basket.

Option A is Correct

# Whole to Part Ratio

Ratio

• Ratio is the comparison between two quantities.

Types of ratio

• There are three types of ratio:
1. Part to part ratio
2. Part to whole ratio
3. Whole to part ratio

Here, we will learn about the whole to part ratio.

## Whole to part ratio

• In the whole to part ratio, we compare the whole with a particular part.
• For example: Consider a hexagonal plate as shown in the figure.
• The hexagonal plate is divided into six equal parts out of which two are shaded.
• We will write the whole to part ratio, i.e. the ratio of total number of parts to the unshaded parts for the hexagonal plate as:

Number of unshaded parts $$=4$$

Total number of parts $$=6$$

Thus, the ratio of total number of parts to the unshaded parts

$$=\dfrac{\text{Total number of parts}}{\text{Number of unshaded parts}}$$

$$=\dfrac{6}{4}$$

$$=6:4$$

• Hence, the ratio of total number of parts to the unshaded parts is a whole to part ratio.

#### A bag contains $$7$$ orange marbles and $$13$$ yellow marbles. What is the ratio of total marbles to orange marbles?

A $$7:13$$

B $$13:7$$

C $$7:20$$

D $$20:7$$

×

Number of orange marbles $$=7$$

Number of yellow marbles $$=13$$

Total number of marbles = Orange marbles + Yellow marbles

$$=7+13$$

$$=20$$

Ratio of total marbles to orange marbles

$$=\dfrac{\text{Total number of marbles}}{\text{Number of orange marbles}}$$

$$=\dfrac{20}{7}$$

$$=20:7$$

Hence, option (D) is correct.

### A bag contains $$7$$ orange marbles and $$13$$ yellow marbles. What is the ratio of total marbles to orange marbles?

A

$$7:13$$

.

B

$$13:7$$

C

$$7:20$$

D

$$20:7$$

Option D is Correct

# Ratio through Figures

Ratio

• Ratio is the relationship between two quantities.
• It can be represented through figures.

For example: What is the ratio of the number of pink triangles to the number of blue triangles?

Number of pink triangles $$=2$$

Number of blue triangles $$=4$$

Total number of triangles $$=6$$

$$\therefore$$ Ratio of pink triangles to blue triangles

$$=\dfrac{\text{Number of pink triangles}}{\text{Number of blue triangles}}$$

$$=\dfrac{2}{4}$$

$$=2:4$$

#### What is the ratio of the number of pink cubes to the total cubes?

A $$7:8$$

B $$8:15$$

C $$8:7$$

D $$15:8$$

×

Given:

Number of pink cubes $$=8$$

Number of yellow cubes $$=7$$

Total cubes $$=8+7$$

$$=15$$

$$\therefore$$ Ratio of pink cubes to total number of cubes $$=\dfrac{\text{Number of pink cubes}}{\text{Total number of cubes}}$$

$$=\dfrac{8}{15}$$

$$=8:15$$

Hence, option (B) is correct.

### What is the ratio of the number of pink cubes to the total cubes?

A

$$7:8$$

.

B

$$8:15$$

C

$$8:7$$

D

$$15:8$$

Option B is Correct