**
Ratio
**Ratio refers to a comparison between two similar things.

Ratio can be represented with a colon.

a:b

Ratio can also be represented as a fraction.

Ratio of yellow beads to green beads = 1 to 2 = 1:2 =

Ratio of yellow beads to green beads = 2 to 4 = 2:4 =

Ratio of yellow beads to green beads = 3 to 6 = 3:6 =

**
Proportion
**Proportion refers to two equal ratios.

a:b = c:d

=

For ratios and to be in proportion **→ **ad = bc

To Prove Ratios are in Proportion, Cross-Multiply

In order to cross-multiply, it is helpful to understand algebraic equations.

It is also helpful to know your multiplication and division tables.

=

For ratios and **→**

ad = 1 × 12

bc = 2 × 6

1 × 12 = 2 × 6

12 = 12

Because ad = bc, ratios and are in proportion.

**To Solve for an Unknown Variable in Proportionate Ratios, Cross-Multiply**

In order to cross-multiply, it is helpful to understand algebraic equations.

It is also helpful to know your multiplication and division tables.

=

For ratios and **→**

ad = bc

ad = 2 × d

bc = 4 × 5

2 × d = 4 × 5

2d = 20

=

d = 10

**Question**

Prove that the ratios of yellow to green beads in the image below are in proportion.

**Answer**

=

**Answer Process**

=

For ratios and **→**

ad = 1 × 4

bc = 2 × 2

1 × 4 = 2 × 2

4 = 4

Because ad = bc, ratios and are in proportion.

Question

In the image below, two ramps are in proportion. Find the length L of the larger ramp.

**Answer**

6

**Answer Process**

=

For ratios and **→**

ad = 2 × L

bc = 3 × 4

2 × L = 3 × 4

2L = 12

=

L = 6

Question

In the image below, two ramps are in proportion. Find the length Q of the smaller ramp.

**Answer**

10

**Answer Process**

=

For ratios and **→**

ad = 20 × Q

bc = 40 × 5

20 × Q = 40 × 5

20Q = 200

=

Q = 10

**
Practice – Questions
**1. Prove that the ratios of yellow to green beads in the image below are in proportion.

2. In the image below, two ramps are in proportion. Find the length L of the larger ramp.

3. In the image below, two ramps are in proportion. Find the length Q of the smaller ramp.

4. In the image below, two rectangular boxes are in proportion. Find the length L of the larger box.

5. In the image below, two rectangular boxes are in proportion. Find the width W of the smaller box.

Practice – Answers

1. For ratios and **→**

ad = 1 × 6

bc = 2 × 3

1 × 6 = 2 × 3

6 = 6

Because ad = bc, ratios and are in proportion.

2. 21

3. 6

4. 21

5. 3