** **

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

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## About Scott Solomon

HowtoPasstheGED.com gears up adult learners for the recently redesigned, newly computerized GED. ScottSolomon.com delves into my literary fiction.