- Ratios and Unit Rates
- Home
- Writing Ratios Using Different Notations
- Writing Ratios for Real-World Situations
- Identifying Statements that Describe a Ratio
- Simplifying a Ratio of Whole Numbers: Problem Type 1
- Simplifying a Ratio of Decimals
- Finding a Unit Price
- Using Tables to Compare Ratios
- Computing Unit Prices to Find the Better Buy
- Word Problem on Unit Rates Associated with Ratios of Whole Numbers: Decimal Answers
- Solving a Word Problem on Proportions Using a Unit Rate
- Solving a One-Step Word Problem Using the Formula d = rt
- Function Tables with One-Step Rules
- Finding Missing Values in a Table of Equivalent Ratios
- Using a Table of Equivalent Ratios to Find a Missing Quantity in a Ratio
- Writing an Equation to Represent a Proportional Relationship

# Writing an Equation to Represent a Proportional Relationship

An expression of **equality of ratios** is called a **proportion**. The proportion expressing the equality of the ratios A:B and C:D is written A:B = C:D or A:B::C:D. This form, when spoken or written, is often expressed as

A is to B as C is to D.

A, B, C and D are called the **terms** of the proportion. A and D are called the **extremes**, and B and C are called the **means**.

For **example**, from a table of equivalent ratios below, proportions can be written as follows 1:3::2:6 and 2:6::3:9

x | y |

1 | 3 |

2 | 6 |

3 | 9 |

The proportional relationship can also be written as

$\frac{y}{x} = \frac{3}{1} = \frac{6}{2} = \frac{9}{3}$

An equation to represent the proportional relationship would be

$y = 3x$

Write an equation to represent the proportional relationship given in the table.

k | 3 | 12 | 15 | 27 | 36 |

l | 7 | 28 | 35 | 63 | 84 |

### Solution

**Step 1:**

The proportional relationship can be written as

$\frac{l}{k} = \frac{7}{3} = \frac{28}{12} = \frac{35}{15}... = \frac{7}{3}$

**Step 2:**

So, the equation representing this proportional relationship is $l = \frac{7}{3} \times \frac{k}{1} = \frac{7k}{3}$

or $l = \frac{7k}{3}$

Write an equation to represent the proportional relationship given in the table.

a | 5 | 7 | 8 | 9 | 11 |

b | 15 | 21 | 24 | 27 | 33 |

### Solution

**Step 1:**

The proportional relationship can be written as

$\frac{b}{a} = \frac{15}{5} = \frac{21}{7} = \frac{24}{8}... = \frac{3}{1}$

**Step 2:**

So, the equation representing this proportional relationship is $b = \frac{3}{1} \times \frac{a}{1} = \frac{3a}{1} = 3a$

or $b = 3a$

Write an equation to represent the proportional relationship given in the table.

r | 10 | 20 | 30 | 40 | 50 |

s | 6 | 12 | 18 | 24 | 30 |

### Solution

**Step 1:**

The proportional relationship can be written as

$\frac{s}{r} = \frac{6}{10} = \frac{12}{20} = \frac{18}{30}... = \frac{3}{5}$

**Step 2:**

So, the equation representing this proportional relationship is $s = \frac{3}{5} \times \frac{r}{1} = \frac{3r}{5}$

or $s = \frac{3r}{5}$