- 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

# Simplifying a Ratio of Whole Numbers: Problem Type 1

A **ratio** is in its **simplest form** when both sides are whole numbers and there is no whole number that both sides can be divided by. Consider ratios of whole numbers for example, 6:4. It can be written as the fraction $\frac{6}{4}$. To write a ratio in its simplest form, keep dividing both sides by the same number until you cannot go any further without going into decimals.

Alternatively, to simplify a ratio of whole numbers, we simplify the corresponding fraction of the whole numbers. We write the prime factors of both the whole numbers and then cancel out the highest common factor from both the numerator and the denominator of the fraction. For the ratio 6:4, $\frac{6}{4} = \frac{6}{2} \div \frac{4}{2} = \frac{3}{2}$ The fraction can be written back into ratio form as 3:2. So the ratio of whole numbers 6:4 when simplified is 3:2

Simplify the ratio 42:54

### Solution

**Step 1:**

The ratio $42:54 = \frac{42}{54}$

**Step 2:**

HCF of 42 and 54 is 6

Simplifying

$\frac{\left ( \frac{42}{6} \right )}{\left ( \frac{54}{6} \right )} = \frac{7}{9} \space or \space 7:9$

**Step 3:**

So, the simplified ratio of 42:54 is 7:9

Simplify the ratio 33:21

### Solution

**Step 1:**

The ratio $33:21 = \frac{33}{21}$

**Step 2:**

HCF of 33 and 21 is 3

Simplifying

$\frac{\left ( \frac{33}{3} \right )}{\left ( \frac{21}{3} \right )} = \frac{11}{7} \space or \space 11:7$

**Step 3:**

So, the simplified ratio of 33:21 is 11:7