Guidelines for Dividing and Multiplying Fractions in Word Problems

Introduction

When approaching word problems that involve fractions, it is essential to understand whether to multiply or divide based on the context and relationships between the quantities involved. This article provides guidelines on when to use multiplication or division to solve such problems effectively.

When to Multiply Fractions

Finding a part of a whole or scaling a quantity are common scenarios where multiplication is required.

Part of a Whole

When a word problem asks for a fractional part of a quantity, multiplication is used. The following example demonstrates this:

Find 1}{3}

of 2}{5}

1}{3} x 2}{5} 2}{15}

Scaling a Quantity

When you need to increase or decrease a quantity by a fraction, multiplication comes into play. Consider the following example:

A recipe calls for 1}{2}

cup of sugar. If you want to make 3}{4}

of the recipe, how much sugar do you need?

1}{2}

x 3}{4}

3}{8}

When to Divide Fractions

Dividing fractions is necessary in scenarios where you need to find how many times one quantity fits into another or when comparing ratios.

Quantity Fit

To determine how many times one fraction fits into another, division is used. The following example illustrates this:

How many 1}{4}

cups are in 3}{2}

cups?

3}{2}

/ 1}{4}

3}{2}

x 4}{1}

6

Comparing Ratios

When comparing the ratios of two fractions, division is also required. The following example demonstrates this:

Compare 2}{3}

to 1}{2}

2}{3}

/ 1}{2}

2}{3}

x 2}{1}

4}{3}

Conclusion and Steps for Problem Solving

Regardless of whether you need to multiply or divide fractions, it is crucial to understand the context of the problem. Here's a step-by-step approach to solving word problems involving fractions:

Translate the Problem: Convert the word problem into mathematical expressions and equations.

Formulate the Equation: Use the information provided to set up equations based on the relationships between the quantities.

Solve the Equation: Apply mathematical techniques, such as equation solving, to find the solution.

Let's consider an example to illustrate these steps:

Example Problem

Mary wants to feed 25 students pizza. Each student eats 2}{5}

of a pizza. Pizzas cost $7 for 2 pizzas but you can buy fractional amounts at the same rate. How much does Mary need to spend on the pizzas?

Step 1: Translate the Problem

Lets s be the number of students, p the number of pizzas, and m the cost in dollars.

s 25

p 2}{5}