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# Fraction Word Problems Study Guide

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Updated on Oct 3, 2011

## Introduction to Fraction Word Problems

—CARL SANDBURG (1878–1967)

This lesson will provide practice performing operations with fractions, as well as strategies that can be used when you are solving word problems with fractions.

If you look up the definition of the set of rational numbers, you may get a description like the one mentioned in the previous lesson. They are the set of numbers that can be expressed as , where b is not equal to zero, and a and b are both integers. This is just a complicated description of very familiar numbers known as fractions. Before embarking on our study of fractions and word problems involving fractions, let's review a few key concepts.

## Factors, Multiples, GCFs, and LCMs

### Factors

A Factor is a number that divides into another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

### Greatest Common Factor (GCF)

The Greatest Common Factor, or GCF, is the largest value that divides each of the terms without a remainder.

Example: Find the greatest common factor of 18 and 24.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
The factors 1, 2, 3, and 6 are common to both lists, but the greatest common factor is 6.

### Multiples

A Multiple is the result of multiplying a number by another whole number. For example, multiples of 4 are 4 × 1 = 4, 4 × 2 = 8, 4 × 3 = 12, and so on.

### Least Common Multiple (LCM)

The Least Common Multiple, or LCM, is the smallest value that each term divides into without leaving a remar.

Example: Find the least common multiple of 12 and 30.
Multiples of 12 are 12, 24, 36, 48, 60, 72 …
Multiples of 30 are 30, 60, 90 …
The smallest common number in each list is 60, so 60 is the least common multiple of 12 and 30.

#### Tip:

To help remember the difference between factors and multiples, think factors fit into a number, and you multiply to get multiples.

## Simplifying Fractions

We learn to simplify fractions in order to make them easier to use. If the numbers are smaller, they are usually less difficult to use.

To simplify a fraction, divide the numerator (top) and the denominator (bottom) by the greatest common factor. For example, take the fraction . The greatest common factor of the numerator and the denominator is 4. Divide each value by 4 to simplify the fraction to its lowest terms: .

An improper fraction has a numerator whose absolute value is greater than or equal to the absolute value of its denominator: is an improper fraction.

A mixed number is a number made up of a whole number part and a fraction part. The number is a mixed number.

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