Fractions Study Guide

What is a Fraction?

A fraction represents a part of a whole or a part of a group. It consists of two numbers separated by a line, where the number on top is called the numerator and the number on the bottom is called the denominator.

Types of Fractions

There are three main types of fractions:

Proper Fraction: A fraction in which the numerator is less than the denominator, such as 2/3.
Improper Fraction: A fraction in which the numerator is greater than or equal to the denominator, such as 5/4.
Mixed Number: A whole number combined with a fraction, such as 1 1/2.

Equivalent Fractions

Equivalent fractions are different fractions that represent the same value. They can be found by multiplying or dividing both the numerator and the denominator by the same non-zero number.

For example, 1/2, 2/4, and 3/6 are all equivalent fractions because they represent the same portion of a whole.

Adding and Subtracting Fractions

When adding or subtracting fractions with the same denominator, simply add or subtract the numerators and keep the denominator the same.

For example, 1/3 + 2/3 = 3/3 = 1 and 5/8 - 3/8 = 2/8 = 1/4.

Multiplying and Dividing Fractions

To multiply fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.

For example, 2/3 * 3/4 = 6/12 = 1/2.

To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

For example, 2/3 ÷ 4/5 = 2/3 * 5/4 = 10/12 = 5/6.

Comparing Fractions

To compare fractions, find a common denominator and then compare the numerators.

For example, to compare 2/5 and 3/8, you can convert both fractions to have a denominator of 40. Then, 2/5 becomes 16/40 and 3/8 becomes 15/40, so 2/5 > 3/8.

Practice Questions

Convert the improper fraction 7/3 to a mixed number.
Find three equivalent fractions for 1/4.
Add the fractions 3/5 and 1/10.
Multiply the fractions 2/3 and 3/4.
Compare the fractions 5/6 and 7/8.

◂Math Worksheets and Study Guides Fourth Grade. Fractions

Create And Print more Fractions worksheets with Comparing Fractions, Equivalent Fractions, and Simplifying Fractions

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Use models, benchmarks, and equivalent forms to judge the size of fractions.

Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Connections to the Grade 4 Focal Points (NCTM)

Number and Operations: Building on their work in grade 3, students extend their understanding of place value and ways of representing numbers to 100,000 in various contexts. They use estimation in determining the relative sizes of amounts or distances. Students develop understandings of strategies for multi-digit division by using models that represent division as the inverse of multiplication, as partitioning, or as successive subtraction. By working with decimals, students extend their ability to recognize equivalent fractions. Students' earlier work in grade 3 with models of fractions and multiplication and division facts supports their understanding of techniques for generating equivalent fractions and simplifying fractions.

Fractions Study Guide

What is a Fraction?

Types of Fractions

Equivalent Fractions

Adding and Subtracting Fractions

Multiplying and Dividing Fractions

Comparing Fractions

Practice Questions

[Fractions] Related Worksheets and Study Guides:

◂Math Worksheets and Study Guides Fourth Grade. Fractions

Create And Print more Fractions worksheets with Comparing Fractions, Equivalent Fractions, and Simplifying Fractions

The resources above cover the following skills: