Understanding Fractions

A fraction represents a part of a whole. The top number of a fraction is called the numerator, and it represents the part being considered. The bottom number is called the denominator and represents the total number of parts that make up the whole.

Adding Fractions

When adding fractions with the same denominator, you simply add the numerators together and keep the denominator the same. For example:

3/5 + 2/5 = (3 + 2)/5 = 5/5 = 1

When adding fractions with different denominators, you need to find a common denominator. To do this, you can find the least common multiple (LCM) of the denominators and then rewrite the fractions with the common denominator, before adding the numerators together. For example:

1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2

Subtracting Fractions

Subtracting fractions follows the same principles as adding fractions. When subtracting fractions with the same denominator, you simply subtract the numerators and keep the denominator the same. For example:

5/8 - 3/8 = (5 - 3)/8 = 2/8 = 1/4

When subtracting fractions with different denominators, you again need to find a common denominator before performing the subtraction. For example:

2/5 - 1/3 = 6/15 - 5/15 = 1/15

Practice Problems

Now let's practice with some problems:

What is 1/4 + 2/5?
What is 3/7 - 1/7?
What is 2/3 + 3/4?
What is 5/6 - 1/9?

Answers

1/4 + 2/5 = 13/20
3/7 - 1/7 = 2/7
2/3 + 3/4 = 17/12
5/6 - 1/9 = 43/54

Remember to always simplify your answers if possible by finding the greatest common divisor of the numerator and denominator and dividing both by it.

Practice makes perfect! Keep practicing to become a master at adding and subtracting fractions.

◂Math Worksheets and Study Guides Fifth Grade. Add/Subtract Fractions

Study Guide

Add/Subtract Fractions

Worksheet/Answer key

Add/Subtract Fractions

Worksheet/Answer key

Add/Subtract Fractions

Worksheet/Answer key

Add/Subtract 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.

Compute fluently and make reasonable estimates.

Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.

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.

Grade 5 Curriculum Focal Points (NCTM)

Number and Operations: Developing an understanding of and fluency with addition and subtraction of fractions and decimals

Students apply their understandings of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They apply their understandings of decimal models, place value, and properties to add and subtract decimals. They develop fluency with standard procedures for adding and subtracting fractions and decimals. They make reasonable estimates of fraction and decimal sums and differences. Students add and subtract fractions and decimals to solve problems, including problems involving measurement.

Connections to the Grade 5 Focal Points (NCTM)

Algebra: Students use patterns, models, and relationships as contexts for writing and solving simple equations and inequalities. They create graphs of simple equations. They explore prime and composite numbers and discover concepts related to the addition and subtraction of fractions as they use factors and multiples, including applications of common factors and common multiples. They develop an understanding of the order of operations and use it for all operations.