Adding and Subtracting Fractions

Adding and Subtracting Fractions

Learn how to add and subtract Fractions in few easy steps.

Step by step guide for Adding and Subtracting Fractions

  • For “like” fractions (fractions with the same denominator), add or subtract the numerators and write the answer over the common denominator.
  • Find equivalent fractions with the same denominator before you can add or subtract fractions with different denominators.
  • Adding and Subtracting with the same denominator:
    \(\frac{a}{\color{blue}{b}} \ + \ \frac{c}{ \color{ blue }{b} } = \frac{a \ + \ c}{ \color{ blue }{b} }\) , \(\frac{a}{ \color{ blue }{b} } \ – \ \frac{c}{ \color{ blue }{b} } =\frac{a \ – \ c}{ \color{ blue }{b} }\)
  • Adding and Subtracting fractions with different denominators:
    \(\frac{a}{ \color{red}{b} } \ + \ \frac{c}{ \color{blue}{d} } = \frac{a \color{blue}{d} \ + \ \color{red}{b} c}{ \color{red}{b} \color{blue}{d} }\) , \(\frac{a}{ \color{red}{b} } \ – \ \frac{c}{ \color{blue}{d} }=\frac{a \color{blue}{d} \ – \ c \color{red}{b} }{ \color{red}{b} \color{blue}{d} }\)

Example 1:

Subtract fractions. \( \frac{4}{6} \ – \ \frac{3}{6} = \)

Solution:

For “like” fractions, subtract the numerators and write the answer over the common denominator. then: \(\frac{4}{6} \ – \ \frac{3}{6}=\frac{4 \ – \ 3}{6}=\frac{1}{6}\)

Example 2:

Add fractions. \(\frac{3}{7} \ + \ \frac{2}{3}=\)

Solution:

For “unlike” fractions, find equivalent fractions with the same denominator before you can add or subtract fractions with different denominators. Use this formula: \(\frac{a}{\color{red}{b}} \ – \ \frac {c}{\color{blue}{d}}=\frac{a \color{blue}{d} \ – \ c \color{red}{b} }{ \color{red}{b} \color{blue}{d} }\)
\(\frac{3}{\color{red}{7}} \ + \ \frac{2}{\color{blue}{3}}=\frac{(3)( \color{blue}{3} ) \ + \ (2)( \color{red}{7} )}{ \color{red}{7} \ \times \ \color{blue}{3} }=\frac{9 \ + \ 14}{21}=\frac{23}{21}\)

Example 3:

Subtract fractions. \(\frac{4}{5} \ – \ \frac{3}{5}=\)

Solution:

For “like” fractions, subtract the numerators and write the answer over the common denominator. then: \(\frac{4}{5}-\frac{3}{5}=\frac{1}{5 }\)

Example 4:

Subtract fractions. \(\frac{2}{3} \ – \ \frac{1}{2}=\)

Solution:

For “unlike” fractions, find equivalent fractions with the same denominator before you can add or subtract fractions with different denominators. Use this formula: \( \frac{a \color{blue}{d} \ – \ c \color{red}{b} }{ \color{red}{b} \color{blue}{d} }\)
\(\frac{2}{3}-\frac{1}{2}=\frac{(2)(2) – (1)(3)}{3 × 2}=\frac{4-3}{6}=\frac{1}{6 }\)

Exercises

Add fractions and Subtract fractions.

  1. \(\color{blue}{\frac{2}{3}+\frac{1}{2}}\)
  2. \(\color{blue}{\frac{3}{5}+\frac{1}{3}}\)
  3. \(\color{blue}{\frac{5}{6}+\frac{1}{2}}\)
  4. \(\color{blue}{\frac{4}{5}-\frac{2}{5}}\)
  5. \(\color{blue}{\frac{3}{5}-\frac{2}{7}}\)
  6. \(\color{blue}{\frac{1}{2}-\frac{1}{3}}\)

Download Adding and Subtracting Fractions Worksheet

  1. \(\color{blue}{\frac{7}{6}}\)
  2. \(\color{blue}{\frac{14}{15}}\)
  3. \(\color{blue}{\frac{4}{3}}\)
  4. \(\color{blue}{\frac{2}{5}}\)
  5. \(\color{blue}{\frac{11}{35}}\)
  6. \(\color{blue}{\frac{1}{6}}\)

Related to "Adding and Subtracting Fractions"

Top 10 SSAT Upper Level Math Practice Questions
Top 10 SSAT Upper Level Math Practice Questions
TABE Math FREE Sample Practice Questions
TABE Math FREE Sample Practice Questions
Grade 4 MEAP Math Worksheets
Grade 4 MEAP Math Worksheets
FREE Grade 6 PARCC Math Practice Test
FREE Grade 6 PARCC Math Practice Test
FREE AFOQT Math Practice Test
FREE AFOQT Math Practice Test
Pre-Algebra Practice Test Questions
Pre-Algebra Practice Test Questions
Top 10 Pre-Algebra Practice Questions
Top 10 Pre-Algebra Practice Questions
ATI TEAS 6 Math FREE Sample Practice Questions
ATI TEAS 6 Math FREE Sample Practice Questions
Grade 5 STAAR Math Worksheets
Grade 5 STAAR Math Worksheets
FREE SAT Math Practice Test
FREE SAT Math Practice Test

Leave a Reply

Your email address will not be published. Required fields are marked *

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…