How to Add and Subtract Fractions? (+FREE Worksheet!)

How to add and subtract fractions, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

• Step 1: Find equivalent fractions with the same denominator before you 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} })
• Step 2: Multiply two denominators (or as many as there are) to get a common denominator.
• Step 3: If one of the denominators was divisible by the other denominators, select the greater denominator as the common denominator.
• Step 4: The numerators are enlarged to fit the common denominator. In this case, the numerators of fractions are added together.
  (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} })

Adding and Subtracting Fractions For education statistics and research

Adding and Subtracting Fractions, 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})

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Adding and Subtracting Fractions, 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})

Adding and Subtracting Fractions, 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{4 – 3}{5}= frac{1}{5 })

Adding and Subtracting Fractions, 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{red}{b} } – frac{c}{ color{blue}{d} }=frac{a color{blue}{d} – c color{red}{b} }{ color{red}{b} color{blue}{d} })
(frac{2}{color{red}{3}}, frac{1}{color{blue}{2}}=frac{(2)( color{blue}{2} ), (1)( color{red}{3} )}{ color{red}{3} times color{blue}{2} }=frac{4 to 3}{6}=frac{1}{6})

Exercises for Adding and Subtracting Fractions

Adding and Subtracting Fractions

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}})

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