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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Using the least common denominator (LCD)

Multiplying the two denominators always gives a common denominator, but it is not always the smallest one. The least common denominator is the smallest number both denominators divide into, and using it keeps the numbers small so there is less to simplify.

Example: 5/6 + 3/8

1. List multiples of 8 until one is also a multiple of 6: 8, 16, 24. The LCD is 24.
2. Rewrite each fraction: 5/6 = 20/24 (multiply top and bottom by 4) and 3/8 = 9/24 (multiply top and bottom by 3).
3. Add the numerators: 20/24 + 9/24 = 29/24.
4. Simplify: 29/24 = 1 5/24.

Compare a subtraction both ways. For 7/10 − 1/4, the LCD is 20, so 14/20 − 5/20 = 9/20. Multiplying the denominators gives 28/40 − 10/40 = 18/40, which still has to be reduced to 9/20. Both are correct, but the LCD gets there faster.

Adding and subtracting mixed numbers with different denominators

Change each mixed number to an improper fraction first, then follow the same steps.

Example: 3 1/4 − 1 2/3

1. Convert: 3 1/4 = 13/4 and 1 2/3 = 5/3.
2. The LCD of 4 and 3 is 12: 13/4 = 39/12 and 5/3 = 20/12.
3. Subtract: 39/12 − 20/12 = 19/12.
4. Write as a mixed number: 19/12 = 1 7/12.

Common mistake: adding straight across. 1/2 + 1/3 is not 2/5. With the LCD of 6, it is 3/6 + 2/6 = 5/6.

Frequently Asked Questions

What is the rule for adding and subtracting fractions?

The fractions must have the same denominator before you add or subtract. Then you add or subtract only the numerators and keep the denominator. For example, 3/8 + 1/8 = 4/8, which simplifies to 1/2. If the denominators are different, rewrite the fractions over a common denominator first. Never add or subtract the denominators themselves.

How do you subtract fractions with different denominators?

Find the least common denominator, rewrite each fraction with it, then subtract the numerators. For 5/6 − 1/4, the LCD is 12, so 5/6 becomes 10/12 and 1/4 becomes 3/12. Then 10/12 − 3/12 = 7/12. Always check if the answer can be simplified; 7/12 cannot, because 7 and 12 share no common factor.

What grade is adding and subtracting fractions?

Under the Common Core standards, students add and subtract fractions with the same denominator, including mixed numbers, in grade 4. Fractions with unlike denominators come in grade 5. Students keep using these skills in grades 6 and 7 with negative fractions, equations and word problems, so a solid start in elementary school pays off later.

How do you add and subtract fractions with whole numbers?

Write the whole number as a fraction with the same denominator. To find 3 − 2/5, rewrite 3 as 15/5, then 15/5 − 2/5 = 13/5, or 2 3/5. Adding is even simpler: 4 + 1/3 is just the mixed number 4 1/3. A quick check is to picture the whole number as that many pies, each cut into the same size slices.

How do you add and subtract fractions with mixed numbers?

Work with the whole numbers and the fractions separately, using a common denominator for the fractions. For 2 3/4 + 1 2/3, add 2 + 1 = 3 and 9/12 + 8/12 = 17/12 = 1 5/12, so the total is 4 5/12. When subtracting, regroup if needed: 5 1/4 − 2 1/2 becomes 4 5/4 − 2 2/4 = 2 3/4.

What is adding and subtracting similar and dissimilar fractions?

Similar fractions share the same denominator, like 2/7 and 3/7, so you combine the numerators right away: 2/7 + 3/7 = 5/7. Dissimilar fractions have different denominators, like 1/2 and 1/5, so you first rewrite them over a common denominator: 5/10 + 2/10 = 7/10. The extra step for dissimilar fractions is the only difference.