Adding and Subtracting Fractions
Adding and subtracting fractions is easy when the denominators are the same. Just add or subtract the numerators and keep the denominator. If the fractions are unlike, first find a common denominator.
Video Lesson
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Adding and Subtracting Like Fractions
- Like fractions have the same denominator.
- Add or subtract the numerators only, keep the denominator the same, then simplify if possible.
Adding and Subtracting Unlike Fractions
- Unlike fractions have different denominators.
- Make the denominators the same first, then add or subtract.
Types of Fractions
- Proper fractions: numerator is smaller than the denominator (e.g. )
- Improper fractions: numerator is greater than or equal to the denominator (e.g. )
- Mixed numbers: a whole number and a fraction together (e.g. )
Converting Between Improper and Mixed Fractions
- Improper → Mixed: divide the numerator by the denominator.
- Mixed → Improper: multiply the whole number by the denominator, then add the numerator.
Practice Questions
Test your understanding
Which of the following is a proper fraction?
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A proper fraction is worth less than one whole, so its numerator must be smaller than its denominator.
In , 3 is smaller than 4, so it is proper.
is top-heavy (improper), is exactly one whole, and is a mixed number worth more than 2.
Add and .
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9 is a multiple of 3, so use 9 as the common denominator.
Multiply the top and bottom of by 3: .
Now add the numerators only, keeping the denominator: (which is ).
Convert into an improper fraction.
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Three whole ones are worth fifths.
Add the 2 fifths that are already there: fifths.
So . The denominator stays as 5 because the pieces are still fifths.
Add and .
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The lowest common denominator of 6 and 4 is 12.
Multiply top and bottom of by 2 to get , and top and bottom of by 3 to get .
Now add the numerators only: (which is ).
Subtract from .
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The lowest common denominator of 12 and 9 is 36.
Multiply top and bottom of by 3 to get , and top and bottom of by 4 to get .
Now subtract the numerators only: , which is already in its simplest form.
Subtract from .
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Change both mixed numbers into improper fractions with the same denominator.
and .
Subtract: , and remainder 3, so the answer is .
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Interactive Activity
Practice adding and subtracting fractions algebraically
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Adding and Subtracting Fractions frequently asked questions
The questions students bump into most on this topic
Like fractions share the same denominator, so you can add or subtract their numerators directly. Unlike fractions have different denominators. Before you add or subtract unlike fractions, you must find a common denominator by using the lowest common multiple of the two denominators.
A proper fraction has a numerator smaller than its denominator, so its value is less than 1. An improper fraction has a numerator greater than or equal to its denominator, so its value is 1 or more. Improper fractions are often converted to mixed numbers for clarity.
List the multiples of each denominator separately. Then identify the smallest number that appears in both lists. This shared multiple becomes the new denominator. For example, the multiples of 6 are 6, 12, 18 and the multiples of 4 are 4, 8, 12, so the LCM is 12.
Fractions with different denominators represent parts of different sizes. You cannot add or subtract parts of different sizes directly. A common denominator converts both fractions into equal-sized parts so the numerators can be added or subtracted meaningfully.
Division is particularly useful for larger numbers where you cannot easily spot the largest whole number by inspection. For smaller numbers, you can split the fraction by finding the nearest multiple of the denominator. Both methods give the same result.
7/7 is an improper fraction because the numerator is equal to the denominator. A proper fraction requires the numerator to be smaller than the denominator. Since 7 equals 7, the fraction represents exactly one whole. Improper fractions have a numerator that is greater than or equal to the denominator.