Subtracting fractions may seem confusing at first, but with basic multiplication and division, you're ready to solve simple subtraction problems. If both fractions have a numerator that is smaller than the denominator (known as a reasonable fraction), make sure the denominators are the same before you subtract the two numerators. If you have a mixed number and an integer, convert the whole number to an improper fraction (a fraction with a larger numerator than the denominator). You also need to make sure both denominators are the same before subtracting the numerator.
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Method 1 of 2: Finding Least Common Multiple and Subtracting Fraction
Step 1. Record the multiples of each denominator if necessary
If the denominators of the two fractions are different, you need to equate them first. Write down the multiples of each denominator so you can find the same number (least common multiple). For example, if you have a problem 1/4 - 1/5, record all the multiples of 4 and 5 until you find the number 20 in both lists of multiples.
- Since multiples of 4 include 4, 8, 12, 16, and 20, and multiples of 5 include 5, 10, 15, and 20, 20 is the lowest multiple that 4 and 5.
- If the denominators of both fractions are the same, you can immediately subtract both numerators.
Step 2. Multiply the numerator and denominator to equal the denominator of both fractions
After finding the least common multiple for the two different fractions, multiply the fractions so that the denominator is the multiple.
For example, multiply 1/4 by 5 to get a fraction's denominator to 20. You'll also need to multiply the numerator by 5 so 1/4 becomes 5/20
Step 3. Make equivalent fractions for all the fractions in the problem
Keep in mind that if you adjust one fraction in a problem, you will also need to change the other fractions so that each fraction is equivalent.
For example, if you change 1/4 to 5/20, multiply 1/5 by 4 to get 4/20. Now, the problem of subtracting 1/4 - 1/5 turns into 5/20 - 4/20
Step 4. Subtract the numerator and leave the denominators of both fractions the same
If you got two fractions with the same denominator from the start or have already created equivalent fractions with a common denominator, subtract both numerators. Write down the answer and include the denominator below it.
- Remember not to subtract the denominator.
- For example, 5/20 - 4/20 = 1/20.
Step 5. Simplify your answer
After getting the answer, find out if it can still be simplified. Find the greatest common factor of the answer's numerator and denominator, and divide both by the number of factors. For example, if you get 24/32 as a result of subtraction, the greatest common factor of 24 and 32 is 8. Divide both numbers by 8 so you get a simplification of 3/4.
You may not be able to simplify fractions, depending on the answer you get. For example, the fraction 1/20 cannot be simplified any further
Method 2 of 2: Subtracting Mixed Numbers
Step 1. Convert mixed numbers to improper fractions
A mixed number is an integer that has a fraction. To make subtraction easier, convert existing integers to fractions. This means that the numerator of the fraction will be greater than the denominator.
For example, subtracting 2 3/4 - 1 1/7 can be changed to 11/4 - 8/7
Step 2. Equate the denominators if necessary
Find the least common multiple of the two fractions' denominators so you can get the same denominator. For example, if you want to subtract 11/4 by 8/7, record all the multiples of 4 and 7 until you find the number 28 from both lists.
Since multiples of 4 include 4, 8, 12, 16, 20, 24, and 28, and multiples of 7 include 7, 14, 21, and 28, 28 is the least common multiple of the two numbers
Step 3. Create equivalent fractions if you need to change the denominator
You need to convert the denominator to its least common multiple. To convert it, multiply the whole fraction.
For example, to change the denominator of the fraction 11/4 to 28, multiply the fraction by 7. Now that fraction is 77/28
Step 4. Adjust all the fractions in the problem so that they are equivalent
If you've changed the denominator of one of the fractions in the problem, you'll also need to change the other fractions so that the ratio is equivalent to the original subtraction problem.
For example, if you've changed 11/4 to 77/28, multiply 8/7 by 4 to get 32/28. Now, the problem of subtracting 11/4 - 8/7 turns into 77/28 - 32/28
Step 5. Subtract the numerator and make sure the denominator remains the same
If both fractions had the same denominator from the start or you've already created equivalent fractions with a common denominator, you can now subtract both numerators. Write the answer and place it above the denominator. Make sure you don't subtract both denominators.
For example, 77/28 - 32/28 = 45/28
Step 6. Simplify the answer
You may need to convert your answer to a mixed number or fraction. Divide the numerator by the denominator to get an integer. After that, write down the difference (remaining number) between the numerator and the result of multiplying the integer with the denominator. The difference will act as the numerator. Place the numerator above the common denominator. Simplify fractions if you can.
