To solve a subtraction of like fractions (with the same denominator), we have to use the same denominator and subtract the numerators. On the other hand, we can subtract unlike fractions (with different denominators) by finding their least common denominator. Then we find equivalent fractions with that denominator and subtract their numerators.
Here, we will look at 10 examples with answers of subtraction of like and unlike fractions. In addition, you will be able to test your skills with some practice problems.
How to subtract fractions?
The process applied to subtract fractions depends on whether the fractions are like fractions (same denominator) or unlike fractions (different denominator).
If the fractions are like, we simply use a single denominator and subtract the numerators of the fractions.
If we have a subtraction of unlike fractions, we can follow the following steps:
Step 1: Calculate the least common denominator (LCD) of the fractions.
Step 2: Divide the LCD by the denominator of each fraction.
Step 3: Multiply both the numerator and the denominator by the result of step 2. With this, we will obtain like fractions, where the LCD is the denominator.
Step 4: Subtract the like fractions obtained from step 3. For this, we use a single denominator and subtract the numerators.
Step 5: Simplify the resulting fraction if possible.
10 Subtracting fractions examples with answers
Each of the following examples has its respective solution. These examples include subtracting like fractions and unlike fractions.
EXAMPLE 1
What is the result of $latex \frac{4}{5}-\frac{2}{5}$?
Solution
We have a subtraction of like fractions because the denominators are the same.
Therefore, we can solve the subtraction by combining the denominators:
$$\frac{4}{5}-\frac{2}{5}$$
$$=\frac{4-2}{5}$$
Subtracting the numerators, we have:
$$=\frac{4-2}{5}$$
$$=\frac{2}{5}$$
EXAMPLE 2
Solve the subtraction of fractions $latex \frac{5}{7}-\frac{3}{7}$.
Solution
The fractions are like since both denominators are equal to 7.
To solve this subtraction, we use a single denominator as follows:
$$\frac{5}{7}-\frac{3}{7}$$
$$=\frac{5-3}{7}$$
Solving the subtraction of numerators, we have:
$$=\frac{2}{7}$$
$$=\frac{2}{7}$$
EXAMPLE 3
Solve the subtraction of fractions $latex \frac{4}{5}-\frac{2}{5}-\frac{1}{5}$.
Solution
We have a subtraction of three like fractions because all three denominators are equal to 5.
We can solve the subtraction by combining the fractions in a single denominator:
$$\frac{4}{5}-\frac{2}{5}-\frac{1}{5}$$
$$=\frac{4-2-1}{5}$$
Subtracting the numerators, we have:
$$=\frac{4-2-1}{5}$$
$$=\frac{1}{5}$$
EXAMPLE 4
Find the result of the subtraction of fractions $latex \frac{15}{9}-\frac{4}{9}-\frac{7}{9}$.
Solution
We have a subtraction of three like fractions because all three fractions have a denominator equal to 9.
Using a single denominator to write the fractions, we have:
$$\frac{15}{9}-\frac{4}{9}-\frac{7}{9}$$
$$=\frac{15-4-7}{9}$$
Solving the subtraction in the numerators, we have:
$$=\frac{15-4-7}{9}$$
$$=\frac{4}{9}$$
EXAMPLE 5
Solve the subtraction of fractions $latex \frac{2}{3}-\frac{1}{4}$.
Solution
Here, we have a subtraction of unlike fractions because their denominators are different.
To solve this subtraction, we have to start by finding the least common denominator (LCD). The denominators are 3 and 4 and the LCD is 12.
Dividing 12 by 3 (first denominator), we get 4. Dividing 12 by 4 (second denominator), we get 3. Now, we multiply the numerator and denominator of each fraction by these numbers:
$$\frac{2\times 4}{3 \times 4}-\frac{1 \times 3}{4 \times 3}$$
$$=\frac{8}{12}-\frac{3}{12}$$
To solve the subtraction, we combine the denominators and subtract the numerators:
$$\frac{8}{12}-\frac{3}{12}$$
$$=\frac{8-3}{12}$$
$$=\frac{5}{12}$$
EXAMPLE 6
Find the result of the subtraction $latex \frac{3}{4}-\frac{2}{5}$.
Solution
Since we have unlike fractions, we have to find the least common denominator. In this case, the LCD of 4 and 5 is 20.
Dividing 20 by 4 (first denominator), we get 5. Dividing 20 by 5 (second denominator), we get 4. Now, we multiply the numerators and denominators of each fraction by these numbers:
$$\frac{3\times 5}{4 \times 5}-\frac{2 \times 4}{5 \times 4}$$
$$=\frac{15}{20}-\frac{8}{20}$$
Solving the subtraction of like fractions, we have:
$$\frac{15}{20}-\frac{8}{20}$$
$$=\frac{15-8}{20}$$
$$=\frac{7}{20}$$
EXAMPLE 7
Solve the subtraction $latex \frac{5}{3}-\frac{1}{4}-\frac{1}{2}$.
Solution
The denominators are different, so we have unlike fractions. Therefore, we have to find the LCD. The LCD of 3, 4, and 2 is 12.
Dividing 12 by 3 (first denominator), we get 4. Dividing 12 by 4 (second denominator), we get 3. Dividing 12 by 2 (third denominator), we get 6.
Now, we multiply the numerator and denominator of each fraction by the numbers found:
$$\frac{5\times 4}{3 \times 4}-\frac{1 \times 3}{4 \times 3}-\frac{1 \times 6}{2 \times 6}$$
$$=\frac{20}{12}-\frac{3}{12}-\frac{6}{12}$$
We solve the subtraction of like fractions as follows:
$$\frac{20}{12}-\frac{3}{12}-\frac{6}{12}$$
$$=\frac{20-3-6}{12}$$
$$=\frac{11}{12}$$
EXAMPLE 8
Solve the subtraction of fractions $latex \frac{7}{5}+\frac{3}{4}+\frac{1}{2}$.
Solution
The fractions have different denominators, so they are unlike fractions. The LCD of these fractions is 20.
Dividing 20 by 5 (first denominator), we get 4. Dividing 20 by 4 (second denominator), we get 5. Dividing 20 by 2 (third denominator), we get 10.
Multiplying both the denominator and the numerator of each fraction by the numbers found, we have:
$$\frac{7\times 4}{5 \times 4}-\frac{3 \times 5}{4 \times 5}-\frac{1 \times 10}{2 \times 10}$$
$$=\frac{28}{20}-\frac{15}{20}-\frac{10}{20}$$
Now, we solve the subtraction as follows:
$$\frac{28}{20}-\frac{15}{20}-\frac{10}{20}$$
$$=\frac{28-15-10}{20}$$
$$=\frac{3}{20}$$
EXAMPLE 9
Solve the subtraction of fractions $latex \frac{2}{3}-\frac{1}{3}+\frac{5}{7}-\frac{3}{7}$.
Solution
The first two fractions have a denominator equal to 3, and the last two fractions have a denominator equal to 7. Then, the LCD of the fractions is 21.
Dividing 21 by 3 (first two denominators), we get 7. Dividing 21 by 7 (last two denominators), we get 3.
Multiplying the numerator and denominator of each fraction by the numbers found, we have:
$$\frac{2\times 7}{3 \times 7}-\frac{1 \times 7}{3 \times 7}+\frac{5 \times 3}{7 \times 3}-\frac{3 \times 3}{7 \times 3}$$
$$=\frac{14}{21}-\frac{7}{21}+\frac{15}{21}-\frac{9}{21}$$
Subtracting the like fractions, we have:
$$\frac{14}{21}-\frac{7}{21}+\frac{15}{21}-\frac{9}{21}$$
$$=\frac{14-7+15-9}{21}$$
$$=\frac{13}{21}$$
EXAMPLE 10
Solve the subtraction of fractions $latex \frac{3}{4}-\frac{2}{3}+\frac{4}{5}-\frac{1}{2}$.
Solution
We have denominators 4, 3, 5, and 2. Then, the LCD of these fractions is 60.
Dividing 60 by 4 (first denominator), we get 15. Dividing 60 by 3 (second denominator), we get 20. Dividing 60 by 5 (third denominator), we get 12. Dividing 60 by 2, we get 30.
We multiply both the numerator and the denominator of each fraction by the numbers found:
$$\frac{3\times 15}{4 \times 15}-\frac{2 \times 20}{3 \times 20}+\frac{4 \times 12}{5 \times 12}-\frac{1 \times 30}{2 \times 30}$$
$$=\frac{45}{60}-\frac{40}{60}+\frac{48}{60}-\frac{30}{60}$$
We subtract the like fractions as follows:
$$\frac{45}{60}-\frac{40}{60}+\frac{48}{60}-\frac{30}{60}$$
$$=\frac{45-40+48-30}{60}$$
$$=\frac{23}{60}$$
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5 Subtracting fractions practice problems
Solve the following practice problems to test your knowledge about the subtraction of fractions.
See also
Interested in learning more about subtracting fractions? You can take a look at these pages:
Jefferson Huera Guzman
Jefferson is the lead author and administrator of Neurochispas.com. The interactive Mathematics and Physics content that I have created has helped many students.
