Addition and Subtraction of Fraction Using Like Denominators

Example 1: The table shows the favorite sports of 120 students for a sports quiz creation. What fraction of the students like football and baseball as their favorite games.

Each  = 6 students

Solution:

Interpret the above given table:

Baseball: 2 = 2 × 6 = 12 and  = 3

                12 + 3 = 15

Football: 4 = 4 × 6 = 24

Write the fraction of the students who likes football and baseball \( =\frac{\text{Number of students}}{\text{Total Students}} \)

Baseball \( =\frac{15}{120} \) and Football \( =\frac{24}{120} \)

Students like football and baseball as their favourite sports: 

\( \frac{15}{120}+\frac{24}{120} \)

= \( \frac{15+24}{120}=\frac{39}{120}\)

Hence, 39 students out of 120 like football and baseball as their favourite sports.

Example 2: Add the fractions \( \frac{1}{8}+\frac{1}{8} \) and write the answer using the number line.

Solution:

Draw the number line to represent addend.

Now the addend is \( \frac{1}{8} \). So, it means that we have to add one part out of 8. Because we’re adding one part, we’ll have to “jump” onwards one step from the maximum.

So, \( \frac{1}{8}+\frac{1}{8}=\frac{2}{8} \)

Example 3: Add the fractions \( \frac{1}{6}+\frac{1}{6} \) and write the answer using the fraction strips.

Solution:

Draw the fraction strip and add the numerator:

As shown in the above image, we have to simply add the numerator.

So, \( \frac{1}{6}+\frac{1}{6}=\frac{2}{6} \)

Example 4: Subtract \( \frac{2}{8}-\frac{1}{8} \) and write the answer.

Draw the number line to represent minuend.

Now the subtrahend is \( \frac{1}{8} \). So, it means that we have to subtract one part out of 8. Because we’re removing one part, we’ll have to “jump” backwards one steps from the minimum.

So, \( \frac{2}{8}-\frac{1}{8}=\frac{1}{8} \)

Example 5: Subtract the fractions \( \frac{3}{6}-\frac{1}{6} \) and write the answer using the fraction strips.

Solution:

Draw the fraction strip and subtract the numerator:

As shown in the above image, we have to simply subtract the numerator.

So, \( \frac{3}{6}-\frac{1}{6}=\frac{2}{6} \)

Example 6: Leo and his friends eat \( \frac{4}{9} \) slices of pizza. What fraction of its slice is left to eat?

Solution:

There is one whole pizza. So, we have to find \( 1-\frac{4}{9} \)

\( 1-\frac{4}{9}=\frac{9}{9}-\frac{4}{9} \)

\( =\frac{9-4}{9} \)    Subtract the numerator

\( =\frac{5}{9} \)

So, there are \( =\frac{5}{9} \) slices of pizza are left for them.

Example 7: An office meeting is 1 hour long. All the members arrived after 20 minutes and settled with their laptops in 10 minutes. What fraction of an hour is left for the meeting?

Solution:

The time spent in settlement = 20 + 10 = 30 minutes

We know that 30 minutes \( =\frac{1}{2} \)hour

So, time left for the meeting \( =1-\frac{1}{2} \)

\( =1-\frac{1}{2}=\frac{2}{2}-\frac{1}{2} \)

\( =\frac{2-1}{2} \)             Subtract the numerator

\( =\frac{1}{2} \)