Subscribe to our YouTube channel for the latest videos, updates, and tips.


Addition of Like Fractions

To add two or more like fractions we simplify add their numerators. The denominator remains same.

1. Let us find the sum of two fractions \(\frac{3}{7}\) and \(\frac{2}{7}\).

3 by 7

\(\frac{3}{7}\) is colored green.


2 by 7

\(\frac{2}{7}\) is colored yellow.


\(\frac{3}{7}\) + \(\frac{2}{7}\) is represented by 

5 by 7

\(\frac{3}{7}\) + \(\frac{2}{7}\)

= \(\frac{3 + 2}{7}\)

= \(\frac{5}{7}\) = \(\frac{\textrm{Sum of Numerators}}{\textrm{Common Denominator}}\)

Addition of Like Fractions Video

Subscribe to our YouTube channel for the latest videos, updates, and tips.


Addition of Fractions with the Same (Like) Denominator

2. Observe the following figures:

Adding Like Fractions

What do we observe?

In the first figure \(\frac{1}{4}\)of the circle is shaded and in the second figure \(\frac{2}{4}\) of the circle is shaded.

In all, we have Hence 3/4 of the circle is shaded.

\(\frac{1}{4}\) + \(\frac{2}{4}\) = \(\frac{1 + 2}{4}\) = \(\frac{3}{4}\)

Thus, to add the fractions with the same denominator, we simply add their numerators and write the common denominator.

Sum of the fractions with like denominators = \(\frac{\textrm{Sum of the Numerators}}{\textrm{Common Denominator}}\)


Solved Examples on Addition of Like Fractions:

1. Find the sum of \(\frac{1}{9}\) and \(\frac{4}{9}\).

Solution:

Sum of \(\frac{1}{9}\) and \(\frac{4}{9}\)

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

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

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


2. Find the sum of \(\frac{7}{27}\) and \(\frac{9}{27}\).

Solution:

Sum of \(\frac{7}{27}\) and \(\frac{9}{27}\)

= \(\frac{7}{27}\) + \(\frac{9}{27}\)

= \(\frac{7 + 9}{27}\)

= \(\frac{16}{27}\)


3. Find the sum of \(\frac{4}{29}\), \(\frac{5}{29}\) and \(\frac{8}{29}\).

Solution:

Sum of \(\frac{4}{29}\), \(\frac{5}{29}\) and \(\frac{8}{29}\).

= \(\frac{4}{29}\) + \(\frac{5}{29}\) + \(\frac{8}{29}\)

= \(\frac{4 + 5 + 8}{29}\)

= \(\frac{17}{29}\)


More Examples on Addition of Like Fractions:

(Fractions having same denominator)

4. Add \(\frac{5}{17}\) + \(\frac{4}{17}\)

Solution:

\(\frac{5}{17}\) + \(\frac{4}{17}\)

= \(\frac{5 + 4}{17}\)

= \(\frac{9}{17}\)  (in lowest terms)


5. Add \(\frac{3}{23}\) + \(\frac{13}{23}\) + \(\frac{4}{23}\)

Solution:

\(\frac{3}{23}\) + \(\frac{13}{23}\) + \(\frac{4}{23}\)

= \(\frac{3 + 13 + 4}{23}\)

= \(\frac{20}{23}\)  (in lowest terms)

Addition of Like Fractions

Addition of Three Like Fractions Video

Subscribe to our YouTube channel for the latest videos, updates, and tips.


6. Find the sum of \(\frac{31}{105}\), \(\frac{41}{105}\) and \(\frac{11}{105}\).

Solution:

Sum of \(\frac{31}{105}\), \(\frac{41}{105}\) and \(\frac{11}{105}\).

= \(\frac{31}{105}\) + \(\frac{41}{105}\) + \(\frac{11}{105}\).

= \(\frac{31 + 41 + 11}{105}\)

= \(\frac{83}{105}\)


7. Find the sum of \(\frac{3}{7}\) and \(\frac{2}{7}\)

Solution:

\(\frac{3}{7}\) + \(\frac{2}{7}\) = \(\frac{3 + 2}{7}\) = \(\frac{5}{7}\)


2. Find the sum of \(\frac{1}{15}\), \(\frac{4}{15}\), \(\frac{7}{15}\)

Solution:

\(\frac{1}{15}\) + \(\frac{4}{15}\) + \(\frac{7}{15}\) = \(\frac{1 + 4 + 7}{15}\) = \(\frac{12}{15}\)


Worksheet on Addition of Like Fractions:

1. Add the following Like Fractions:

(i) \(\frac{2}{5}\) + \(\frac{3}{5}\)

(ii) \(\frac{1}{8}\) + \(\frac{3}{8}\) + \(\frac{7}{8}\)

(iii) \(\frac{11}{23}\) + \(\frac{10}{23}\) + \(\frac{5}{23}\)

(iv) \(\frac{2}{10}\) + \(\frac{1}{10}\) + \(\frac{3}{10}\)

(v) \(\frac{5}{11}\) + \(\frac{7}{11}\) + \(\frac{4}{11}\) + \(\frac{2}{11}\)


Answer:

1. (i) 1

(ii) 1\(\frac{3}{8}\)

(iii) 1\(\frac{3}{23}\) 

(iv) \(\frac{3}{5}\) 

(v) 1\(\frac{7}{11}\) 


2. Find the sum:

(i) \(\frac{1}{9}\) + \(\frac{4}{9}\)

(ii) \(\frac{1}{4}\) + \(\frac{2}{4}\)

(iii) \(\frac{5}{21}\) + \(\frac{8}{21}\)

(iv) \(\frac{4}{15}\) + \(\frac{7}{15}\)

(v) \(\frac{7}{16}\) + \(\frac{8}{16}\)

(vi) \(\frac{13}{19}\) + \(\frac{2}{19}\)


Answer:

2. (i) \(\frac{5}{9}\)

(ii) \(\frac{3}{4}\)

(iii) \(\frac{13}{21}\)

(iv) \(\frac{11}{15}\)

(v) \(\frac{15}{16}\)

(vi) \(\frac{15}{19}\)


3. Using the figures, fill in the blanks:

(i)

Like Fraction Addition




     \(\frac{1}{8}\) + \(\frac{2}{8}\) = \(\frac{--- + ---}{8}\) = \(\frac{---}{8}\)

(ii)

Add 2 Like Fractions




     \(\frac{1}{5}\) + \(\frac{2}{5}\) = \(\frac{--- + ---}{5}\) = \(\frac{---}{5}\)

(iii)

Addition of 2 Like Fraction



     \(\frac{1}{8}\) + \(\frac{2}{8}\) + \(\frac{2}{8}\) = \(\frac{--- + --- + ---}{8}\) = \(\frac{---}{8}\)

(iv)



Addition of Two Like Fraction




     \(\frac{2}{7}\) + \(\frac{4}{7}\) = \(\frac{--- + ---}{7}\) = \(\frac{---}{7}\)

You might like these






4th Grade Math Activities

From Addition of Like Fractions to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Speed Distance and Time | Relation between Speed Distance and Time

    May 21, 25 12:58 PM

    Speed is defined as the distance covered per unit time. Speed = (Distance Travelled)/(Time Taken) Or, S = D/T. Speed also requires a unit of measurement. If the distance is in kilometres

    Read More

  2. Math Problem Answers | Solved Math Questions and Answers | Free Math

    May 21, 25 12:45 PM

    Partial fraction
    Math problem answers are solved here step-by-step to keep the explanation clear to the students. In Math-Only-Math you'll find abundant selection of all types of math questions for all the grades

    Read More

  3. Test of Divisibility | Divisibility Rules| Divisible by 2, 3, 5, 9, 10

    May 21, 25 10:29 AM

    The test of divisibility by a number ‘x’ is a short-cut method to detect whether a particular number ‘y’ is divisible by the number ‘x’ or not. Test of divisibility by 2: A number is divisible by 2

    Read More

  4. Divisible by 7 | Test of Divisibility by 7 |Rules of Divisibility by 7

    May 21, 25 10:17 AM

    Divisible by 7
    Divisible by 7 is discussed below: We need to double the last digit of the number and then subtract it from the remaining number. If the result is divisible by 7, then the original number will also be

    Read More

  5. Average Word Problems | Worksheet on Average Questions with Answers

    May 20, 25 05:40 PM

    In average word problems we will solve different types of problems on basic concept of average. 1. Richard scored 80, 53, 19, 77, 29 and 96 runs in 6 innings in a series. Find the average runs scored…

    Read More