Addition of Like Fractions

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

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

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

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

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


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

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 \(\frac{11}{105}\).

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

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

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


Questions and Answers 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\(\frac{7}{11}\) 






4th Grade Math Activities

From Addition of Like Fractions to HOME PAGE


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.



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.



Share this page: What’s this?

Recent Articles

  1. Measuring Capacity | Standard Unit of Capacity | Litre | Millilitres

    Nov 29, 23 01:15 AM

    2 Tablespoonful of Water
    We will discuss about measuring capacity. The milkman measures milk in liters. Petrol is given in liters. Mobil oil is sold in liters. Two milk bottles contain 1 liter of milk. One milk bottle

    Read More

  2. Addition and Subtraction of Units of Measurement | Metric Units

    Nov 29, 23 12:54 AM

    Addition of Lengths
    We can add the units of measurement like decimal numbers. 1. Add 5 m 9 dm and 11 m and 5 dm Solution: 5 m 9 dm = 5.9 m 11 m 5 dm = 11.5 m Hence, 5 m 9 dm + 11 m 5 dm = 17 m 4 dm or 17.4 m 2. Add 15 cm…

    Read More

  3. 1 to 10 Times Tables | 1 - 10 Times Table Chart |Multiplication Tables

    Nov 29, 23 12:50 AM

    1 to 10 Times Tables
    Memorizing 1 to 10 Times Tables are very important for mental math and quick calculations. Times Tables are used during multiplication and division. Let us learn all the times tables from 1 to 10 to i…

    Read More