We will learn how to solve addition of mixed fractions or addition of mixed numbers. There are two methods to add the mixed fractions.

For example, add 2$$\frac{3}{5}$$ and 1$$\frac{3}{10}$$.

We can use the two methods to add the mixed numbers.

Method 1:

 2$$\frac{3}{5}$$ + 1$$\frac{3}{10}$$ = (2 + 1) + $$\frac{3}{5}$$ + $$\frac{3}{10}$$  = 3 + $$\frac{3}{5}$$ + $$\frac{3}{10}$$ = 3 + $$\frac{3 × 2}{5 × 2}$$ + $$\frac{3 × 1}{10 × 1}$$, [L.C.M. of 5 and 10 = 10] = 3 + $$\frac{6}{10}$$ + $$\frac{3}{10}$$= 3 + $$\frac{6 + 3}{10}$$  = 3 + $$\frac{9}{10}$$ = 3$$\frac{9}{10}$$ Step I: We add the whole numbers, separately. Step II: To add fractions, we take L.C.M. of the denominators and change the fractions into like fractions. Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Method 2:

 2$$\frac{3}{5}$$ + 1$$\frac{3}{10}$$ = (5 × 2) + $$\frac{3}{5}$$ + (10 × 1) + $$\frac{3}{10}$$ = $$\frac{13}{5}$$ + $$\frac{13}{10}$$ = $$\frac{13 × 2}{5 × 2}$$ + $$\frac{13 × 1}{10 × 1}$$, [L.C.M. of 5 and 10 = 10] = $$\frac{26}{10}$$ + $$\frac{13}{10}$$ = $$\frac{26 + 13}{10}$$ = $$\frac{39}{10}$$ = 3$$\frac{9}{10}$$ Step I: We change the mixed fractions into improper fractions. Step II: We take L.C.M. of the denominators and change the fractions into like fractions. Step III: We add the like fractions and express the sum to its simplest form.

Now let us consider some of the examples on addition of mixed numbers using Method 1.

1. Add 1$$\frac{1}{6}$$ , 2$$\frac{1}{8}$$ and 3$$\frac{1}{4}$$

Solution:

1$$\frac{1}{6}$$ + 2$$\frac{1}{8}$$ + 3$$\frac{1}{4}$$

Let us add whole numbers and fraction parts separately.

= (1 + 2 + 3) + ($$\frac{1}{6}$$ + $$\frac{1}{8}$$ + $$\frac{1}{4}$$)

= 6 + ($$\frac{1}{6}$$ + $$\frac{1}{8}$$ + $$\frac{1}{4}$$)

= 6 + $$\frac{1 × 4}{6 × 4}$$ + $$\frac{1 × 3}{8 × 3}$$ + $$\frac{1 × 6}{4 × 6}$$; [Since, the L.C.M. of 6, 8 and 4 = 24]

= 6 + $$\frac{4}{24}$$ + $$\frac{3}{24}$$ + $$\frac{6}{24}$$

= 6 + $$\frac{4 + 3 + 6}{24}$$

= 6 + $$\frac{13}{24}$$

= 6$$\frac{13}{24}$$

2. Add 5$$\frac{1}{9}$$, 2$$\frac{1}{12}$$ and $$\frac{3}{4}$$.

Solution:

5$$\frac{1}{9}$$ + 2$$\frac{1}{12}$$ + $$\frac{3}{4}$$

Let us add whole numbers and fraction parts separately.

= (5 + 2 + 0) + ($$\frac{1}{9}$$ + $$\frac{1}{12}$$ + $$\frac{3}{4}$$)

= 7 + $$\frac{1}{9}$$ + $$\frac{1}{12}$$ + $$\frac{3}{4}$$

= 7 + $$\frac{1 × 4}{9 × 4}$$ + $$\frac{1 × 3}{12 × 3}$$ + $$\frac{3 × 9}{4 × 9}$$, [Since the L.C.M. of 9, 12 and 4 = 36]

= 7 + $$\frac{4}{36}$$ + $$\frac{3}{36}$$ + $$\frac{27}{36}$$

= 7 + $$\frac{4 + 3 + 27}{36}$$

= 7 + $$\frac{34}{36}$$

= 7 + $$\frac{17}{18}$$,

= 7$$\frac{17}{18}$$.

3. Add $$\frac{5}{6}$$, 2$$\frac{1}{2}$$ and 3$$\frac{1}{4}$$

Solution:

$$\frac{5}{6}$$ + 2$$\frac{1}{2}$$ + 3$$\frac{1}{4}$$

Let us add whole numbers and fraction parts separately.

= (0 + 2 + 3) + $$\frac{5}{6}$$ + $$\frac{1}{2}$$ + $$\frac{1}{4}$$

= 5 + $$\frac{5}{6}$$ + $$\frac{1}{2}$$ + $$\frac{1}{4}$$

= 5 + $$\frac{5 × 2}{6 × 2}$$ + $$\frac{1 × 6}{2 × 6}$$ + $$\frac{1 × 3}{4 × 3}$$, [Since, the L.C.M. of 6, 2 and 4 = 12]

= 5 + $$\frac{10}{12}$$ + $$\frac{6}{12}$$ + $$\frac{3}{12}$$

= 5 + $$\frac{10 + 6 + 3}{12}$$

= 5 + $$\frac{19}{12}$$; [Here, fraction $$\frac{19}{12}$$ can write as mixed number.]

= 5 + 1$$\frac{7}{12}$$

= 5 + 1 + $$\frac{7}{12}$$

= 6$$\frac{7}{12}$$

4. Add 3$$\frac{5}{8}$$ and 2$$\frac{2}{3}$$.

Solution:

Let us add whole numbers and fraction parts separately.

3$$\frac{5}{8}$$ + 2$$\frac{2}{3}$$

= (3 + 2) + ($$\frac{5}{8}$$ + $$\frac{2}{3}$$)

5 + ($$\frac{5}{8}$$ + $$\frac{2}{3}$$)

L.C.M. of denominator 8 and 3 = 24.

= 5 + $$\frac{5 × 3}{8 × 3}$$ + $$\frac{2 × 8}{3 × 8}$$, (Since, L.C.M. of 8 and 3 = 24)

= 5 + $$\frac{15}{24}$$ + $$\frac{16}{24}$$

= 5 + $$\frac{15 + 16}{24}$$

= 5 + $$\frac{31}{24}$$

= 5 + 1$$\frac{7}{24}$$.

= 6$$\frac{7}{24}$$.

Now let us consider some of the examples on addition of mixed numbers using Method 2.

1. Add 2$$\frac{3}{9}$$, 1$$\frac{1}{6}$$ and 2$$\frac{2}{3}$$

Solution:

2$$\frac{3}{9}$$ + 1$$\frac{1}{6}$$ + 2$$\frac{2}{3}$$

= $$\frac{(9 × 2) + 3}{9}$$ + $$\frac{(6 × 1) + 1}{6}$$ + $$\frac{(3 × 2) + 2}{3}$$

= $$\frac{21}{9}$$ + $$\frac{7}{6}$$ + $$\frac{8}{3}$$, (L.C.M. of 9, 6 and 3 = 18)

= $$\frac{21 × 2}{9 × 2}$$ + $$\frac{7 × 3}{6 × 3}$$ + $$\frac{8 × 6}{3 × 6}$$

= $$\frac{42}{18}$$ + $$\frac{21}{18}$$ + $$\frac{48}{18}$$

= $$\frac{42 + 21 + 48}{18}$$

= $$\frac{111}{18}$$

= $$\frac{37}{6}$$

= 6$$\frac{1}{6}$$

2. Add2$$\frac{1}{2}$$, 3$$\frac{1}{3}$$ and 4$$\frac{1}{4}$$.

Solution:

2$$\frac{1}{2}$$ + 3$$\frac{1}{3}$$ + 4$$\frac{1}{4}$$

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

= $$\frac{5}{2}$$ + $$\frac{10}{3}$$ + $$\frac{17}{4}$$, (L.C.M. of 2, 3 and 4 = 12)

$$\frac{5 × 6}{2 × 6}$$ + $$\frac{10 × 4}{3 × 4}$$ + $$\frac{17 × 3}{4 × 3}$$, (Since, L.C.M. of 2, 3 and 4 = 12)

= $$\frac{30}{12}$$ + $$\frac{40}{12}$$ + $$\frac{51}{12}$$

= $$\frac{30 + 40 + 51}{12}$$

= $$\frac{121}{12}$$

= 10$$\frac{1}{12}$$

3. Add 3$$\frac{5}{8}$$ and 2$$\frac{2}{3}$$.

Solution:

3$$\frac{5}{8}$$ + 2$$\frac{2}{3}$$

Let us convert the mixed fractions into improper fractions.

= $$\frac{(8 × 3) + 5}{8}$$ + $$\frac{(3 × 2) + 2}{3}$$

= $$\frac{29}{8}$$ + $$\frac{8}{3}$$,

L.C.M. of denominator 8 and 3 = 24.

$$\frac{29 × 3}{8 × 3}$$ + $$\frac{8 × 8}{3 × 8}$$, (Since, L.C.M. of 8 and 3 = 24)

= $$\frac{87}{24}$$ + $$\frac{64}{24}$$

= $$\frac{87 + 64}{24}$$

= $$\frac{151}{24}$$

= 6$$\frac{7}{24}$$.

Word Problem on Addition of Mixed Fraction:

The doctor advises every child to drink 3$$\frac{1}{2}$$ litres of water in morning, 4$$\frac{1}{4}$$ litres in the after noon and $$\frac{1}{2}$$ litre before going to bed. How much water should a child drink every day?

Solution:

3$$\frac{1}{2}$$ + 4$$\frac{1}{4}$$ + $$\frac{1}{2}$$

Let us add whole numbers and fraction parts separately.

= (3 + 4 + 0) + ($$\frac{1}{2}$$ + $$\frac{1}{4}$$ + $$\frac{1}{2}$$)

7 + ($$\frac{1}{2}$$ + $$\frac{1}{4}$$ + $$\frac{1}{2}$$)

L.C.M. of denominators 2, 4 and 2 = 4.

= 7 + $$\frac{1 × 2}{2 × 2}$$ + $$\frac{1 × 1}{4 × 1}$$ + $$\frac{1 × 2}{2 × 2}$$, [Since, the L.C.M. of 2, 4 and 2 = 4.]

= 7 + $$\frac{2}{4}$$ + $$\frac{1}{4}$$ + $$\frac{2}{4}$$

= 7 + $$\frac{2 + 1 + 2}{4}$$

= 7 + $$\frac{5}{4}$$

[Here, the fraction $$\frac{5}{4}$$ can write as mixed number.]

= 7 + 1$$\frac{1}{4}$$

= 8$$\frac{1}{4}$$

Therefore, 8$$\frac{1}{4}$$ litres of water should a child drink every day.

Related Concepts

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.

## Recent Articles

1. ### 2nd Grade Place Value | Definition | Explanation | Examples |Worksheet

Sep 14, 24 04:31 PM

The value of a digit in a given number depends on its place or position in the number. This value is called its place value.

2. ### Three Digit Numbers | What is Spike Abacus? | Abacus for Kids|3 Digits

Sep 14, 24 03:39 PM

Three digit numbers are from 100 to 999. We know that there are nine one-digit numbers, i.e., 1, 2, 3, 4, 5, 6, 7, 8 and 9. There are 90 two digit numbers i.e., from 10 to 99. One digit numbers are ma

3. ### Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 14, 24 02:12 PM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…

4. ### Comparison of Three-digit Numbers | Arrange 3-digit Numbers |Questions

Sep 13, 24 02:48 AM

What are the rules for the comparison of three-digit numbers? (i) The numbers having less than three digits are always smaller than the numbers having three digits as: