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.

## You might like these

• ### Worksheet on Word Problems on Multiplication of Mixed Fractions | Frac

Practice the questions given in the worksheet on word problems on multiplication of mixed fractions. We know to solve the problems on multiplying mixed fractions first we need to convert them

• ### Word Problems on Division of Mixed Fractions | Dividing Fractions

We will discuss here how to solve the word problems on division of mixed fractions or division of mixed numbers. Let us consider some of the examples. 1. The product of two numbers is 18.

• ### Word Problems on Multiplication of Mixed Fractions | Multiplying Fract

We will discuss here how to solve the word problems on multiplication of mixed fractions or multiplication of mixed numbers. Let us consider some of the examples. 1. Aaron had 324 toys. He gave 1/3

• ### Dividing Fractions | How to Divide Fractions? | Divide Two Fractions

We will discuss here about dividing fractions by a whole number, by a fractional number or by another mixed fractional number. First let us recall how to find reciprocal of a fraction

• ### Reciprocal of a Fraction | Multiply the Reciprocal of the Divisor

Here we will learn Reciprocal of a fraction. What is 1/4 of 4? We know that 1/4 of 4 means 1/4 × 4, let us use the rule of repeated addition to find 1/4× 4. We can say that $$\frac{1}{4}$$ is the reciprocal of 4 or 4 is the reciprocal or multiplicative inverse of 1/4

• ### Multiplying Fractions | How to Multiply Fractions? |Multiply Fractions

To multiply two or more fractions, we multiply the numerators of given fractions to find the new numerator of the product and multiply the denominators to get the denominator of the product. To multiply a fraction by a whole number, we multiply the numerator of the fraction

• ### Subtraction of Unlike Fractions | Subtracting Fractions | Examples

To subtract unlike fractions, we first convert them into like fractions. In order to make a common denominator, we find LCM of all the different denominators of given fractions and then make them equivalent fractions with a common denominators.

• ### Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

• ### Subtraction of Fractions having the Same Denominator | Like Fractions

To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numerators of the fractions.

• ### Properties of Addition of Fractions |Commutative Property |Associative

The associative and commutative properties of natural numbers hold good in the case of fractions also.

• ### Addition of Unlike Fractions | Adding Fractions with Different Denomin

To add unlike fractions, we first convert them into like fractions. In order to make a common denominator we find the LCM of all different denominators of the given fractions and then make them equivalent fractions with a common denominator.

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

• ### Fractions in Descending Order |Arranging Fractions an Descending Order

We will discuss here how to arrange the fractions in descending order. Solved examples for arranging in descending order: 1. Arrange the following fractions 5/6, 7/10, 11/20 in descending order. First we find the L.C.M. of the denominators of the fractions to make the

• ### Fractions in Ascending Order | Arranging Fractions an Ascending Order

We will discuss here how to arrange the fractions in ascending order. Solved examples for arranging in ascending order: 1. Arrange the following fractions 5/6, 8/9, 2/3 in ascending order. First we find the L.C.M. of the denominators of the fractions to make the denominators

• ### Comparison of Unlike Fractions | Compare Unlike Fractions | Comparing

In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a number to convert them to like fractions. Let us consider some of the

• ### Comparison of Like Fractions | Comparing Fractions | Like Fractions

Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example $$\frac{7}{13}$$ > $$\frac{2}{13}$$ because 7 > 2. In comparison of like fractions here are some

• ### Changing Fractions|Fraction to Whole or Mixed Number|Improper Fraction

In changing fractions we will discuss how to change fractions from improper fraction to a whole or mixed number, from mixed number to an improper fraction, from whole number into an improper fraction. Changing an improper fraction to a whole number or mixed number:

• ### Comparison of Fractions having the same Numerator|Ordering of Fraction

In comparison of fractions having the same numerator the following rectangular figures having the same lengths are divided in different parts to show different denominators. 3/10 < 3/5 < 3/4 or 3/4 > 3/5 > 3/10 In the fractions having the same numerator, that fraction is

• ### Fraction in Lowest Terms |Reducing Fractions|Fraction in Simplest Form

There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1(one), then the fraction is said to be in its simple form or in lowest

• ### Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with respect to the whole shape in the figures from (i) to (viii) In; (i) Shaded

Related Concepts