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


Addition of Mixed Fractions

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\(\frac{7}{24}\).

Addition of Mixed Fractions


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







4th Grade Math Activities

From Addition of Mixed 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. Calculating Profit Percent and Loss Percent | Profit and Loss Formulas

    Jun 12, 25 12:48 PM

    In calculating profit percent and loss percent we will learn about the basic concepts of profit and loss. We will recall facts and formula while calculating profit percent and loss percent. Now we wil

    Read More

  2. Word Problems on Profit and Loss Worksheet |Cost Price |Selling Price

    Jun 11, 25 04:26 PM

    Word Problems on Profit and Loss Worksheet
    In word problems on profit and loss worksheet you will get different types of problems on cost price and selling price, profit and loss, calculating profit o loss, calculating selling price and cost p…

    Read More

  3. Round off to Nearest 1000 |Rounding Numbers to Nearest Thousand| Rules

    Jun 11, 25 03:12 PM

    Round off to Nearest 1000
    Round off to nearest 1000 is discussed here. While rounding off to the nearest 1000, if the digit in the hundreds place is between 0 – 4 i.e., < 5, then the hundreds place is replaced by ‘0’. If the d…

    Read More

  4. Round off to Nearest 100 | Rounding Numbers To Nearest Hundred | Rules

    Jun 11, 25 03:13 AM

    Round off to Nearest 100
    While rounding off to the nearest hundred, if the digit in the tens place is between 0 – 4 i.e. < 5, then the tens place is replaced by ‘0’. If the digit in the units place is equal to or >5, then the…

    Read More

  5. Round off to Nearest 10 |How To Round off to Nearest 10?|Rounding Rule

    Jun 10, 25 05:36 PM

    Rounding to the Nearest 10
    Round off to nearest 10 is discussed here. Rounding can be done for every place-value of number. To round off a number to the nearest tens, we round off to the nearest multiple of ten. A large number…

    Read More