Subtraction of Mixed Fractions

We will learn how to solve subtraction of mixed fractions or subtraction of mixed numbers.

There are two methods to subtract the mixed fractions.


1. Subtract 3\(\frac{1}{12}\) from 3\(\frac{1}{12}\).

Solution:

Method I.

6\(\frac{1}{3}\) – 3\(\frac{1}{12}\)

= (6 - 3) + (\(\frac{1}{3}\) – \(\frac{1}{12}\))

= 3 + (\(\frac{1}{3}\) – \(\frac{1}{12}\))

= 3 + (\(\frac{1 × 4}{3 × 4}\) – \(\frac{1 × 1}{12 × 1}\))

(L.C.M. of 12 and 3 = 12)

= 3 + \(\frac{4}{12}\) – \(\frac{1}{12}\)

= 3 + \(\frac{4 - 1}{12}\)

= 3 + \(\frac{3}{13}\)

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

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

Step I: Subtract the whole numbers.


Step II: To subtract the fractions we convert them into like fractions.


Step III: Add the differences of whole numbers and like fractions.


Method II:

6\(\frac{1}{3}\) – 3\(\frac{1}{12}\)

= \(\frac{(6 × 3) + 1}{3}\) + \(\frac{(3 × 12) + 1}{12}\)

= \(\frac{19}{3}\) – \(\frac{37}{12}\)

= \(\frac{19 × 4}{3 × 4}\) – \(\frac{37 × 1}{12 × 1}\),

(L.C.M. of 3 and 12 = 12)

= \(\frac{76}{12}\) – \(\frac{37}{12}\)

= \(\frac{76 - 37}{12}\)

= \(\frac{39}{12}\)

= \(\frac{13}{4}\)

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

Step I: Change the mixed numbers into improper fractions.


Step II: Make the fractions like fraction to have a common denominator.


Step III: Subtract and express the fraction in the simplest form.


2. Subtract 1\(\frac{5}{12}\) from 3\(\frac{3}{8}\)

Solution:

We first convert the mixed numbers into improper fractions.

1\(\frac{5}{12}\) = \(\frac{1  × 12 + 5}{12}\) = \(\frac{17}{12}\)

3\(\frac{3}{8}\) = \(\frac{3  × 8 + 3}{8}\) = \(\frac{27}{8}\)

Now, \(\frac{27}{8}\) - \(\frac{17}{12}\) = \(\frac{27 × 3}{8 × 3}\) - \(\frac{17 × 2}{12 × 2}\)

LCM of 8 and 12 is 24

\(\frac{81}{24}\) - \(\frac{34}{24}\) = \(\frac{81 - 34}{24}\)

            = \(\frac{47}{24}\)

            = 1\(\frac{23}{24}\)

Hence, 3\(\frac{3}{8}\) - 1\(\frac{5}{12}\) = 1\(\frac{23}{24}\)

Subtraction of Mixed Fractions


Word Problems on Subtraction of Mixed Fractions:

3. Ron used 3\(\frac{1}{4}\) litres of paint from a tin of 5\(\frac{1}{2}\) l, to color the walls of his room. What fraction of paint is still left in the tin?

Answer: \(\frac{9}{4}\) litres


4. Sam has a cloth of length 16 m. He took 13\(\frac{1}{4}\) m of cloth from it to make curtains for the house. How much cloth is still left with him for further use?

Answer: 2\(\frac{3}{4}\) m


5. Ten years ago a forest was spread up to a distance of 33 km. Due to forest fires and industrial set up now it is spread upto a distance of 16\(\frac{1}{5}\) km. What fraction of forest has been destroyed in the last 10 years? What measures can be taken to protect these forests?

Answer: 16\(\frac{4}{5}\) km


6. A drum full of rice weighs 84\(\frac{1}{2}\) kg. If the weight of empty drum is 12\(\frac{1}{6}\) kg, find the weight of the rice.

Answers: 72\(\frac{1}{3}\) kg

● Related Concepts







4th Grade Math Activities

From Subtraction 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

RSS

  1. Multiplication Table | Learn Tables from 0 – 25 | Multiplication Table

    Jan 14, 25 11:53 PM

    multiplication table
    In math multiplication table we will learn the tables from 0 – 25. These multiplication tables help the students to learn the essential multiplication facts. Multiplication tables are very important f…

    Read More

  2. 3rd Grade Math Worksheets |3rd Grade Math Sheets|3rd Grade Math Lesson

    Jan 14, 25 11:02 PM

    3rd Grade Math Worksheets
    3rd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students. Teachers and parents can also follow the worksheets to guide the students.

    Read More

  3. 3rd Grade Subtraction Worksheet | 3-Digit Subtraction Worksheets | Ans

    Jan 14, 25 01:57 PM

    Fill in the Missing Numbers Subtraction and Addition
    In 3th Grade Addition Worksheet we will solve how to subtract 3-digit numbers by expansion, subtraction of 3-digit numbers without regrouping, subtraction of 3-digit numbers with regrouping, propertie…

    Read More

  4. Facts about Subtraction | Subtraction of Small Numbers|Solved Examples

    Jan 14, 25 12:29 AM

    The operation to finding the difference between two numbers is called subtraction. Let us know some facts about subtraction which will help us to learn subtraction of large numbers. 1. Subtraction wit…

    Read More

  5. Word Problems on Subtraction |Worksheet on Subtraction Word Problems |

    Jan 14, 25 12:21 AM

    Subtraction Problem
    In word problems on subtraction we need to read the question carefully and understand what we need to find out. We know, in subtraction the larger number from which we subtract the other number (the s…

    Read More