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\(\frac{23}{24}\)
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
You might like these
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
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.
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
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
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
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
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.
In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.
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.
The associative and commutative properties of natural numbers hold good in the case of fractions also.
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.
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
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
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
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
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:
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
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
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
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.
Share this page:
What’s this?
|
|
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.