OPERATIONS WITH FRACTIONS

Operations with Fractions : 

In this section, you will learn, how to do the four binary operations with fractions. 

(i) Addition

(ii) Subtraction

(iii) Multiplication

(iv) Division

Addition and Subtraction of Fractions with Same Denominator

If we add or subtract two or more fractions with the same denominator, we have to take the denominator once and simplify the values in numerator. 

Example : 

Find the value of : 

1/7 + 3/7 - 2/7

Solution : 

In all the above fractions, the denominator is same. 

So take the denominator once and simplify the values in numerator. 

1/7 + 3/7 - 2/7  =  (1 + 3 - 2) / 7

1/7 + 3/7 - 2/7  =  2/7

Addition and Subtraction of Fractions with Different Denominators

If we add or subtract two or more fractions with different denominators, we have to follow the steps given below. 

Step 1 : 

Find the least common multiple (LCM) of the denominators. 

Step 2 : 

Mae the result of step 1 (LCM) as denominator for each fraction using multiplication.

Step 3 : 

In step 2, all the fractions will have the same denominator. Now take the denominator once and simplify the values in numerator.  

Example : 

Find the value of : 

1/4 + 5/6 - 3/8

Solution : 

Find the least common multiple of the denominators.

LCM of (4, 6, 8)  =  24

Make the denominator of each fraction as 24 using multiplication. 

1/4  =  (1 ⋅ 6) / (4 ⋅ 6)  =  6/24

5/6  =  (5 ⋅ 4) / (6 ⋅ 4)  =  20/24

3/8  =  (3 ⋅ 3) / (8 ⋅ 3)  =  9/24

Then, we have

1/4 + 5/6 - 3/8  =  6/24 + 20/24 + 9/24

1/4 + 5/6 - 3/8  =  (6 + 20 + 9)/24

1/4 + 5/6 - 3/8  =  35/24

Multiply a Fraction by a Whole Number

To multiply a proper or improper fraction by a whole number, first, we have to multiply the whole number and numerator of the fraction, keeping the denominator same.

For example, 

2 ⋅ 3/5   =  (2 ⋅ 3)/5  =  6/5

3 ⋅  7/11  =  (3 ⋅ 7)/11  =  21/11

Multiply a Fraction by a Fraction

To multiply a proper or improper fraction by another proper or improper fraction, we have to multiply the numerators and denominators. 

For example, 

2/3 ⋅ 4/5   =  8/15

1/3 ⋅  7/11  =  7/33

Divide a Whole Number by a Fraction 

To divide a whole number by any fraction, multiply the whole number by the reciprocal of the fraction.

For example, 

6 ÷ 2/5  =  6 ⋅ 5/2

6 ÷ 2/5  =  (6 ⋅ 5)/2

6 ÷ 2/5  =  (3 ⋅ 5)/1

6 ÷ 2/5  =  15  

Divide a Fraction by a Whole Number

To divide a fraction by a whole number, we have to multiply the denominator of the fraction by the whole number and simplify, if possible. 

For example, 

2/5 ÷ 6  =  2/(5 ⋅ 6)

2/5 ÷ 6  =  1/(5 ⋅ 3)

2/5 ÷ 6  =  1/15

Divide a Fraction by a Fraction

To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction.

For example,

1/5 ÷ 3/7  =  1/5 ⋅ 7/3

1/5 ÷ 3/7  =  (1 ⋅ 7) / (5 ⋅ 3)

1/5 ÷ 3/7  =  7/15

After having gone through the stuff given above, we hope that the students would have understood, how to do the binary operations with fractions.  

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6