What is a fraction in mathematics? 
In this lecture, we are going to discuss addition and subtraction of fractions. 
Fractions are rational numbers with the form ab for every a,bQ, where Q is the set of rational number and a is called the numerator, b  the denominator. There are three types of fractions namely:
  1. Proper fraction
  2.  Improper fraction
  3. Mixed fraction 
Proper fractions are fractions whose denominator is greater than the numerator e.g 
27,13,713.

Improper fractions are fractions whose denominator is less than the numerator e.g 72,32,137.

Mixed fractions are fractions that consist of a whole number and a fraction e.g 312,725,189.
Mixed fractions can be converted to improper fraction by simply multiplying the whole number by the denominator and adding the result to the numerator. 

Example
  1.  312=3×2+12=72.
  2.  734=7×4+34=314
  3. 589=5×9+89=539

Addition and Subtraction of Mixed Fraction


In this post, I will be showing you two methods for solving questions that involves addition and subtraction of mixed fractions. 

  1.  Evaluate 223+112
Method
This method involves adding the whole numbers first before adding the fractions.
223+112
=2+1(23+12).
Whole number=2+1=3
To add the fraction, first find the LCM of the denominators 3 and 2 which is 6. The LCM is obtained by multiplying the denominators of both fractions since 3 cannot be divided by 2, therefore, LCM=3×2=6. Next divide each denominator by 6 and multiply by the numerator of each fraction.
3(23+12)=3(2×2)+(3×1)6
=34+36=376.

Method II
This method involves converting the mixed fractions to improper fraction.
223+112
223=2×3+23=83
112=1×2+12=32
Now add the converted fractions
83+32=16+96=256

  1. Evaluate 513278
Method I
Subtract the whole numbers before adding the fractions 
513278
=52(1378)
=31378
LCM=3×8=24
=3((8×1)(3×7)24)
=382124=31324
Convert the result to an improper fraction
=3×241324
=5924

Method II
Convert 513278 to improper fraction before subtracting the result.
513=5×3+13
=163
278=2×8+78
=238
Subtract the resulting fractions
=163238
=8×163×2324
=1286924=5924.

  1. Evaluate 158+12
Method I
Add the whole numbers and then the fractions.
1+0=(58+12)
=1(1×5)+(4×1)8
=15+48=198=178.

Method II
158+12
=1×8+58+12
=138+12
=1×13+4×18
=13+48=178