Title: Addition and subtraction of fractions.

Objective :

At the end of this lesson, you will be able to solve addition and subtraction of fractions.

What you should know :

To fully understand this lesson, you should be familiar with

• Types of fractions - Mixed, Improper, and Proper fractions.
• Converting mixed fractions to improper fractions: a^b/_c = ^{(a x c + b)}/ _{c ,}
• e.g. 3¹/₄ = ^{(3 x 4 + 1)}/₄ = ¹³ /_4.
• Finding the LCM of two or more numbers.
• Knowing which mathematical operator to solve first before another.

Introduction :

Solving fractions is the most basic arithmetic operation and knowing which arithmetic operator to solve first before another is important.

Presentation / Steps:

Giving the following fractions to solve:

1. ¹/₂ - ²/₃
2. ² /₃ + ¹/₄
3. 9¹/₃ + 5³/₄ - 6¹/₂

The following steps will be used :

Soln 1:

=> Find the LCM of the denominators of the fractions, 2 and 3 which is 6.

=> Use 6 to divide the first fraction denominator and multiply the result by the numerator, do the same for the second fraction.

=> 1st: 6÷2 = 3, 3*1 = 3;

=> 2nd: 6÷3 = 2, 2*1 = 2.

=> Arithmetic operation with the above results: 3 - 2 =1.

=> Therefore, the result will be, 1 over the LCM 6 = ¹/₆

Soln 2:

=> Find the LCM of the fractions denominators 3 and 4 which is 12.

=> Use 12 to divide the first fraction denominator and multiply the result by the numerator, do the same for the second fraction.

=> 1st: 12÷3 = 4, 4 * 2 = 8; 2nd: 12÷4 = 3, 3 * 1= 3.

=> Arithmetic operation with the above results: 8 + 3 = 11.

=> Therefore, the result will be, 11 over the LCM 12 = ¹¹/₁₂

Soln 3:

=> Change all the mixed fractions to improper fractions.

=> 9¹/₃ = ²⁸ /₃

=> 5³/₄ = ²³ /₄

=> 6¹/₂ = ¹³/₂

=> Find the LCM of all the fractions denominators 3, 4, and 2, which is 12.

=> Use 12 to divide the first fraction denominator and multiply the result by 28, do the same for the second, and third fractions.

1. 12 ÷ 3 = 4, 4 * 28 = 112.
2. 12 ÷ 4 = 3, 3 * 23 = 69.
3. 12 ÷ 2 = 6, 6 * 13 = 78

=> Arithmetic operation with the above results, 112 + 69 - 78 = 103.

=> Therefore, the result will be, 103 over the LCM 12 = ¹⁰³/_12.

=> You can further divide your result to make it a mixed fraction, 8⁷/₁₂

Summary / Conclusion

=> The above steps are recommended for internal examinations where all steps matter.

=> The numerator is a number on top while the denominator is a number under a fraction divisor line, ^Numerator / _{Denominator .}

=> If your final answer is an improper fraction, divide it further to make it a mixed fraction.

Exercise : 2³/₄ - ⁴/₅