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Simplifying fractions guided notes

How do you simplify fractions? Step by step guide.

Examples of simplifying fraction

Problem : Simplify the fraction

45
63

Solution.

1. Factor the numerator and denominator.

45 = 
63
3 * 3 * 5
3 * 3 * 7

See 45 prime factorization.

See 63 prime factorization.

2. Find common factors to both the numerator and denominator.

The common factors are 3 and 3.

3. Cancel down all the common factors.

3 * 3 * 5 = 
3 * 3 * 7
 3 * 3  * 5 = 
 3 * 3  * 7
5
7

The problem is solved.

Problem 2: Simplify a fraction

5a5b7 + 25a21b7
25a5b7 + 125a21b7

Solution.

1. Factorise the numerator and denominator.

5a5b7 + 25a21b7 = 
25a5b7 + 125a21b7
5a5b7(1 + 5a16) = 
25a5b7(1 + 5a16)
5a5b7(1 + 5a16)
5 * 5a5b7(1 + 5a16)

2. Find common factors to both the numerator and denominator.

The common factors are 5a5b7 and (1 + 5a16).

3. Cancel down all the common factors.

5a5b7(1 + 5a16) = 
5 * 5a5b7(1 + 5a16)
 5a5b7  (1 + 5a16 = 
5 *  5a5b7  (1 + 5a16
1
5

The problem is solved.