Four Processes of Fractions

Addition

(Always obtain a common denominator before adding.)
1. 3/5 + 1/5 = 4/5 (Same denominator)
2. 5/8 + 1/8 = 6/8 = 3/4 (Same denominator, need to cancel/simplify)
3. 4/5 + 3/5 = 7/5 = 1 2/5 (Same denominator, need to change improper fraction to mixed number)
4. 3/8 + 1/4 = 3/8 + 2/8 = 5/8 (Different denominators, with one factor of the other)
5. 3/5 + 1/4 = 12/20 + 5/20 = 17/20 (Different denominators, one not factor of the other)
6. 1 1/2 + 1/4 = 1 2/4 + 1/4 = 1 3/4 (Mixed number plus a proper fraction)
7. 1 3/5 + 1 1/2 = 1 6/10 + 1 5/10 = 2 11/10 = 3 1/10 (Two mixed numbers, with sum a whole number and improper fraction)
8. 1 7/8 + 1 5/8 = 2 12/8 = 3 4/8 = 3 1/2 (Two mixed numbers, with sum a whole number and improper fraction, need to cancel/simplify)

Subraction

(Always obtain a common denominator before subtracting.)
1. 3/5 - 1/5 = 2/5 (Same denominator)
2. 5/8 - 1/8 = 4/8 = 1/2 (Same denominator, need to cancel/simplify)
3. 3/8 - 1/4 = 3/8 - 2/8 = 1/8 (Different denominators, with one factor of the other)
4. 3/5 - 1/4 = 12/20 - 5/20 = 7/20 (Different denominators, one not factor of the other)
5. 1 1/2 - 1/4 = 1 2/4 - 1/4 = 1 1/4 (Mixed number plus a proper fraction)
6. 1 7/8 - 1 5/8 = 2/8 = 1/4 (Two mixed numbers, need to cancel/simplify)
7. 2 1/4 - 1/2 = 2 1/4 - 2/4 = 1 5/4 - 2 /4 = 1 3/4 (Two mixed numbers, one denominator factor of the other, need to borrow)
8. 3 2/5 - 2 1/2 = 3 4/10 - 2 5/10 = 2 14/10 - 2 5/10 = 7/10 (Two mixed numbers, different denominators, need to borrow)

Multiplication

(In each example, multiply the final numerators and multiply the final denominators. However, cancel before equal sign, if possible.)
1. 3/4 x 1/4 = 3/16 (There is no cancelling/simplifying available.)
2. 3/5 x 1/2 = 3/10 (There is no cancelling/simplifying available.)
3. 2/5 x 3/4 = 3/10 (Divide numerator 2 and denominator 4 by 2.)
4. 1 1/2 x 3/4 = 3/2 x 3/4 = 9/8 = 1 1/8 (There is no cancelling/simplifying available. Change improper fraction to mixed number.)
5. 3 3/4 x 2 2/5 = 15/4 x 12/5 = 9 (Divide numerator 15 and denominator 5 by 5. Divide numerator 12 and denominator 4 by 4.)

Division

(Always change ÷ to x and invert the divisor fraction to its reciprocal before continuing to solve. In each example, multiply the final numerators and multiply the final denominators. However, cancel/simplify before equal sign, if possible.)
1. 3/4 ÷ 1/4 = 3/4 x 4/1 = 3 (Divide numerator 4 and denominator 4 by 4.)
2. 3/5 ÷ 1/2 = 3/5 x 2/1 = 6/5 = 1 1/5 (There is no cancelling/simplifying available. Change improper fraction to mixed number.)
3. 1 1/2 ÷ 3/4 = 3/2 x 4/3 = 2 (Change mixed number to improper fraction. Divide the numerator 3 and denominator 3 by 3. Divide numerator 4 and denominator 2 by 2.)
4. 3 3/4 ÷ 2 2/5 = 15/4 x 5/12 = 25/16 = 1 9/16 (Change mixed numbers to improper fractors. Divide numerator 15 and denominator 12 by 4. Change improper fraction to mixed number.)

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