Examples: 3/5 + 4/5 = 2/3 + 5/8 = 1 2/3 + 2 ¾ = 5/7 – 1/3 = 4 7/8 – 2 ¾ = 5 1/3 – 2 5/6 = 4 x 6/7 = 2/3 x 9/16 = 1 2/3 x 3 4/5 = 4/5 ÷ 6/7 = 7/8 ÷ 5 = 12. 2 2/3 ÷ 3 3/8 =

Examples: 3/5 + 4/5 = Since denominators are the same, just add numerators and put over the common denominator. (3 + 4)/5 = 7/5 simplified. 3/5 + 4/5 = 7/5 or 1 2/5.

2/3 + 5/8 = Find the LCD – 24. Multiply each fraction by 1 to get an equivalent fraction with common denominators. 2/3 x 8/8 = 16/24 5/8 x 3/3 = 15/24 2. 16/24 + 15/24 = Now add the numerators and put over common denominator. (16 + 15)/24 = 31/24 2. 2/3 + 5/8 = 31/24 or 1 7/24.

3. 1 2/3 + 2 ¾ = Add the whole numbers then add the fractions after getting common denominators. LCD – 12. . Multiply each fraction by 1 to get an equivalent fraction with common denominators. 1 + 2 = 3 2/3 x 4/4 = 8/12 ¾ x 3/3 = 6/12 1 8/12 + 2 6/12 = 3 14/12 reduce 3 14/12 ÷ 2/2 = 3 7/6 simplify 3 7/6 = 3 + 1 1/6 = 4 1/6 3. 1 2/3 + 2 ¾ = 4 1/6 or 25/6.

5/7 – 1/3 = Find the LCD – 21. Multiply each fraction by 1 to get an equivalent fraction with common denominators. 5/7 x 3/3 = 15/21 1/3 x 7/7 = 7/21 4. 15/21 – 7/21 = Now subtract the numerators and put over common denominator. (15-7)/21 = 8/21 simplified. 4. 5/7 – 1/3 = 8/21.

5. 4 7/8 – 2 ¾ = Find the LCD – 8. Multiply each fraction by 1 to get an equivalent fraction with common denominators. 7/8 x 1/1 = 7/8 ¾ x 2/2 = 6/8 4 7/8 – 2 6/8 = Subtract the numerators of the fractions then subtract the whole numbers. No borrowing needed on this problem. (7-6)/8 = 1/8 4 – 2 = 2 4 7/8 – 2 6/8 = 2 1/8 simplified. 5. 4 7/8 – 2 ¾ = 2 1/8 or 17/8.

6. 5 1/3 – 2 5/6 = Find the LCD – 6. Multiply each fraction by 1 to get an equivalent fraction with common denominators. 1/3 x 2/2 = 2/6 5/6 x 1/1 = 5/6 5 2/6 – 2 5/6 = Must borrow from the whole number since 5 is bigger than 2. 2/6 + 6/6 = 8/6 5 – 1 = 4 4 8/6 – 2 5/6 = Now subtract the fractions then the whole numbers. (8 – 5)/6 = 3/6 simplify 3/6 = ½ 4 – 2 = 2 thus answer is 2 ½. 6. 5 1/3 – 2 5/6 = 2 ½ or 5/2.

4 x 6/7 = Must change whole number into a fraction. 4/1 x 6/7 = Now multiply the numerators together then multiply the denominators together and simplify if possible. 4 x 6 = 24 1 x 7 = 7 Fraction = 24/7 The fraction is in simplest form. 7. 4 x 6/7 = 24/7 or 3 3/7.

8. 2/3 x 9/16 = Simply multiply the numerators together then multiply the denominators together and simplify if possible. 2 x 9 = 18 3 x 16 = 48 Fraction = 18/48 Fraction is not in simplest form: GCF of 6 will go into both the numerator and denominator. 18/48 ÷ 6/6 = 3/8 simplified. Cross Cancelling is very helpful to make simplifying the fraction easier. 2 and 16 are divisible by 2. 3 and 9 are divisible by 3. 2/3 x 9/16 = 1/1 x 3/8 = 3/8. 8. 2/3 x 9/16 = 3/8.

9. 1 2/3 x 3 4/5 = First must convert all mixed numbers into improper fractions to multiply as two fractions. 1 2/3 = [(1 x 3) + 2 ]/ 3 = 5/3 3 4/5 = [(3 x 5) + 4]/5 = 19/5 9. 5/3 x 19/5 = Simply multiply the numerators together then multiply the denominators together and simplify if possible. 5 x 19 = 95 3 x 5 = 15 Fraction 95/15 Fraction is not in simplest form: GCF of 5 will go into both the numerator and denominator. 95/15 ÷ 5/5 = 19/3 simplified. Cross Cancelling is very helpful to make simplifying the fraction easier. 5 and 5 are divisible by 5. 5/3 x 19/5 = 1/3 x 19/1 = 19/3. 9. 1 2/3 x 3 4/5 = 19/3 or 6 1/3.

4/5 ÷ 6/7 = Cannot divide fractions. Rule: Keep-change-flip. (First fraction stays the same, change division to multiplication, then flip (reciprocal) the second fraction.)Then multiply the fractions. 4/5 x 7/6 = Simply multiply the numerators together then multiply the denominators together and simplify if possible. 4 x 7 = 28 5 x 6 = 30 Fraction 28/30. Fraction is not in simplest form: GCF of 5 will go into both the numerator and denominator. 28/30 ÷ 2/2 = 14/15 simplified. Cross Cancelling: 2/7 x 5/3 = 14/15. 10. 4/5 ÷ 7/6 = 14/15.

11. 7/8 ÷ 5 = First must convert all mixed numbers and whole numbers into improper fractions to multiply as two fractions. 5 = 5/1 11. 7/8 ÷ 5/1 = Cannot divide fractions. Rule: Keep-change-flip. (First fraction stays the same, change division to multiplication, then flip (reciprocal) the second fraction.)Then multiply the fractions. 7/8 x 1/5 = Simply multiply the numerators together then multiply the denominators together and simplify if possible. 7 x 1 = 7 8 x 5 = 40 7/40 11. 7/8 ÷ 5 = 7/40.

2 2/3 ÷ 3 3/8 = First must convert all mixed numbers and whole numbers into improper fractions to multiply as two fractions. 2 2/3 = 8/3 3 3/8 = 27/8 8/3 ÷ 27/8 = Cannot divide fractions. Rule: Keep-change-flip. (First fraction stays the same, change division to multiplication, then flip (reciprocal) the second fraction.)Then multiply the fractions. 8/3 x 8/27 = 64/81 simplified. 12. 2 2/3 ÷ 3 3/8 = 64/81.