5. 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 =
/3 ÷ 3 3/8 =

6. 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.

7. 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 =
Now add the numerators and put over common denominator.
( )/24 = 31/24
2. 2/3 + 5/8 = 31/24 or 1 7/24.

8. 3. 1 2/3 + 2 ¾ =
Add the whole numbers then add the fractions after getting common denominators.
LCD – 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 = 3 14/12 reduce
3 14/12 ÷ 2/2 = 3 7/6 simplify
3 7/6 = /6 = 4 1/6
/3 + 2 ¾ = 4 1/6 or 25/6.

9. 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.

10. 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.
/8 – 2 ¾ = 2 1/8 or 17/8.

11. /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.
/3 – 2 5/6 = 2 ½ or 5/2.

12. 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.

13. 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 = 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.

14. 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.

15. 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.

16. 11. 7/8 ÷ 5 =
First must convert all mixed numbers and whole numbers into improper fractions to multiply as two fractions.
5 = 5/ /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
11. 7/8 ÷ 5 = 7/40.

17. 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/ /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.
/3 ÷ 3 3/8 = 64/81.