Here are the solutions and answers for each question:
Addition and Subtraction - Find the common denominator then add or subtract the numerator and retain the common denominator. Finally, simplify into its lowest terms.
1. 5/14 + 1/6
(3/3)(5/14) + (7/7)(1/6) = 15/42 + 7/42 = 22/42 = 11/21
2. 5/12 - 3/20
(5/5)(5/12) - (3/3)(3/20) = 25/60 - 9/60 = 16/60 = 4/15
3. 5/12 - 3/8
(2/2)(5/12) - (3/3)(3/8) = 10/24 -9/24 = 1/24
4. 1 3/10 + 1/4
1 3/10 = ((1x10) + 3)/10 = 13/10
(4/4)(13/10) +(10/10)(1/4) = 52/40 + 10/40 = 62/40 = 31/20
5. 2/3 + 6 1/5
6 1/5 = ((6x5)+1)/5 = 31/5
(5/5)(2/3) +(3/3)(31/5) = 10/15 + 93/15 = 103/15
6. 3 1/6 - 1/7
3 1/6 = ((3x6)+1)/6 =19/6
(7/7)(19/6) - (6/6)(1/7) = 133/42 - 6/42 = 127/42
7. 3/8 + 5/24
(3/3)(3/8) + (1/1)(5/24) = 9/24 + 5/24 = 14/24 = 7/12
8. 1/20 + 5/12
(3/3)(1/20) + (5/5)(5/12) = 3/60 + 25/60 = 28/60 = 7/15
9. 9/20 - 1/4
(1/1)(9/20) - (5/5)(1/4) = 9/20 - 5/20 = 4/20 = 1/5
10. 9/10 - 3/14
(7/7)(9/10) - (5/5)(3/14) = 63/70 - 15/70 = 48/70 = 24/35
11. 3 3/8 + 5/12
3 3/8 = ((3x8)+3)/8 = 27/8
(3/3)(27/8) + (2/2)(5/12) = 81/24 + 10/24 = 91/ 24
12. 5 7/10 - 5/18
5 7/10 = ((5x10)+7)/10 = 57/10
(9/9)(57/10) - (5/5)(5/18) = 513/90 - 25/90 = 488/90 = 244/45
Multiplication - simply multiply the numerator by the numerator of the other fraction and the denominator by the denominator of the other fraction
1. 1/2 x 5/8 = 5/16
2. 3/5 x 5/9 = 15/45 = 1/3
3. 3/8 x 2/5 = 6/40 = 3/20
4. 2 3/8 x 16
2 3/8 = ((2x8)+3)/8 = 19/8
19/8 x 16 = 304/8 = 38
5. 1 4/5 x 5/12
1 4/5 = ((1x5)+4)/5 = 9/5
9/4 x 5/12 = 45/48 = 15/16
6. 1 2/10 x 5
1 2/10 = ((1x10)+2)/10 = 12/10
12/10 x 5 = 60/10 = 6
Find each amount - Simply multiply the two given values.
1. 1/4 of 12 bottles of water = 3 bottles
1/4 x 12 = 12/4 = 3
2. 2/3 of 24 bananas = 16 bananas
2/3 x 24 = 48/3 = 16
3. 3/5 of $40 restaurant bill = $ 24
3/5 x 40 = 120/5 = 24
4. 5/6 of 18 pencils = 15 pencils
5/6 x 18 = 90/6 = 15
