Notes:
1  In this page, fractions are written with diagonal bars. For example 5/8 is the fraction whose numerator is 5 and denominator is 8.
11 1/4 is a mixed number meaning 11 + 1/4.
2  Do not use the calculator to solve the questions below.

Find fraction F with denominator less than 8 such that 2 / 8 + F = 1
Solution
Solve for F
F = 1  2 / 8
= 8 / 8  2 / 8 , common denominator
= 6 / 8 , subtract numerator
= 3 / 4 , reduce fraction

Find two fractions F1 and F2 with same denominator equal to 6 such that F1 + F2 = 1 and F1  F2 = 2/3
Solution
Let us write F1 + F2 and F1  F2 as follows
F1 + F2 = 1 = 6 / 6
F1  F2 = 2 / 3 = 4 / 6
F1 and F2 are fractions with denominator 6. Their numerator must add up to 6 and their difference is 4. Hence F1 and F2 are equal to
F1 = 5 / 6 and F2 = 1 / 6

Which fraction is equivalent to 16%?
Solution
16% is written as a fraction and reduced
16% = 16 / 100 = 4 / 25

Which fraction is equivalent to 300 / 1000
 3 / 100
 3 / 1000
 3 / 10

300 / 10
Solution
Reduce given fraction
300 / 1000 = 3 / 10 , divide numerator and denominator by 100.
300 / 1000 is equivalent to 3 / 10

1/2 + 1/5 + 1/6 =
Solution
The LCM of 2, 5 and 6 is first calculated
2 = 2
5 = 5
6 = 2 × 3
LCM = 2 × 5 × 3 = 30
We use the LCM as the lowest common denominator for all 3 fractions
1 / 2 + 1 / 5 + 1 / 6 = (1×15) / (2×15) + (1×6) / (5×6) + (1×5) / (6×5)
Simplify
= 15 / 30 + 6 / 30 + 5 / 30
Add and reduce
= 26 / 30 = 13 / 15

3 3/5 + 5 1/2 =
Solution
Add whole parts together and fractional parts together
3 3/5 + 5 1/2 = (3 + 5) + (3/5 + 1/2)
Common denominator for fractions 3/5 and 1/2
= 8 + (6/10 + 5/10) = 8 + 11/10
Change improper fraction 11/10 into mixed number and add
= 8 + 10/10 + 1/10 = 8 + 1 + 1/10 = 9 1/10

1/7 × 2 2/5 =
Solution
Change the mixed number 2 2/5 into fraction and multiply
1/7 × 2 2/5 = 1/7 × 12/5 = 12 / 35

1/12 × 0.2 =
Solution
Change decimal number 0.2 into fraction
0.2 = 2/10 = 1/5
Multipliply the two fractions
1/12 × 0.2 = 1/12 × 1/5 = 1 / 60

2/5 ÷ 6 =
.
Solution
Use division rule
2/5 ÷ 6 = 2/5 ÷ 6/1 = 2/5 × 1/6 = 2/30
Reduce fraction
= 1/15

9/7 + 2 =
.
Solution
Change 2 into fraction 2/1 and set common denominator.
9/7 + 2 = 9/7 + 2/1 = 9/7 + 14/7 = 23/7 = 3 2/7

2 1/3 + 4/2 =
.
Solution
Simplify 4/2 and add.
2 1/3 + 4/2 = 2 1/3 + 2 = 4 1/3

3 1/5 ÷ 5 =
Solution
Change mixed number 3 1/5 into frcation and rewrite 5 as fraction 5/1.
3 1/5 ÷ 5 = 16/5 ÷ 5/1 =
Apply rule of division of fractions and simplify.
= 16/5 × 1/5 = 16/25

1/2 + 4 1/3  3 2/5 =
Solution
Add/subtract whole parts and fractional parts separately.
1/2 + 4 1/3  3 2/5 = 4  3 + 1/2 + 1/3  2/5
Find LCM of 2, 3 and 5 .
2 = 2
3 = 3
5 = 5
LCM(2,3,5) = 2×3×5 = 30
Use LCM as common denominator.
= 1 + (15/30 + 10/30  12/30) = 1 + 13/30 = 1 13/30

5/2 ÷ 7/2  1/5 =
Solution
Order of operation division first
5 / 2 ÷ 7 / 2  1 / 5 = 5 / 2 × 2 / 7  1 / 5
Simplify
= 5 / 7  1 / 5
Common denominator and subtract
= 25 / 35  7 / 35 = 18 / 35

(0.2 + 1/5) × 2/7 =
Solution
Change decimal number 0.2 into fraction 1/5
(0.2 + 1/5) × 2/7 = (1/5 + 1/5) × 2/7
Use order of opeartions
= 2/5 × 2/7
= 4 / 35

(3 1/2 + 3/5) × 1/7 =
Solution
Change mixed number 3 1/2 into fraction
(3 1/2 + 3/5) × 1/7 = (7/2 + 3/5) × 1/7
Find common denominator to 7/2 and 3/5 and add
= (35/10 + 6/10) × 1/7 = 41/10 × 1/7
Multiply fractions
= 41 / 70

40/4000 =
 1%
 40%
 4%

10%
Solution
Reduce fraction so that its denominator is equal to 100
40/4000 = 1 / 100 = 1%

(1/2 + 2/3) ÷ 0.2 =
Solution
Add the fractions within the brackets and write 0.2 as a fraction 1/5
(1/2 + 2/3) ÷ 0.2 = (3/6 + 4/6) ÷ 1/5 = 7/6 ÷ 1/5
Use rule of division of fractions
= 7/6 × 5/1 = 35 / 6 = 5 5/6

Order from least to greatest: 3 4/7 , 3 3/5 , 3 1/2 , 3 11/20.
Solution
The given mixed numbers all have same whole parts but different fractions.
It is easier to compare fractions when they have common denominator. The common denominator of the fractional parts is the LCM of 7,5,2,and 20.
7 = 7
5 = 5
2 = 2
20 = 2^{2} × 5
LCM(7,5,2,20) = 7 × 5 × 2^{2} = 140
We now rewrite all mixed with fractional parts with same denominator
3 4/7 = 3 80/140
3 3/5 = 3 84/140
3 1/2 = 3 70/140
3 11/20 = 3 77/140
We now order mixed numbers from least to greatest
3 1/2 , 3 11/20 , 3 4/7 , 3 3/5

Order from least to greatest: 2 7/8 , 2.66 , 262% , 25/8.
Solution
We need to rewrite the given numbers in a single form. Let us write them in decimal form
2 7/8 = 2 + 7/8 = 2 + 0.875 = 2.875
2.66 = 2.66
262% = 262 / 100 = 2.62
25/8 = 24/8 + 1/8 = 3 + 0.125 = 3.125
We now use the decimal form of the given numbers to order them from least to greatest.
262% , 2.66 , 2 7/8 , 25/8
