# Solutions to Questions on Fractions and Percentages

The solutions, with detailed explanations, to fractions and percentages questions are presented.

## Solutions

1. Solution
1/3 of 300 is mathematically translated as
1/3 � 300
Simplify
= 300 / 3 = 100

2. Solution
"2/7 of x is equal to 6" is mathematically translated as
(2/7) � x = 6
Solve for x
2x = 42
x = 21

3. Solution
"15% of 45% of 1.4" is mathematically translated as
15%(45% � 1.4)
Simplify
= (15/100) � (45 / 100 � 1.4)
= (15 � 45 � 1.4) / 10,000
= 945 / 10,000
= 0.0945

4. Solution
"2/3 of 1/5 of 12,000" is mathematically translated as
(2/3)( 1/5 � 12,000) =
Simplify
(2/3)( 1/5 � 12,000) =
= (2/3)(12,000/5)
= (2/3)(2,400)
= 2 � 2,400 / 3
= 1,600

5. Solution
"x% of 23 is 9.2" is mathematically translated as
(x%) � (23) = 9.2
Solve for x
(x / 100) � 23 = 9.2
23 x = 9.2 � 100
x = 40

6. Solution
60% of the 10 algebra questions correct
60% * 10 = 6
80% of the 10 geometry questions correct
80% * 10 = 8
60% of the 5 trigonometry questions correct
60% * 5 = 3
Total number of questions correct
6 + 8 + 3 = 17
Percentage of correct questions that Peter got correct is
17 / 25 = 0.68 = 68%

7. Solution
"25% of y is x" is mathematically translated as
(25 / 100) y = x
Solve for y
25 y = 100 x
y = (100 x) / 25
y = 4x

8. Solution
Let x be the fraction to be subtracted. Hence
(1/2 + 4/5) - x = 1
Solve for x
x = (1/2 + 4/5) - 1
x = (5/10 + 8/10) - 10/10 = 3/10

9. Solution
One out of 5 may be written as a fraction equal to
1/5
and in percent as
20%
The total number of students in percent is 100%. Since 20% took math and 28% took science, the percent of those who took history is
100% - 20% - 28% = 52%

10. Solution
"one fifth of y + 1 is equal to 2" is mathematically translated as
(1/5)(y + 1) = 2
Multiply both sides by 5 and simplify
y + 1 = 10
Add 1 to each side of the above equation
y + 1 + 1 = 10 + 1
Simplify
y + 2 = 11