Percentage
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PSAT Math › Percentage
Write as a fraction: 22%
4/9
2/3
4/7
11/50
11/100
Explanation
22% = 22/100
Divide everything by 2:
22/100 = 11/50
11 is a prime number, so this is as reduced as this fraction can get.
Three hens each lay 20 eggs for a farmer. Two-fifths of the first hen's eggs are brown. One-fourth of the second hen's eggs are brown. Seven-tenths of the third hen's eggs are white. What percentage of all the eggs are brown?
Explanation
The first hen lays 8 brown eggs: 2/5 * 20 = 8
The second lays 5 brown eggs: 1/4 * 20 = 5
The third lays 6 brown eggs: 3/10 * 20 = 6
Add up the brown eggs and divide by 60, the total number of eggs:
19/60 = 0.31666667 = 31.67%, or 32%.
Write as a fraction: 22%
4/9
2/3
4/7
11/50
11/100
Explanation
22% = 22/100
Divide everything by 2:
22/100 = 11/50
11 is a prime number, so this is as reduced as this fraction can get.
Write 7.5% as a fraction.
Explanation
First convert the percentage to a decimal:
7.5% = .075
Then turn this into a fraction:
.075 = 75/1000
Simplify by dividing the numerator and denominator by 25:
75/1000 = 3/40
Three hens each lay 20 eggs for a farmer. Two-fifths of the first hen's eggs are brown. One-fourth of the second hen's eggs are brown. Seven-tenths of the third hen's eggs are white. What percentage of all the eggs are brown?
Explanation
The first hen lays 8 brown eggs: 2/5 * 20 = 8
The second lays 5 brown eggs: 1/4 * 20 = 5
The third lays 6 brown eggs: 3/10 * 20 = 6
Add up the brown eggs and divide by 60, the total number of eggs:
19/60 = 0.31666667 = 31.67%, or 32%.
Write 7.5% as a fraction.
Explanation
First convert the percentage to a decimal:
7.5% = .075
Then turn this into a fraction:
.075 = 75/1000
Simplify by dividing the numerator and denominator by 25:
75/1000 = 3/40
Write as a fraction: 22%
4/9
2/3
4/7
11/50
11/100
Explanation
22% = 22/100
Divide everything by 2:
22/100 = 11/50
11 is a prime number, so this is as reduced as this fraction can get.
Three hens each lay 20 eggs for a farmer. Two-fifths of the first hen's eggs are brown. One-fourth of the second hen's eggs are brown. Seven-tenths of the third hen's eggs are white. What percentage of all the eggs are brown?
Explanation
The first hen lays 8 brown eggs: 2/5 * 20 = 8
The second lays 5 brown eggs: 1/4 * 20 = 5
The third lays 6 brown eggs: 3/10 * 20 = 6
Add up the brown eggs and divide by 60, the total number of eggs:
19/60 = 0.31666667 = 31.67%, or 32%.
Write 7.5% as a fraction.
Explanation
First convert the percentage to a decimal:
7.5% = .075
Then turn this into a fraction:
.075 = 75/1000
Simplify by dividing the numerator and denominator by 25:
75/1000 = 3/40
The radius of a given circle is increased by 20%. What is the percent increase of the area of the circle.
20%
40%
44%
100%
144%
Explanation
If we plug-in a radius of 5, then a 20% increase would give us a new radius of 6 (which is 1.2 x 5). The area of the new circle is π(6)2 = 36π, and the area of the original circle was π(5)2 = 25π . The numerical increase (or difference) is 36π - 25π = 11π. Next we have to divide this difference by the original area: 11π/25π = .44, which multiplied by 100 gives us a percent increase of 44%. The percent increase = (the numerical increase between the new and original values)/(original value) x 100. The algebraic solution gives us the same answer. If radius r of a certain circle is increased by 20%, then the new radius would be (1.2)r. The area of the new circle would be 1.44 π r2 and the area of the original circle πr2. The difference between the areas is .44 π r2, which divided by the original area, π r2, would give us a percent increase of .44 x 100 = 44%.