How to work with percentages

HSPT Math · Learn by Concept

Help Questions

HSPT Math › How to work with percentages

1 - 10

Which of the following operations is equivalent to taking of a number?

Dividing the number by

CORRECT

Dividing the number by

Moving the decimal point one place to the left, then doubling the result

Moving the decimal point one place to the left, then tripling the result

Explanation

Let's just pick a number at random, for example .

of this number is , which is divided by .

We can also work by simplifying the fractional form of . A percent can be written as the number divided by .

$=\frac{25}{100}$

We can simplify this fraction: $\frac{25}{100}=\frac{5}{20}=\frac{1}{4}$ .

Either way, we get the same answer.

There are 500 students at the high school. There are only two menu options: chicken or fish. If 15% of students ordered fish, how many students ordered chicken?

$425\ students$

CORRECT

$75\ students$

$85\ students$

$450\ students$

$325\ students$

Explanation

If 15% of students ordered fish, then 85% of the students must have ordered chicken. Then multiply 85% or $.85\times 500 = 425$ .

What number increased by 25% is equal to 7?

$5 \frac{3}{5}$

CORRECT

$5\frac{1}{4}$

$5\frac{5}{6}$

$4\frac{2}{3}$

Explanation

To increase a number by 25% is to take

of the number, or, equivalently, multiply it by

$\frac{125}{100} = \frac{125 \div 25 }{100 \div 25 } = \frac{5}{4}$ .

Therefore, we divide 7 by $\frac{5}{4}$ :

$7 \div \frac{5}{4} = \frac{7 }{1}\div \frac{5}{4} = \frac{7 }{1}\times \frac{4} {5}= \frac{7\times 4 }{1\times 5} = \frac{28}{5}$

$28 \div 5 = 5 \textup{ R }3$ , so

$\frac{28}{5} = 5 \frac{3}{5}$ .

If sales tax on a pair of jeans is , and the jeans cost $\$ 50$ before tax, what is the final price of the jeans including tax?

\$58

CORRECT

\$66

\$56

\$60

\$62

Explanation

Since the jeans are the only item being purchased, and they cost $ $\small 50$ , we must first find $\small 16$ % of $ $\small 50$ . In order to do that we multiply $ $\small 50$ by the decimal form of $\small 16$ %, which is $\small .16$ .

Note: In order to find the decimal form of a percent, we divide it by $\small 100$ . $\small 16/100 = .16$

Find the tax:

$\small .16\cdot 50 = 8$

Therefore the sales tax added to the original price is $ $\small 8$ .

$\small 50+8= 58$

The final cost of the jeans is $ $\small 58$ .

Write as a decimal.

CORRECT

Explanation

To convert a percentage into a decimal, divide the number by 100.

Here's a trick: Simply pretend there is a decimal point at the end of the number, and then move the decimal point two places to the left.

You can think of 42 as 42.0 (or 42. - the zero doesn't matter). Now move the decimal point two places to the left.

Answer:

Which is larger?

a. 10% of 90

b. 5% of 160

c. 20% of 50

d. 30% of 40

CORRECT

Explanation

First find the percentage amount for each choice by multiplying the number by the percentage amount

a. $90\ast .10=9$

b. $160\ast .5=8$

c. $50\ast .20=10$

d. $40 \ast .30= 12$

Then compare the amounts to find the largest.

The answer is (d) 12.

For her birthday, Susan asks her mother to buy her a car. Susan’s mother agrees to give Susan 150 percent of whatever amount Susan can save up in six months. If Susan saves $\$ 600$ , how much does Susan’s mother owe her?

\$900

CORRECT

\$750

\$300

\$700

\$550

Explanation

When Susan's mother agreed to match her savings plus fifty percent, she agreed to give Susan $\small 100$ % plus $\small 50$ %.

$\small 100+50=150$

Before multiplying by the amount Susan saved, we must convert $\small 150$ % to a decimal by dividing by $\small 100$ .

$\small 150/100=1.5$

Now we multiply $\small 1.5$ time $ $\small 600$ .

$\small 1.5\cdot 600=900$

Susan's mother owes her $ $\small 900$ .

Exactly $\frac{1}{3}$ of the plants in a garden are tomato plants. Which of the following could be the total number of plants in the garden?

CORRECT

Explanation

The total number of plants has to be divisible by 3. Of the answer choices, the only one that is divisible by 3 is 18. You can check this because numbers that are divisible have the sum of their digits also divisible by 3. For example,

which is divisible by 3, so 18 is divisible by 3.

A class has 25 students. If 60% of them are boys, how many students are girls?

CORRECT

Explanation

We know that 40% of the class are girls because 60% are boys. To express 40% as a fraction of the 25 total students, we set up a proportion to find the number of girls in the class.

$\frac{40}{100} = \frac{x}{25}$