Ratios - Introduction and word problems

Proportions

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Percent

Source: Source: Contemporary's GED Mathematics Jerry Howett 


A percent, like a decimal or a fraction, describes a part of a whole. (like p/W *100)

With percent, one whole is always divided into 100 parts.

A percent is indicated with the % sign.

Percent can be expressed as a two-place decimal (hundredths) or as a fraction with a denominator of 100.



Understanding Percent

One whole is 100%.

• A percent greater than 50% is greater than ½.
• A percent less than 50% is less than ½.
• A percent greater than 100% is greater than one whole.

Percents, Decimals, and Fractions

To change a percent to a decimal, follow these steps:

• Drop the % sign.
• Move the decimal point two places to the left.

25 % then 25 and 0.25

To change a decimal to a percent, follow these steps:

• Move the decimal point two places to the right.
• Write the percent sign after the last digit.

0.25 then 25 and 25 %

To change a percent to a fraction, follow these steps:

• Drop the % sign.
• Write 100 as the denominator.
• Reduce.

50 % then 50 and 50/100=1/2

To change a fraction to a percent, multiply the fraction by 100%.

1/4 *100= 25 %

9 is what percent of 36?

A) 25%
B) 20%
C) 15%
D) 10%
E) 5%

63 is 150% of what number?

A) 21
B) 31.5
C) 42
D) 47.25
E) 94.5

Change 12% to a common fraction and reduce to lowest terms.

A) 1/12
B) 1/4
C) 5/12
D) 3/25
E) 12/25

Which of the following is NOT a way to find 20% of 65?

A) 65 ÷ 5
B) 65 x 1/5
C) 65 x 0.2
D) 65 x 20/100
E) 65 ÷ 1/5

A microfiber jacket costs $89. Which of the following represents the total price in dollars including a 6% sales tax?

A) 89 x 1.06
B) 89 x 0.06
C) 89 – 1.06
D) 89 + 0.06
E) 89

Ratio and Proportion

Source: Contemporary's GED Mathematics Jerry Howett 

Ratio

A ratio is a comparison of numbers by division. A ratio can be written in the following ways:

• with the word to
• with a colon [:]
• as a fraction

Like a fraction, a ratio should be reduced to lowest terms.

In order to solve a ratio problem, you may have to calculate one of the numbers in a ratio.



In one neighborhood, 7 homeowners have snow-blowers and 28 home owners use shovels. What is the ratio of snow-blowers to shovels?


A) 1:4
B) 7:4
C) 1:28
D) 4:1
E) 28:7

Of the 359 workers at a company, 62 are office workers. What is the approximate ratio of office workers to non-office workers?

A) 1:5
B) 1:6
C) 5:6
D) 60:360
E) 62:359


Proportion

A proportion is a statement that two ratios are equal.

Each of the four numbers in a proportion is called an element, or a term.
The cross products in a proportion are equal.

To solve a proportion, follow these steps:

Write a statement with two equal cross products.

Divide both sides of the statement by the number in front of the missing term.


What is the missing term in the proportion?

9/x = 15/10


A) 90
B) 13.5
C) 10
D) 6
E) 4

A clerical assistant earns $45.20 in 8 hours. At this rate, how much does he earn in 40 hours?

A) $180.00
B) $226.00
C) $361.60
D) $404.00
E) $1,808.00

Ratio and Proportion - Interactive Mathematics Lesson Module