Teaching Models

Use Percent

Setting Up Percent Problems
Remind students that a percent is a ratio of a number to 100. A percent tells what part of 100 is being considered. To solve percent problems, either proportions or equations can be used. Students already know how to solve proportions and equations. If n is the percent, x is the part, and w is the whole, students can write and solve a proportion, using part-to-whole ratios.

example

The percent equation is set up as “whole × percent = part.” Students can write the equation using either the decimal form or the fraction form of the percent.

w × 0.01n = x or w × n over 100 = x

Find a Percent of a Number
In these types of problems the percentage and the whole are known and the part is the unknown. Having students do many exercises of the type “Find 40% of 230” allows them to become skilled in finding a percent of a number before applying those skills to problem solving.

Example: Find 40% of 230.

Using a Proportion

[n/100 = x/w]
forty-hundredths = x over two-hundred thirty
100x = 40 × 230
one hundred x over one hundred = nine-thousand two-hundred over one-hundred
x = 92

Using Decimals in an Equation

w × 0.01n = x
230 × 0.40 = x
92 = x

Using Fractions in an Equation

w × n over 100 = x
230 × forty-hundredths = x
92 = x

Solution: 40% of 230 is 92.

Finding a Percent
In these types of problems the part and the whole are known and the percent is the unknown. Having students do many exercises of the type “What percent of 250 is 40?” or “40 is what percent of 250?” allows them to become skilled in finding a percent before applying their skills to problem solving.

Example: 40 is what percent of 250?

Using a Proportion

[n/100 = x/w]
n over 100 = forty over two-hundred-fifty
250n = 40 × 100
two-hundred-fifty n over two-hundred-fifty = four thousand over two-hundred-fifty
n = 16

Using Decimals in an Equation

w × 0.01n = x
250 × 0.01n = 40
(250 × 0.01)n = 40
two point five over two-hundred-fifty = forty over two point five
n = 16

Using Fractions in an Equation

w × n over 100 = x
250 × n over 100 = 40
two-hundred-fifty n over one-hundred = one-hundred over two-hundred-fifty = 40 × one-hundred over two-hundred-fifty
n = 16

Solution: 40 is 16% of 250.

Finding a Number When a Percent Is Known
In these types of problems the part and the percentage are known and the whole is the unknown. Having students do many exercises of the type “40% of what number is 25?” or “25 is 40% of what number?” allows them to become skilled in finding the whole when the part and percent are known before applying their skills to problem solving.

Example: 25 is 40% of what number?

Using a Proportion

[n/100 = x/w]
forty-hundredths = twenty-five over w
40w = 100 × 25
forty w over one-hundred = two-thousand five-hundred over forty
w = 62.5

Using Decimals in an Equation

w × 0.01n = x
w × 0.40 = 25
w times zero point forty over zero point forty = twenty-five over zero four zero
w = 62.5

Using Fractions in an Equation

w × n over 100 = x
w × forty-hundredths = 25
w × forty-hundredths × one-hundred over forty = 25 × one-hundred over forty
w = 62.5

Solution: 25 is 40% of 62.5.

Estimating With Percents
Remind students that, when estimating, their estimates may vary. Estimating with percents can be done in the same way as estimating with decimals. Numbers are rounded in order to make computation easier. Sometimes percents can be estimated mentally.

Example:

Estimate a 15% tip on a bill of $37.50.
Round $37.50 to $40 and find 15% of $40, or $6.

Example:

Estimate a 15% tip on a bill of $37.50.
Think: 15% = 10% + one-half of 10%
10% of $37.50 is about $3.80 and one-half of $3.80 is $1.90, so 15% is about $5.70.

Sometimes estimating with percents is more easily done by using fractions. As students gain experience and confidence in converting between percents, decimals, and fractions, they may find this method easier.

Example:

An $84 coat is on sale for 33% off. Estimate how much you save by buying the coat on sale. Then estimate the sale price.
33% is about one-third and $84 can be rounded to $90.
one-third of $90 is $30. You save about $30.
$84 − $30 = $54. The sale price is about $54.

Example:

A $1,199 computer is on sale for 75% of its regular price. Estimate the sale price.
75% is three-fourths and $1,199 is close to $1,200.
one-fourth of $1,200 is $300, so three-fourths of $1,200 is 3 × $300, or $900.
The sale price is about $900.

Teaching Model 18.1: Find a Number When a Percent Is Known


Houghton Mifflin Math Grade 6