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Solving Percent Problems

Area/Skill Mathematics
Language Arts, Reading
Language Arts, Writing
Cognitive Skill Level
Comprehension, Application,
Analysis, Synthesis
Submitted by
Monica Watson
Southwest MS Community College
Students will comprehend and analyze what differentiates the part and the whole
in percent problems

Lesson Outline:

Math: Determine the part and whole to set up a proportion to solve percent problems.
Language Arts, Reading: Use the Internet to find and read biographical essays or comments
on mathematicians.
Language Arts, Writing: Demonstrate proficiency in holistic writing practices.

This lesson provides a step by step approach to solving problems with unknowns, thus an intro for solving linear
equations with one variable. Students will use cognitive skill levels to classify, arrange, solve, research, decipher, and
compare unknown quantities and actual savings versus proposed savings. Students will also utilize the
logical/mathematical and linguistic learning styles.

Refer to handout information sheet.
1) Discuss the three types of questions in percent problems. Explain to students how to differentiate between
the part and whole of a percent problem and use a proportion to solve for the missing number.
2) Have students use the graphic organize to brainstorm what they think they know about percents and then
write a journal writing describing the steps taken to solve for the missing number in one of the types of percent
3) Have students utilize the Internet or periodicals to search for biographies on mathematicians. Also have
students search for advertisements indicating percentage discounts on similar name brand products and
survey any proposed savings.

Debriefing/Evaluation Activity: Ask students to discuss any difficulties in determining the part and the whole. Ask
students to draw charts or explain the process of substituting the known values into the correct position when setting
up a proportion.

Newspaper Sales
Graphic Organizer
Articles from the Internet
Extension Activity

ESE Accommodations

Hand out indicating steps for solving a
percent problem using a proportion.

Allow calculators for computations.

Graphic organizer for brainstorming
ideas and comparing similar products
vs. discounted prices.










Real-Life Connection:
Since adults are also consumers, the lesson’s reference to real-life consumer practices will address how viable it will
be to understand how percentages are derived and demonstrated comparison techniques regarding advertised
discounted prices. Percents are commonly used in many of the adult learners’ livelihood such as calculating percents
for interest on various types of loans, discounts and taxes.

Solving Percent Problems
A percent problem can be solved by setting up a proportion that shows that the relationship
between the part and the whole is the same as the relationship of a percent part to 100%.

proportion occurs when two ratios are equal to each other. The proportion below can be
stated as: “a is to b as c is to d.” This also can be written in the fractional form as:

Example 1) What is 40% of 120? You are looking for the part of 120.
Set up the proportion:

Example 2) 18 is what percent of 72? You are looking for the percent part.
Set up the proportion:

Example 3) 24 is 40% of what number? You are looking for the whole.
Set up the proportion:

Solving Percent Problems

Use the proportion sample to set up a percent problem. To solve a percent problem you must

% Read the problem carefully
% Next decide if the number you are looking for is the part, the whole, or the percent part.
% The percent whole is always 100%.
% Often, to find the whole or the percent part, it is usually most reliable to use a proportion
to solve the problem.