Find One Hundred Percent Given Another Percent

Examples, videos, and solutions to help Grade 7 students find 100% of a quantity (the whole) when given a quantity that is a percent of the whole by using a variety of methods including finding 1%, equations, mental math using factors of 100, and double number line models.

New York State Common Core Math Grade 7, Module 4, Lesson 5

Download worksheets for Grade 7, Module 4, Lesson 5

Lesson 5 Student Outcomes

• Students find 100% of a quantity (the whole) when given a quantity that is a percent of the whole by using a variety of methods including finding 1%, equations, mental math using factors of 100, and double number line models.
• Students solve word problems involving finding 100% of a given quantity with and without using equations.

Lesson 5 Classwork

Opening Exercise
What are the whole number factors of 100? What are the multiples of those factors? How many multiples are there of each factor (up to 100)?

Example 1
The 42 students who play wind instruments represent 75% of the students who are in band. How many students are in band?
Exercises 1–3

1. Bob’s Tire Outlet sold a record number of tires last month. One salesman sold 165 tires, which was 60% of the tires sold in the month. What was the record number of tires sold?
2. Nick currently has 7,200 points in his fantasy baseball league, which is 20% more points than Adam. How many points does Adam have?
3. Kurt has driven 276 miles of his road trip but has 70% of the trip left to go. How many more miles does Kurt have to drive to get to his destination?

Example 2
Answer each part below using only mental math and describe your method.
a. If 39 is 1% of a number, what is that number? How did you find your answer?
b. If 39 is 10% of a number, what is that number? How did you find your answer?
c. If 39 is 5% of a number, what is that number? How did you find your answer?
d. If 39 is 15% of a number, what is that number? How did you find your answer?
e. If 39 is 25% of a number, what is that number? How did you find your answer?

Exercises 4–5
4. Derrick had a 0.250 batting average at the end of his last baseball season, which means that he got a hit 25% of the times he was up to bat. If Derrick had 47 hits last season, how many times did he bat?
5. Nelson used 35% of his savings account for his class trip in May. If he used $140 from his savings account while on his class trip, how much money was in his savings account before the trip?

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