115r. Review Percentages and Percentage Calculations

Learning Intentions

• To understand that a percentage is a number out of
• convert percentages to fractions and decimals
• convert fractions and decimals to percentages
• express one quantity as a percentage of another quantity
• Solve a certain percentage of a quantity

Pre-requisite Summary

• Know that a fraction represents part of a whole
• Know that a decimal represents parts of a whole Use place value
• Understand that means “per hundred” or “out of ”
• Be able to Simplify fractions
• Be able to convert between some simple fractions and decimals
• Be able to multiply and divide whole numbers and decimals
• Understand that “of” in percentage problems usually means multiply
• Be able to compare two quantities using division

Worked Examples

Worked Example 1

Write each percentage as a fraction and a decimal:

a)

b)

c)

Worked Example 2

Write each fraction or decimal as a percentage:

a)

b)

c)

Worked Example 3

Express one quantity as a percentage of another quantity:

a) as a percentage of

b) as a percentage of

Worked Example 4

Find each percentage of a quantity:

a) of

b) of

c) of

Worked Example 5

Find each percentage of a quantity:

a) of

b) of

c) of

Worked Example 6

Express one quantity as a percentage of another quantity:

a) out of

b) out of

c) out of

Problems

Problem 1

Write each percentage as a fraction and a decimal:

a)

b)

c)

Problem 2

Write each fraction or decimal as a percentage:

a)

b)

c)

Problem 3

Express one quantity as a percentage of another quantity:

a) as a percentage of

b) as a percentage of

Problem 4

Find each percentage of a quantity:

a) of

b) of

c) of

Problem 5

Find each percentage of a quantity:

a) of

b) of

c) of

Problem 6

Express one quantity as a percentage of another quantity:

a) out of

b) out of

c) out of

Exercises

Understanding and Fluency

Exercise 1.

Write each percentage as a fraction out of , then simplify where possible, and write it as a decimal:

a)

b)

c)

d)

Exercise 2.

Convert each fraction or decimal to a percentage:

a)

b)

c)

d)

Exercise 3.

Convert each fraction to a percentage:

a)

b)

c)

d)

Exercise 4.

Convert each decimal to a percentage:

a)

b)

c)

d)

Exercise 5.

Express one quantity as a percentage of another quantity:

a) out of

b) out of

c) out of

d) out of

Exercise 6.

Express one quantity as a percentage of another quantity:

a) as a percentage of

b) as a percentage of

c) as a percentage of

d) as a percentage of

Exercise 7.

Find each percentage of a quantity:

a) of

b) of

c) of

d) of

Exercise 8.

Find each percentage of a quantity:

a) of

b) of

c) of

d) of

Reasoning

Exercise 9.

Explain why .

Exercise 10.

A student says that because the number is . Explain the mistake.

Exercise 11.

Noah says that to convert a decimal to a percentage, you divide by . Is he correct? Explain.

Exercise 12.

Explain why finding of a quantity is the same as finding one quarter of it.

Exercise 13.

A student says that is of because . Describe the error.

Problem-solving

Exercise 14.

A test has questions. A student gets correct. Express this score as a percentage.

Exercise 15.

A shirt costs $ . It is discounted by . Find the discount amount.

Exercise 16.

A water bottle is full and holds mL when full. How much water is in the bottle?

Exercise 17.

In a class of students, students walk to school. What percentage of the class walks to school?

Exercise 18.

A packet contains g of cereal. One serving is of the packet. How many grams is one serving?

Exercise 19.

A basketball player scored successful shots out of attempts. Express this as a percentage.

Potential Misunderstandings

• Students may think a percentage is just a whole number with a percent sign, rather than a number out of
• Students may forget that means “per hundred”
• Students may confuse converting to a decimal with converting to a percentage
• Students may move the decimal point in the wrong direction when converting between decimals and percentages
• Students may forget to simplify a fraction after writing a percentage as a fraction
• Students may think percentages cannot be greater than
• Students may express one quantity as a percentage of another using subtraction instead of division
• Students may reverse the two quantities when finding a percentage
• Students may forget that “of” means multiply in percentage-of-a-quantity questions
• Students may calculate the percentage amount correctly but forget to include the unit

Next: 116. Percentage Change