029. Fractions and Percentages

Learning Intentions

• To understand that a percentage can be thought of as a fraction with a denominator of
• convert a percentage to a fraction in simplest form
• convert a fraction to a percentage

Pre-requisite Summary

• Understand that a fraction represents part of a whole
• Know the meaning of numerator and denominator
• Be able to write equivalent fractions
• Be able to Simplify fractions Use common factors
• Understand that “percent” means “out of ”
• Be able to multiply or divide by powers of ten
• Recognise common benchmark fractions such as

Worked Examples

Worked Example 1

a) Explain why can be written as .

b) Explain what the denominator represents.

c) Write as a fraction with denominator .

Worked Example 2

Convert each percentage to a fraction in simplest form:

a)

b)

c)

Worked Example 3

Convert each percentage to a fraction in simplest form:

a)

b)

c)

Worked Example 4

Convert each fraction to a percentage:

a)

b)

c)

Worked Example 5

Convert each fraction to a percentage:

a)

b)

c)

Worked Example 6

a) Decide whether and represent the same quantity.

b) Convert to a percentage.

c) Convert to a fraction in simplest form.

Problems

Problem 1

a) Explain why can be written as .

b) Explain what the denominator represents.

c) Write as a fraction with denominator .

Problem 2

Convert each percentage to a fraction in simplest form:

a)

b)

c)

Problem 3

Convert each percentage to a fraction in simplest form:

a)

b)

c)

Problem 4

Convert each fraction to a percentage:

a)

b)

c)

Problem 5

Convert each fraction to a percentage:

a)

b)

c)

Problem 6

a) Decide whether and represent the same quantity.

b) Convert to a percentage.

c) Convert to a fraction in simplest form.

Exercises

Understanding and Fluency

Exercise 1.

Write each percentage as a fraction with denominator :

a)

b)

c)

Exercise 2.

Convert each percentage to a fraction in simplest form:

a)

b)

c)

Exercise 3.

Convert each percentage to a fraction in simplest form:

a)

b)

c)

Exercise 4.

Convert each fraction to a percentage:

a)

b)

c)

Exercise 5.

Convert each fraction to a percentage:

a)

b)

c)

Exercise 6.

Convert each fraction to a percentage:

a)

b)

c)

Exercise 7.

Match each fraction and percentage:

a)

b)

c)

Exercise 8.

Convert in either direction as needed:

a)

b)

c)

Reasoning

Exercise 9.

Explain why .

Exercise 10.

A student says . Explain the mistake.

Exercise 11.

Explain why converting to a percentage involves making an equivalent fraction with denominator .

Exercise 12.

A student says . Explain why this is incorrect.

Problem-solving

Exercise 13.

A test score is out of . Write this fraction as a percentage.

Exercise 14.

A shirt is labelled as being made from cotton. Write this percentage as a fraction in simplest form.

Exercise 15.

A class completed of a project. What percentage of the project was completed?

Exercise 16.

A water tank is full. Write this as a percentage.

Exercise 17.

A student answered out of questions correctly. Write the fraction correct as a percentage.

Exercise 18.

A battery is at charge. Write this as a fraction in simplest form.

Potential Misunderstandings

• Students may think percent means “out of ” instead of “out of ”
• Students may write a percentage as a fraction with the wrong denominator
• Students may forget to simplify the fraction after writing it over
• Students may confuse the numerator and denominator when converting
• Students may not recognise that converting a fraction to a percentage often requires an equivalent fraction with denominator
• Students may incorrectly scale only the numerator or only the denominator
• Students may assume that the percent sign can be ignored without changing the meaning
• Students may think all fractions convert to percentages without using equivalent fractions or multiplication

Next: 030. Finding Percentages of Quantities