Grade 8 Percentages

By Jeff, Zach, and Karishma

Learning Targets

By the end of this lesson, you should be able to say…

• I know what a percentage is and where it’s used
• I can calculate the percentage of a number
• I can convert fractions to percentages
• I can see how percentages are used in news

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Where are we going?

Grade 8:

• Percentages less than 1
• Percentages greater than 100
• Word problems with real-life context
• Beading

How could you find what percentage of the total beads are used in the Eagle design?

Source: http://www.aboriginalperspectives.uregina.ca/workshops/workshop2011/percentages1.shtml

Review

What is a percentage?

Where are they used?

Example: Calculate 50% of 70

Hints:

• What do we need to convert the percentage to before calculation?
• What does “of” mean in math?

Example: Calculate the price after GST (5%) is added to a $10 item.

Fractions to Percentages

Example 1: 4/5

= 0.8 → 0.8 x 100 = 80%

Example 2: 1/3

= 0.33333… → 0.33333… x 100 = 33.3%

Steps: convert to decimal then multiply by 100

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Fractions to Percentages

Example 3: 183/366

= 1/2 = 0.5 → 0.5 x 100 = 50%

Example 4: 6/12

= 1/2 = 0.5 → 0.5 x 100 = 50%

What do we notice? Equivalent fractions are equivalent percentages

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Word Problem

5 million people live in BC and 38 million people live in Canada. What percentage of people live in BC?

Percentages to Fractions

Example 1: 70%

= 70/100 = 7/10

Example 2: 70% of the class is sleepy this afternoon. If there are 10 students in class, how many are sleepy?

= 7/10 x 10 = 7 students

Steps: divide by 100, multiply fraction by number of things

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Real-World Example

The new vaccine for the coronavirus is 90% effective. How many people are still susceptible to the virus in BC if everybody gets vaccinated? Recall that 5 million people live in BC.

Activity: Percentages in the news

• News stories often use percentages to communicate information
• Look online for an article involving percentages
• What advantages do percentages have when communicating?

A Final Problem

Your job pays $100,000 per year. One year, your boss says that the company is struggling, and proposes the following deal: they will lower your salary by 30% this year, then raise it by 40% next year. Should you take the deal? Why or why not?

Solution

• If you take the deal, your salary will go down 30% this year.

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Solution

• If you take the deal, your salary will go down 30% this year.
• 30% of $100,000 is $30,000, so your salary this year will be $100,000 - $30,000 =$70,000

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Solution

• If you take the deal, your salary will go down 30% this year.
• 30% of $100,000 is $30,000, so your salary this year will be $100,000 - $30,000 =$70,000
• Next year, your salary will increase by 40%

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Solution

• If you take the deal, your salary will go down 30% this year.
• 30% of $100,000 is $30,000, so your salary this year will be $100,000 - $30,000 =$70,000
• Next year, your salary will increase by 40%
• 40% of $70,000 is $28,000, so your salary this year will be $70,000+$28,000 = $98,000

Solution

• If you take the deal, your salary will go down 30% this year.
• 30% of $100,000 is $30,000, so your salary this year will be $100,000 - $30,000 =$70,000
• Next year, your salary will increase by 40%
• 40% of $70,000 is $28,000, so your salary this year will be $70,000+$28,000 = $98,000

Your salary will end up lower than it started!

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Summary

• Percentages represent parts out of 100
• We can convert from fractions to percentages, and percentages to fractions
• Percentages are used to communicate many quantities in news articles and other media

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