1. Unit 5: Percent, Ratio, and Rate
MATH 8
Unit 5: Percent, Ratio, and Rate

2. Relating Fractions, Decimals, and percent
Unit 5.1
Relating Fractions, Decimals, and percent

3. Percent to Fraction Percent to fraction
Step 1: Divide the number by 100
Step 2: Take out the percentage sign
Step 3: Eliminate the decimals in the fraction
Step 4: Reduce to lowest term
1) 19%
4) 92.5%
2) 36%
5) 47.25%
3) 85%

4. Percent to Fraction to Decimal
Step 1: Get the denominator in a power of 10.
Step 2: Divide the numbers.
1) 19%
4) 92.5%
= 0.19
= 0.925
2) 36%
= 0.36
5) 47.25% =
3) 85%
= 0.85

5. Fraction to Decimal
If fraction has a denominator that is difficult to get to base 10, use calculator to divide 1)
= 0.75 2)
= 0.625

6. Fraction to Decimal to Percentage
Put it back to fraction with base 10- denominator
Get denominator to be 100.
Take the numerator as the percentage. 1)
= 0.75
= 75% 2)
= 0.625
= 62.5%

7. More Questions
Try to get the following fractions to decimal and then to percentage form 3)
=0.6
= 60% 4)
=0.4725 =
= 47.25%

8. Unit 5.2
Calculating Percent

9. Steps… Calculating Percent of a number
Step 1: Get percent in decimal form.
Step 2: Multiply decimal to the number (i.e. 200).

10. Calculating Percent of a Number
Question 1 What is 180% of 200?
200 ?? 0%
100%
180%

11. Calculating Percent of a Number
Question 1 What is 180% of 200?
200 ?? 0%
100%
180%
180%
= 1.8
1.8 * 200
= 360

12. Question 2 Question 2 What is 37.55% of 95? ?? 95 0% 37.55% 100%=
* 95 =

13. Problem
Question 3
Of the people who watched the Lego Movie, 30% of the viewers were adults. If there were 300 people watching over the weekend. How many of them were adults?
30%
= 0.3
0.3 * 300
= 90

14. Terms
Cost price is the price that the store has to pay to get the merchandise
Selling price is the price that the store sells the merchandise

15. Question 4
Question 4 The cost price of a Wal-Mart T-shirt is $5.00. The selling price is 300% of the cost price. What is the selling price of the T-shirt? Illustrate the answer in a number line.
300%
= 3
5* 3 = $15.00

16. Solving Percent Problems
Unit 5.3
Solving Percent Problems

17. Question 1 a)
Spiderman’s height was 165cm last year. After drinking some special juice, his height increased by 25%. What is his height now?
Solution A 25% = 0.25
165×0.25 =41.25 cm = cm
Solution B
100% + 25% = 125% (+) if increase, (-) if decrease 125% = × 1.25 = cm

18. Question 1 b) Solution A 30% = 0.30 Solution B
The effect of this juice is weight loss. In the past, Spiderman kept a constant weight of 140 lbs. But after taking the juice, his weight decreased by 30%. What is his new weight.
Solution A 30% = 0.30
140×0.3 =42 lbs = 98 lbs
Solution B
100% - 30% = 70% % = × 0.7= 98 lbs

19. Question 2 a) Step 1: Get the percent in decimal form.
70% of a number is 63. What is the number? 63 ?? 0%
70%
100%
Step 1: Get the percent in decimal form.
Step 2: Divide the number by the decimal
Solution: 70%
= 0.7
63 ÷ 0.7
= 90

20. Question 2 b) Solution: 200% = 2 200% of a number is 96 ?? 96 0% 100%
96÷ 2
= 38

21. Percent Increase/Decrease
The price of a T-shirt in Wal-Mart increased from $20 to $25.
To find the percent increase/decrease Step 1: Divide final value to initial value Step 2: Subtract 100% to/from it
Solution: 25 ÷ 20
= 1.25
1.25 = 125%
125% - 100% = 25%

22. More Percent Increase/Decrease
A purse went on sale in Michael Kors. The bag’s original price was $500. After a marked down deduction, the price became $420. What was the percent decrease of the bag?
Solution: 420÷500 = = 84% 100% - 84% = 16%

23. Unit 5.4
Sales Tax and discount

24. GST, PST, and HST GST – Goods and Services Tax Federal tax 5%
PST – Provincial Sales Tax
Provincial tax
Depends on the province
HST- Harmonized Sales Tax
PST + GST combined
Depends on the Province

25. Tax in our provinces
The following link sends you to a website showing the current taxes in each provinces

26. Tax questions
A pair of jeans in American Eagle cost $55. How much is the final price of this jeans in… a) BC –(GST= 5% and PST = 7%) b) Quebec (GST=5% and PST= 9.975%)
Solution a) tax = 5% + 7% = 12% %= × 0.12 = 6.60
= $61.60

27. Tax questions
A pair of jeans in American Eagle cost $55. How much is the final price of this jeans in… a) BC –(GST= 5% and PST = 7%) b) Quebec (GST=5% and PST= 9.975%)
Solution b) tax = 5% % = % %= × = 8.24
= $63.24

28. Discount and Taxes
A dress shirt in Banana Republic is priced at $80. For the weekend, there is an additional 20% off. How much do I have to pay considering there is a tax of 12% in BC.
Solution 1: 0.2 × 80 = $ = $64 64 × 0.12 = $ = $71.60

29. Double Discounts
James work at Sport Chek as a cashier. He gets an employee discount of 10% on everything he buys. He wants to buy a new pair of Nike running shoes that is regularly priced at $ The shoe is currently on sale for 30% off. How much is the shoe after the discounts.
Discount #1 10% = × 0.1 = – =
Discount #2 30% = × 0.3 =
– = $