unit 5: percent, ratio, and rate math 8. relating fractions, decimals, and percent unit 5.1

UNIT 5: PERCENT, RATIO, AND RATE

MATH 8

RELATING FRACTIONS, DECIMALS, AND PERCENT

Unit 5.1

Percent to Fraction

Percent to fraction

1) 19%

2) 36%

4) 92.5%

5) 47.25%

3) 85%

Step 4: Reduce to lowest termStep 3: Eliminate the decimals in the fraction

Step 2: Take out the percentage signStep 1: Divide the number by 100

Percent to Fraction to Decimal

Percent to fraction

1) 19%

2) 36%

4) 92.5%

5) 47.25%

3) 85%

to decimal

• Step 1: Get the denominator in a power of 10.

• Step 2: Divide the numbers.

= 0.36

= 0.85

= 0.925

= 0.4725

= 0.19

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

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

2) = 0.625 = 62.5%

= 75%

More Questions

Try to get the following fractions to decimal and then to percentage form

3)

4)

=0.6

=0.4725 =

= 60%

= 47.25%

CALCULATING PERCENT

Unit 5.2

Steps…

Calculating Percent of a number

Step 1: Get percent in decimal form.Step 2: Multiply decimal to the number

(i.e. 200).

Calculating Percent of a Number

0% 100% 180%

200 ??

Question 1What is 180% of 200?

Calculating Percent of a Number

Question 1What is 180% of 200?

180% = 1.8

1.8 * 200 = 360

0% 100% 180%

200 ??

Question 2

Question 2What is 37.55% of 95?

0% 37.55% 100%

?? 95

37.55% = 0.3755

0.3755 * 95 = 35.6725

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

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

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

SOLVING PERCENT PROBLEMS

Unit 5.3

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 A25% = 0.25165×0.25 =41.25 cm165+ 41.25 = 206.25 cm

Solution B100% + 25% = 125% (+) if increase, (-) if decrease125% = 1.25165 × 1.25 = 206.25 cm

Question 1 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 A30% = 0.30140×0.3 =42 lbs140 - 42 = 98 lbs

Solution B100% - 30% = 70% 70% = 0.7140 × 0.7= 98 lbs

Question 2 a)

70% of a number is 63. What is the number?

Step 1: Get the percent in decimal form.Step 2: Divide the number by the decimal

0% 70% 100%

63 ??

Solution: 70%= 0.763 ÷ 0.7= 90

Question 2 b)

200% of a number is 96

0% 100% 200%

96??

Solution: 200% = 2

96÷ 2= 38

Percent Increase/Decrease

The price of a T-shirt in Wal-Mart increased from $20 to $25.

To find the percent increase/decreaseStep 1: Divide final value to initial valueStep 2: Subtract 100% to/from it

Solution: 25 ÷ 20

= 1.25

1.25 = 125%

125% - 100% = 25%

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 = 0.84 0.84= 84%

100% - 84% = 16%

SALES TAX AND DISCOUNT

Unit 5.4

GST, PST, and HST

GST – Goods and Services TaxFederal tax5%

PST – Provincial Sales TaxProvincial taxDepends on the province

HST- Harmonized Sales TaxPST + GST combinedDepends on the Province

Tax in our provinces

The following link sends you to a website showing the current taxes in each provinces

http://www.retailcouncil.org/quickfacts/taxrates

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% 12%= 0.12 55 × 0.12 = 6.60 55 + 6.6 = $61.60

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% + 9.975% = 14.975% 14.975%= 0.14975 55 × 0.14975 = 8.24 55 + 8.24 = $63.24

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 = $1680-16 = $6464 × 0.12 = $7.6064 + 7.60 = $71.60

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 $79.99. The shoe is currently on sale for 30% off. How much is the shoe after the discounts.Discount #110% = 0.179.99 × 0.1 = 7.99979.99 – 7.999 = 71.991

Discount #230% = 0.371.991 × 0.3 = 21.597371.991 – 21.5973 = $50.3937