• Ratio—comparison of 2 quantities by division

• Written using to, : , fraction

• Ex: 10 to 15, 10:15, 10/15

• Rate—ratio that compares quantities in different units

• Unit Rate--denominator of 1

• Can be used when finding the “best buy”

• Ex: miles/gallon

Ex: 2 L of soda for $1.98, how much for 1 L?

1.98 = 0.99 2 1

Fractions, Decimals, Percents

Percent to Fraction• Write each percent as a fraction and

reduce

Ex: 5 % = 5 = 1 100 20

Ex: 125 % = 125 = 5 = 1 ¼ 100 4

Fraction to Percent• Divide numerator by denominator• Then move decimal point 2 places to the

right

Ex: 5 = 0.3125 = 31.25 % 16

Ex: 3 = 0.27 = 27 % 11

Percent to Decimal• Move decimal point 2 places to left

Ex: 16 % = 0.16

Ex: 9.7 % = 0.097 add a zero in front of the 9 for extra place

Decimal to Percent• Move decimal point 2 places to right

• Ex: 0.33 = 33 %

• Ex: 0.023 = 2.3 %

Proportion—equation with 2 equal ratios

Cross Product—the product of the numerator in one ratio and the denominator in the other ratio

Cross Products are used to find a missing quantity in a proportion When the two ratios are equal, then the cross

products are equal You can use cross products to find out if 2 ratios

form a proportion

Ex: x = 4 9 6 6x = 9 * 4 6x = 36 6 6 x = ?

Ex: h = 2 9 3 3h = 2 * 9 3h = 18 3 3

h = ?

Ex: Do the ratios 6/9 and 4/6 form a proportions?

6 = 49 6

6 * 6 = 9 * 4? = ?

*Remember* a percent is part of a whole and is out of 100

To solve:Multiply the number by the percent

1.) 15% of 40 2.) 80% of 460 3.) 20% of 25 4.) 49% of 300 5.) 11% of 720

Use a proportion to solve

Don’t forget that % are out of 100

Remember: is/of for the correct placement of numbers in the proportion

Always: Part/whole

Finding the Percent

Ex: What % of 40 is 6? n = 6 part 100 40 whole

Finding the Part:

Ex: What is 15% of 40? 15 = n part 100 40 whole

Finding the Whole

Ex: 6 is 15% of what number? 15 = 6 part 100 x whole

Ex: What percent of 250 is 138?

Ex: 207 is 46 % of what number?

Ex: What percent of 60 is 52?

Ex: What is 85% of 62?

Ex: 0.96 is what percent of 10?

Ex: 19.2 is 32 % of what?

Ex: What percent of 48 is 54?

Ex: What is 145.5% of 20?

Ex: 380 is 125% of what number?

Tax = % times purchase priceTo find the total, add the answer back to the price

Ex: $159.99 desksales tax 6%159.99 x 6% =9.5994 (9.60)

Tip = % times the priceTo find the total, add the tip amount back to the price

Ex: $9.68 meal, 7% tip9.68 x 7% = 0.6776 (0.68)9.68 + 0.68 = 10. 36

Commission= % times the price

Ex: $500 with 12.5% commission

500 x 12.5% = 62.50

1st method: Discount = percent of discount * regular price Subtract answer from regular price

Ex: A pair of shoes costs $85.99 and are on sale for 20% off. Find the discount.

20% * 85.99

0.20 * 85.99 = 17.20 85.99 – 17.20 = $68.79

2nd method: Subtract the percent from 100 then multiply new % to regular price

Ex: A video game costs $39.95 and is on sale for 20% off. What is the sale price?

100 – 20 = 80%80% * 39.95 = $31.96

Ex: A pair of pants cost $21.99 and are marked 15% off. Find the discount.

100 – 15 = 85%85% x 21.99 = $18.70

15% x 21.99 = 3.3021.99 – 33.30= 18.70

Ex: A book cost $21.99 and is on sale for 25% off. What is the sale price?

100 – 25 = 75%75% x 21.99 = 16.50

Ex: A singer receives a 5% royalty on each CD sale. Find the royalty for a $16.99 CD.

C = 5% * 16.99 C = 0.05 * 16.99 C = ?

Ex: How many people were surveyed if 1023 people is 93% of the population?

1023 = 93% * n 1023 = 0.93 * n ? = n

Ex: In a survey, 922 people or 68.6% preferred smooth peanut butter. How many people were surveyed?

922 = 68.6% * p 922 = 0.686 * p ? = p

Percent a quantity increases or decreases from its original amount

Percent of change = amount of change

original amount

Percent of increase = amount of change

original amount

Ex: Find percent of increase from 4 to 7.57.5 – 4 = 3.5

= 3.5 4

Ex: from 100 to 114 114 – 100 = 14

14 = 100

Ex: from 2.0 to 3.2 3.2 – 2.0 = 1.2

1.2 = 2.0

Ex: from 4000 to 8500 8500 – 4000 = 4500

4500 = 4000

Percent of decrease = amount of change original amount

Ex: Find percent of decrease from 1500 to 1416 1500 – 1416 = 84

= 84 1500

Ex: from 9.6 to 4.8 9.6 – 4.8 = 4.8

4.8 = 9.6

Ex: from 202 to 192 202 – 192 = 10

10 = 202

Ex: from 854.5 to 60.6 854.5 – 60.6 = 793.9

793.9 = 854.5

Selling price– store’s cost plus the markup

Multiply the cost to the % then add back to the original cost to find the selling price

Ex: $5.25 with 10% mark-up5.25 x 10 % = ? 5.25 + ? = ?

Ex: Percent mark-up for a music store is 67% and the CD costs $10.15. Find the mark-up.

Ex: A jacket costs $56 and the percent mark-up is 75%. Find the mark-up.

Ex: A computer store pays $6 for a mouse and the percent mark-up is 75%. What is the selling price?

Ex: A $5 hat has a 70% mark-up. Find the selling price.

Ex: A bike that cost $525 a year ago is now worth $472.50. What is the percent decrease?

Ex: A $70 coat is now worth $59. What is the percent decrease?

Ex: A new stereo cost $425 now costs $382.50. What is the percent discount?