Review of Percents

Percent means out of ___________. The symbol for percent is _______. Percents can also be represented by fractions and decimals.

This grid represents or or

1. What percent is shown on each grid?

__________ __________ __________

2. Shade hundred grids to represent each percent.a) 7% b) 54% c)88%

3. Show as a repeating decimals by using a bar on the repeating part.a) 0.4444444 ___________b) 0.3838383 ___________c) 0.64164164 ___________

4. Show each fraction as a repeating decimal and as a percent. i.e. 0.6 = 66.6%

a) 49

b) 711

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c) 56

5. Show each diagram as a fraction, a decimal and a percent.Diagram Fraction Decimal Percent

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Lesson 1: Representing Percents

Learning Target #1 - I can determine and represent percent from diagrams.

Shade the grid below to represent 100%. Shade the circle below to represent 75%.

How many sides of the cube would you have to shade to represent 50% of the surface area?

Shade the image to show 20% of the white pentagons.

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QUESTIONS

If the shaded square below represents 1% of the grid.

a) What fraction of this enlarged square represents half of 1%?

b) What fraction of a 1% square would you have to shade to

represent 0.28%?

EXAMPLE 1A complete shaded grid represents 100%. What percent does each diagram represent?

a)

b)

c)

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EXAMPLE 2Represent the percent in each of the situations below on a grid.

a) The number of Canuck tickets sold in Round 4 of the Stanley Cup Playoffs rose by 212%.

b) In BC retail sales were only up 0.2% in the month of August.

c) Mrs. Samra’s Mortgage rate is .

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Complete Practice: Representing Percents

1. What percent does each diagram represent?

a) b)

_________________________ ________________________

c) d)

_______________________ _______________________

2. Represent each percent on the grids provided.

a) 136.2 % b) 7 ¾ %

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3. How many hundred grids are needed to show each of the following percents?

a) 285 %

b) 740 %

c) 1630 %

Lesson 2: Fractions, Decimals and Percents

Learning Target #2 – I can convert between percents, decimals and fractions.

EXPLORE

1. What fraction of the figure is shaded?

2. What is this fraction as a percent?

Recall: any percent can be written as a fraction with the percent in the ____________ and _____________ in the denominator. i.e. 35 %

Set up the following proportion

3. What is this fraction as a decimal?

PERCENT CONVERSIONS – SUMMARY

Example:

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numerator ÷ denominator × 100 and add % sign

12= numerator

denominator

Conversion How? ExampleFraction to Decimal

numerator ÷ denominator58

Fraction to Percent (numerator ÷ denominator) × 100%

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Decimal to Percentdecimal number × 100% 0.625

Percent to Decimalpercent ÷ 100 62.5%

Decimal to Fraction Write the number without the decimal in the numerator and write the place value of the number in the denominator. Then reduce the fraction if possible.

0.625

Percent to Fraction percent → decimal → fraction 55%

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FRACTION PERCENDECIMA

÷ 100 (or move decimal 2 places left). Drop the % sign. Write the decimal as a fraction (see rule decimal →fraction)

numerator ÷ denominator

× 100 (or move decimal 2 places right. Zero fills any gaps). Add % sign. i.e. 0.5 × 100 = 50% or 0.5 = 50%

÷ 100 (or move decimal 2 places left. Zero fills any gaps). Drop % sign. i.e. 50% ÷ 100 = 0.5 or 5 0 % = 0.5

Number without decimal in numerator over place value. Reduce fraction.

i.e. 0.5 = 5

10=1

2

For fractional percents changeto decimal percents (see rulefraction → decimal) then ÷ 100

i.e. 4 12

% = 4.5% = 4.5 ÷ 100 =

0.045

Try these:Fraction Decimal Percent

0.04

1725

1.5

23

0.9

3 %

EXAMPLE 1Convert each fraction to decimal and then a percent.

c) b) 52

400 c) 1816

Try These: Convert to a decimal and then a percent!

a)34 b)

8850

EXAMPLE 2Convert each decimal to a percent and a fraction.

a) 2.28 Percent: Fraction:

b) 0.625 Percent: Fraction:

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c) Percent: Fraction:

Try These: Convert to a percent and a fraction

a) 0.0064 b) 0.268 c) 3.4

Percent: Percent: Percent:

Fraction: Fraction: Fraction:

EXAMPLE 3Convert each percent to a fraction and a decimal. Try These:a) 180%

Decimal:

Fraction:

750%

Decimal:

Fraction:

b) 0.45% 0.3 %

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Decimal:

Fraction:

Decimal:

Fraction:

c)

Decimal:

Fraction:

12 ¾ %

Decimal:

Fraction:

EXAMPLE 4: Over five years, the circulation of a magazine increased from 25 000 copies to 150 000 copies. What percent is the new circulation of the circulation five years ago? What is this percent as a decimal and as a fraction?

Homework: Complete Practice on following page

Fractions, Decimals and Percents Practice

1. Rewrite each fraction as a decimal and a percent.

a) 45 b)

32800 c)

38 d)

560

2. Convert each decimal to a percent and a fraction in lowest terms.

a) 6.75 b) 0.255 c) 0.048 d) 0.0072

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3. Convert each percent to a decimal, then a fraction.

a) 845% b) 17 ¼ % c) 0.9% d) 25.8%

4. Express the shaded portion of each diagram as a fraction, a decimal, and a percent.

Fraction:

Decimal:

Percent:

5. Kristina buys coffee every morning for $3.25. The coffee prices have now increased to $3.90. What is the new rate as a percent of the old rate?

Lesson 3: Percent of a Number

Learning Target #3 – I can calculate percent of a number.

Determining the Percent of a Number:

i.e. What is 50% of 60?

Step 1: Convert % to decimal Step 2: Of = X so multiply decimal by number

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Alternate Method: Set up equivalent ratio and solve algebraically

EXAMPLE 1Use mental math to determine each of the following.

a) 125% of 4 of 600

EXAMPLE 2What is the percent of each number? Give your answer to the nearest hundredth.

a) of 320 b) of 24 c) of 35

EXAMPLE 3 500 tickets were being sold for a school draw.

a) If you bought 9 tickets, what would your chance of winning the draw be? Express your answer as a percent.

b) If you wanted to have a 35% chance of winning, how many tickets would you have to buy?

Complete Practice: Percent of a Number

1. What is the percent of each number? (Use a calculator)

a) 16

% of 420 b) 12 38

%of 580 c) 815 % of 900

d) 225 % of $135.99 e) 75 25

%of 230 f) 33. 4 %of $ 657.24

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2. A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly.

3. A metal bar weighs 8.15 ounces. 93% of the bar is silver. How many ounces of silver are in the bar? Round to the nearest thousandths.

4. A woman put $580 into a savings account for one year. The rate of interest on the account was 6½%. How much was the interest for the year in dollars and cents? (Round to the nearest cent)

5. Manuel found a wrecked Trans-Am that he could fix. He bought the car for 65 ¾ % of the original price of $7200. What did he pay for the car?

6. Ben earns $12,800 a year. About 14.9% is taken out for taxes. How much is taken out for taxes?

7. ** At a sale, shirts were sold for $15 each. This price was 80% of their original price. What was the original price?

Lesson 4: Finding Percents Mentally and Estimating Percents

Learning Target #4 – I can use mental math and estimation to determine the percent of a number.

Example 1: Percents of multiples of ten

(a) 10% of 60 (b) 80% of 50 (c) 30% of 110

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(d) 10% of 76 (e) 1% of 122 (f) 1% of 264

Example 2: Percents of multiple of ¼ s

(a) 75% of 24 (b) 50% of 92 (c) 25% of 64 (d) 75% of 84

Example 3: Percents greater than 100%

(a) 120% of 50 (b) 130% of 90

Example 4: Other types of percents

(a) 23

% of 900 (b) 15% of 700

Example 5: Estimating by rounding. Then use mental math!

(a) 39% of 81 (b) 92% of 51 (c) 63% of 205 (d) 17% of 32

e) Mr. Williams ordered 4 pizzas for a birthday party. The cost of the pizzas was $57.96. He wants to tip the delivery person about 15%. What is a reasonable amount for the tip?

Complete the following without a calculator using mental math

Find the percent of each number

1. 75% of 16 2. 10% of 37 3. 1% of 400

4. 25% of 280 5. 40% of 80 6. 1% of 72

7. 20% of 50 8. 10% of 259 9. 12 ½% of 48

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Estimate – Round then use mental math to solve!

1. 11% of 70 2. 87% of 42 3. 13 % of 598 4. 110 % of 39

5. Last basketball season, Carlos made 38% of the baskets he attempted. At this rate, about how many baskets will he make if he attempts 30 baskets?

6. 16% of 20 7. 148% of 30 8. 194% of 15

9. ½ % of 503 10. 45 % of 30 11. 25% of 49

12. The total cost for Soledad’s manicure was $32.99. She wants to give the manicurist a 20% tip. What would be a reasonable tip?

13. On a family trip, Jenna’s family drove 310 miles from Gainesville to Ft. Lauderdale.a. Her dad drove 52% of the way. About how many miles did he drive?

b. Jenna’s mom drove 58% of the distance her dad drove. About how far did she drive?

c. Her older brother drove the remaining miles. About how many miles did he drive?

Lesson 5: Combining Percents

Learning Target 5: I can solve problems involving percents.

Examples:1. A 32 GB iPhone 7 is regularly priced at $900. Assume GST is 5% and

PST is 7%. Also assume the store is having a 10% sale on all iPhones to clear old stock and make room for the newer version – iPhone 8.

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a) Determine the sale price of the iPhone 7 after the 10% discount.

Method 1 Method 2

b) Write an expression to show how to determine the total amount of tax on the iPhone.

Method 1 Method 2

c) What is the total cost of the iPhone?

2. Walmart has a sale buy three video games at $24.88 each and the forth is free. What is your percent savings on this deal?

3. Suppose GST is 5% and PST is 7% and the regular price of this Plasma TV is $2000.

a) What is the total cost of this TV at its regular price?

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b) Suppose Future Shop is offering 10% off on Friday and an additional 10% off on Saturday. Costco on the other hand is offering a one time 20% discount. Which store offers the better deal?

c) What would Costco’s percent discount have to be if it wanted to offer the same deal Future Shop was offering across the two days?

Complete the following two pages as practice!

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(WITH CALCULATORS!)

off

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(WITH CALCULATORS!)

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Assignment: Practical Math – Combining Percents (for marks)

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