Fractions, Percentages, & Percent Review

Fractions, Percentages, & Percent Review

​Dr. Tom Giles

What are the characteristics of a proper fraction?

Characteristics of Fractions:
When the numerator is less than the denominator, the fraction is proper, i.e., less than unity (1). When the reverse is true, e.g., 5/2, the fraction is improper, i.e., greater than unity. When a fraction is written with a whole number, e.g., 3 1/2, the expression is called a mixed number.

Fraction Basics​

a fraction has a NUMERATOR and a DENOMINATOR

​The small piece

​The whole thing

Multiple Choice

What is the denominator?

$$\frac{3}{5}$$  

• 3

• 5

Multiple Choice

In which problem is the numerator greater than 5?

• $$\frac{3}{5}$$

• 4

• $$\frac{7}{3}$$

• $$\frac{1}{8}$$

Fraction Basics​

Express each piece as a fraction

​=

​=

​=

Match

Match the fraction with the correct circle.

1/5

1/4

1/2

1/3

3/4

• 1/5

• 1/4

• 1/2

• 1/3

• 3/4

EQUIVALENT FRACTIONS

​represent the SAME AMOUNT of the whole thing

​What can we do to the first fraction to make it equal to the second fraction?

Match

Match the following

• 1/2

• 1/4

• 2/3

• 3/4

• 4/5

12/24

3/12

18/27

15/20

12/15

• 12/24

• 3/12

• 18/27

• 15/20

• 12/15

Multiple Select

Which fractions below are equivalent to $$\frac{3}{8}$$  ?

(more than one answer)

• $$\frac{6}{16}$$  

• $$\frac{15}{40}$$  

• $$\frac{5}{10}$$  

• $$\frac{9}{17}$$  

• $$\frac{31}{81}$$  

Adding and Subtracting Fractions

Like denominators and unlike denominators

Add Fractions with Like Denominators

• If denominators are the same...

• Add the numerators

• Denominator does not change

Multiple Choice

$$\frac{7}{9}+\frac{1}{9}=$$  

• $$\frac{8}{9}$$  

• $$\frac{6}{9}$$  

• $$\frac{8}{18}$$  

• $$\frac{7}{81}$$  

Multiple Choice

Add.

$$\frac{1}{5}+\frac{3}{5}$$  

• $$\frac{4}{10}$$  

• $$\frac{2}{5}$$  

• $$\frac{4}{5}$$  

Subtract Fractions with Like Denominators

• If denominators are the same...

• Subtract the numerators

• Denominator does not change

Multiple Choice

In order to add or subtract fractions, what needs to be true?

• The fractions have the same numerator

• The fractions have the same denominator

• Combine the numerators and denominators together

• The fractions have different denominators.

Multiple Choice

$$\frac{12}{17}-\frac{5}{17}$$  

• $$\frac{17}{17}$$  

• $$\frac{7}{17}$$  

• $$\frac{6}{17}$$  

• 1

• 0

Multiple Choice

Subtract.

$$\frac{9}{14}-\frac{6}{14}$$  

• $$\frac{3}{14}$$  

• $$\frac{3}{0}$$  

• $$\frac{3}{28}$$  

Finding common denominators (multiples)

• Identify the denominators •

• Write or think of the multiples for each number

• Find the Least Common Denominator

Unlike Denominators

• Find LCM of denominators * Busque LCM

• Multiply numerator and denominator of each fraction by the multiple

• Write the equivalent fractions * Escribe fracciones equivalentes (1/2=5/10)

• Add or subtract the numerators * Agregar o restar las numeradores

Multiple Select

Find a common denominator for the fractions below.

$$\frac{2}{3}+\frac{1}{2}$$  

• 2

• 3

• 6

• 9

Multiple Choice

$$\frac{1}{8}-\frac{1}{6}$$  

What is the Least Common Denominator?

• 8

• 6

• 48

• 14

• 24

Multiple Choice

$$\frac{3}{5}+\frac{10}{15}$$  

What is the Least Common Denominator?

• 5

• 15

• 75

• 20

• 30

Multiple Choice

Is this a correct answer?

$$\frac{2}{5}+\frac{3}{7}=\frac{5}{12}$$  

• Yes, the student correctly added.

• No, you cannot add unlike denominators

• No, 5 + 7 is not 12

• No, 2 + 3 is not 5

Multiple Choice

What is the sum of these fractions?

$$\frac{1}{4}+\frac{3}{5}$$  

• $$\frac{4}{5}$$  

• $$\frac{3}{20}$$  

• $$\frac{17}{20}$$  

• $$\frac{4}{20}$$  

Multiple Choice

$$\frac{9}{15}+\frac{4}{15}$$  

• $$\frac{5}{15}$$  

• $$\frac{1}{5}$$  

• $$\frac{13}{15}$$  

• $$\frac{13}{30}$$  

Multiple Choice

What is the sum of these fractions?

• 4/5

• 3/20

• 17/20

• 4/20

Multiple Choice

Find the difference. 

$$\frac{5}{6}-\frac{1}{3}$$

• $$\frac{1}{2}$$

• $$\frac{3}{3}$$

• $$\frac{3}{18}$$

• $$\frac{1}{54}$$

Multiple Choice

• 1/12

• 1

• 2/35

• 23/25

The first step in multiplying fractions is to put what you're going to be multiplying in the same spot

For example: numerators should be with numerators and denominators should be with denominators

Multiplying Fractions

The second step is to simplify any numbers that you can...but be careful and mindful that you CANNOT simplify any numbers that are on the same line!

Explanation Slide...

​

Multiple Choice

What does reciprocal mean?

• Stay the same

• Flip

Multiple Choice

What is the reciprocal of:

$$\frac{2}{5}$$  

• $$\frac{2}{5}$$  

• $$\frac{5}{2}$$  

Multiple Choice

What is the reciprocal of:

$$\frac{5}{7}$$  

• $$\frac{7}{5}$$  

• 7

• $$\frac{5}{7}$$  

Multiple Choice

What is the reciprocal of 2?

• $$\frac{2}{1}$$  

• 2

• $$\frac{1}{2}$$  

Percentages

Percentages & Percentages Increase/Decrease

Dr. Tom Giles

Percentages

Daily Percentages Use

-Calculating a grade

-MONEY

-Leaving a tip at a restaurant

-Sales and Discounts

-Commission

-Sales Tax and Interest

Multiple Choice

$$\frac{1}{5}$$  of the animals at the zoo are monkeys.   $$\frac{5}{7}$$  of the monkeys are male.  What fraction of the animals at the zoo are male monkeys? (Simplest Form)

• $$\frac{1}{7}$$  
  

• $$\frac{5}{7}$$  
  

• $$\frac{7}{25}$$  
  

• $$\frac{5}{35}$$  

Multiple Choice

Mr. Owen went camping.  He sat outside at the lake for 2  $$\frac{1}{3}$$  hours.  He fell asleep for the last  $$\frac{1}{2}$$  of that time and woke up terribly sunburned.  How long was Mr. Owen asleep?

• 2 hours
  

• 4 $$\frac{2}{3}$$  hours
  

• 2 $$\frac{1}{6}$$  hours
  

• 1  $$\frac{1}{6}$$  hour

Basic Percentage Facts

-Percent = "Per 100" always out of 100

Percents and Decimals:

-Percent to Decimal (divide by 100%)

-Decimal to Percent (multiply by 100%)

Percents and Fractions:

-Percent to Fraction (write over 100%)

-Fraction to Percent (divide numerator by denominator & multiply by 100%)

Multiple Choice

Nurse Sue had  $$\frac{3}{7}$$  cups of laundry detergent.  She used  $$\frac{7}{9}$$  of that detergent to wash a load of dirty socks.  How many cups of laundry detergent did she use?

• $$\frac{27}{49}$$  cups
  

• $$\frac{1}{3}$$  cups
  

• $$\frac{10}{16}$$  cups
  

• $$\frac{5}{8}$$  Cups

Multiple Choice

What is 35% as a decimal?

• 35

• 3.5

• 0.35

• 0.035

Multiple Choice

What is 8% as a decimal?

• 8

• 0.8

• 0.08

• 80

Multiple Choice

What is 0.46 as a percent?

• 46%

• 4.6%

• 0.46%

• 460%

Multiple Choice

What is 0.04 as a percent?

• .4%

• 4%

• 40%

• 400%

Using Percents

To find the percent of a number or amount you need to:

1. Write the percent as a decimal (divide by 100%)

2. Multiply by the number or amount

Multiple Choice

What is 5% of 16?

• 8

• 0.8

• 80

• 11

Multiple Choice

What is 20% of 64?

• 128

• 1.28

• 12.8

• 44

Calculating Grades

How to find your percentage of a grade:

-take the points you earned (top number) and divide by the total points possible (bottom number) and multiply by 100%

Example: You took a Math test and scored 42 points out of 50. What is your percentage?

Multiple Choice

On last night's homework, you scored a 17out of 25. What is your percentage on this homework assignment?

• 80%

• 68%

• 120%

• 83.3%

Multiple Choice

On your quick check, you scored a 9 out of 10. What is your percentage on this quick check?

• 87.5%

• 114%

• 90%

• 70%

Calculating a Tip Amount

Example: You are out to eat with your family at Boondock Eddie's. The total bill was $42.50. If you want to leave a 20% tip, how much money should you leave to pay for the bill and tip combined?

Percentage Increase & Decrease

​Percent Increase: Add the % increase to 100% and multiply by the original amount.

Percent Decrease: Subtract the % decrease from 100% and multiply by the original amount.

Multiple Choice

Discount is ____________ from the price.

The resulting price is lower than the original price.

• subtracted

• added

• multipled

• divided

DISCOUNT TIME

Example: You go to Dollar Tree and want to buy something that costs $50. You have a coupon for 15% off. How much will you have to pay after the discount?

Multiple Choice

You go to Walmart and want to buy a video game for $30. You have a coupon for 10% off. How much do you have to pay after the coupon discount?

• $20

• $27

• $29

• $33

Multiple Choice

You go to Ellis & Chapman's to buy some clothes. You have a coupon for 30% off. If your total is $67, how much will you pay with the coupon?

• $37.00

• $20.10

• $46.90

• $64.00

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