All Things Fractions

Introduction to Fractions

Objective: Understand and successfully complete calculations with equivalent fractions

​Dr. Tom Giles

Multiple Choice

What fraction of the rectangle is shaded?

• $$\frac{3}{4}$$  

• $$\frac{1}{4}$$  

• $$\frac{1}{3}$$  

• $$\frac{4}{3}$$  

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

​=

​=

​=

Fill in the Blanks

Write a fraction that represents the pink part of the circle.

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?

​Some answers to the previous question

Fill in the Blanks

Rewrite the given fractions as equivalent fractions given the indicated denominator.

$\frac{3}{7}=\frac{?}{21}$  

Fill in the Blanks

Rewrite the given fractions as equivalent fractions given the indicated denominator.

$\frac{?}{9}=\frac{14}{18}$  

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

The Basics

• Numerator: Top of fraction (dividend)

• Denominator: Bottom of fraction (divisor)

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 • Identificar los denominadores

• Write or think of the multiples for each number • Escribe los multiplicars

• Find the Least Common Denominator • Busque el denomindor en común

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!

Fill in the Blanks

What is the product of these two fractions?

Explanation Slide...

​

Fill in the Blanks

What is the product of these fractions?

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

• $$\frac{1}{2}$$  

Multiple Choice

What would this division sentence look like if you were solving it using a reciprocal?

$$\frac{2}{3}\div\frac{4}{5}$$  

• $$\frac{2}{3}\times\frac{4}{5}$$  

• $$\frac{3}{2}\times\frac{4}{5}$$  

• $$\frac{2}{3}\times\frac{5}{4}$$  

Explanation Slide...

​

Fill in the Blanks

What is the quotient of dividing these two fractions?

(Hint: Multiply by the reciprocal.)

Explanation Slide...

​

Fill in the Blanks

Find the quotient.

Explanation Slide...

​

Fill in the Blanks

Find the quotient.

Explanation Slide...

​

Fill in the Blanks

No spaces

Explanation Slide...

​

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

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