Fractions

Fractions

by Luis Bello

​Learning Outcome

​Add and subtract fractions

• Find the common denominator of two or more fractions

• Use the common denominator to add or subtract fractions

• Simplify a fraction to its lowest terms

• Multiply fractions

  • Multiply two or more fractions

  • Multiply a fraction by a whole number

• Divide fractions

  • Find the reciprocal of a number

  • Divide a fraction by a whole number

  • Divide a fraction by a fraction

​Introduction

​Before we get started, here is some important terminology that will help you understand the concepts about working with fractions in this section.

• product: the result of the multiplication

• factor: something being multiplied – for  3⋅2=6, both 3 and 2 are factors of 6

• numerator: the top part of a fraction – the numerator in the fraction 2/3 is 2

• denominator: the bottom part of a fraction – the denominator in the fraction 2/3 is 3

​​Adding Fractions

When you need to add or subtract fractions, you will need to first make sure that the fractions have the same denominator. The denominator tells you how many pieces the whole has been broken into, and the numerator tells you how many of those pieces you are using.

​​Adding Fractions with Unlike Denominators

1. Find a common denominator.

2. Rewrite each fraction using the common denominator.

3. Now that the fractions have a common denominator, you can add the numerators.

4. Simplify by canceling out all common factors in the numerator and denominator.

​​Simplifying a Fraction

Often, if the answer to a problem is a fraction, you will be asked to write it in lowest terms.

​Subtracting Fractions

​When you subtract fractions, you must think about whether they have a common denominator, just like with adding fractions. Below are some examples of subtracting fractions whose denominators are not alike.

​​Multiply Fractions

​

Just as you add, subtract, multiply, and divide when working with whole numbers, you also use these operations when working with fractions.   

​

There are many times when it is necessary to multiply fractions.

​

​Divide Fractions

​There are times when you need to use division to solve a problem.

​

There will also be times when you need to divide by a fraction. Suppose painting a closet with one coat only required 1/2 quart of paint.

​

How many coats could be painted with the 6 quarts of paint? To find the answer, you need to divide 6 by the fraction, 1/2.

​​Before we begin dividing fractions, let’s cover some important terminology.

​

• reciprocal: two fractions are reciprocals if their product is 1

• quotient: the result of the division

• ​Dividing fractions requires using the reciprocal of a number or fraction. If you multiply two numbers together and get 1 as a result, then the two numbers are reciprocals. Here are some examples of reciprocals.

• ​Dividing is Multiplying by the Reciprocal. For all division, you can turn the operation into multiplication by using the reciprocal. Dividing is the same as multiplying by reciprocal.

Multiple Choice

FInd the sum.

$$\frac{1}{4}+\ \frac{1}{2}$$  

• $$\frac{1}{6}$$  

• $$\frac{1}{8}$$  

• $$\frac{1}{2}$$  

• $$\frac{3}{4}$$  

Multiple Choice

Find the sum.

$$\frac{4}{5}\ +\ \frac{1}{3}$$  

• $$\frac{5}{8}$$  

• $$1\ \frac{2}{15}$$  

• $$\frac{7}{15}$$  

• $$\frac{2}{15}$$  

Multiple Choice

Find the sum.

$$\frac{1}{4}\ +\ \frac{3}{6}=$$  

• $$\frac{9}{12}$$  

• $$\frac{3}{10}$$  

• $$\frac{3}{12}$$  

• 1

Multiple Choice

$$4\ \frac{7}{8\ }$$  +  $$\frac{1}{8}$$  

• 5

• $$5\frac{1}{8}$$  

• $$5\ \frac{8}{8}$$  

Multiple Choice

$$4\ \frac{7}{8}$$  +  $$\frac{1}{4}$$  

• 5
  

• $$5\ \frac{1}{8}$$  

• $$5\ \frac{2}{8}$$  

Multiple Choice

$$\frac{8}{9}\ -\ \frac{1}{3}\ =\$$  

• $$\frac{7}{6}$$  

• $$\frac{5}{9}$$  

• $$\frac{2}{3}$$  

• $$\frac{8}{27}$$  

Multiple Choice

What is  $$\frac{8}{9}$$  -  $$\frac{5}{6}$$ =  ?

• $$\frac{6}{7}$$  

• $$\frac{3}{4}$$  

• $$\frac{1}{18}$$  

• $$\frac{10}{12}$$  

Multiple Choice

$$\frac{18}{6}-\frac{3}{6}$$  

• $$\frac{15}{6}$$  

• $$2\frac{3}{6}$$  

• $$\frac{12}{6}$$  

• $$\frac{5}{6}$$  

Open Ended

$$\frac{20}{3}-\frac{15}{3}$$  

Multiple Choice

• 3/8
• 3-1/8
• 1/24
• 4/8

Multiple Choice

• 1/5 x 8 = 8/5
• 2/5 x 8 = 16/5
• 1/5 x 4 = 4/5
• 2/5 + 4 = 6/5

Multiple Choice

Solve. Make sure answer is in simpliest form

• $$\frac{5}{15}$$  

• $$\frac{6}{25}$$  

• $$\frac{3}{50}$$  

• $$\frac{3}{25}$$  

Multiple Choice

Solve. Make sure answer is in simplest form.

• $$\frac{5}{8}$$

• $$\frac{8}{10}$$

• $$\frac{15}{8}$$

• $$\frac{8}{24}$$

Multiple Choice

Solve. Make sure answer is in simplest form.

• $$2\frac{1}{2}$$

• $$5\frac{1}{4}$$

• $$3\frac{1}{2}$$

• $$6\frac{ }{ }$$

Multiple Choice

¹/₄  ÷  ¹/₂

• ²/₆
• ¹/₈
• ³/₅
• ²/₄

Multiple Choice

¹/₄  ÷  ²/₅

• ⁵/₈
• 2/20
• ¹/₁₀
• ³/₉

Multiple Choice

Divide. 8 ÷ 1/3

• 24
• 2  2/3
• 3/8
• 1/24

Explanation Slide...

Similar Example:

Multiple Choice

¹/₄  ÷  ²/₅

• ⁵/₈
• 2/20
• ¹/₁₀
• ³/₉

Explanation Slide...

Example: Remember when you have an improper fraction the numerator goes inside the house of division and the denominator stays outside the house of division.

Multiple Choice

What is the recriprocal of 4/5

• 4/5
• 5/4
• 5/1
• 1/5

Explanation Slide...

Example:

Multiple Choice

What is another name of flip?

• Flip
• Reciprocal

Multiple Choice

Find the reciprocal1/8

• 8
• 1/8

Multiple Choice

What is the reciprocal of the mixed number above?

• 25/6

• 6/25

• 4 6/1

Multiple Choice

Convert the mixed number to an improper fraction

• 8/5
• 7/5
• 6/5
• 13/5

Multiple Choice

Convert the mixed number to an improper fraction

• 7/2
• 8/2
• 9/2
• 5/2

Multiple Choice

Which mixed number does the model represent?

• 1  2/7
• 1  3/8
• 1  3/7
• 1  5/7

Multiple Choice

Which of the following is an improper fraction?

• 2/3
• 3/2
• 1  2/3
• 1/3

Multiple Choice

What fraction is shown in the picture?

• 50/10

• 5/100

• 5/10

Multiple Choice

Convert into an improper fraction.

• 28/7
• 29/4
• 29/7
• 7/1

Multiple Choice

Which mixed number is represented by the model?

• 3  1/4
• 3 4/1
• 3  3/4
• 4  1/4

Multiple Choice

Write the improper fraction as a mixed number in simplest form.
⁷/₃ =

• 2¹/₃
• 1³/₇
• 2³/₇
• 1⁴/₃