1.5 Visualize fractions (Page 4/12)

<< Chapter < Page

Elementary algebra

Page 4 / 12

Chapter >> Page >

Find the quotient: $- \frac{7}{27} \div (- \frac{35}{36}) .$

$\frac{4}{15}$

Got questions? Get instant answers now!

Find the quotient: $- \frac{5}{14} \div (- \frac{15}{28}) .$

$\frac{2}{3}$

Got questions? Get instant answers now!

There are several ways to remember which steps to take to multiply or divide fractions. One way is to repeat the call outs to yourself. If you do this each time you do an exercise, you will have the steps memorized.

“To multiply fractions, multiply the numerators and multiply the denominators.”
“To divide fractions, multiply the first fraction by the reciprocal of the second.”

Another way is to keep two examples in mind:

$This is an image with two columns. The first column reads “One fourth of two pizzas is one half of a pizza. Below this are two pizzas side-by-side with a line down the center of each one representing one half. The halves are labeled “one half”. Under this is the equation “2 times 1 fourth”. Under this is another equation “two over 1 times 1 fourth.” Under this is the fraction two fourths and under this is the fraction one half. The next column reads “there are eight quarters in two dollars.” Under this are eight quarters in two rows of four. Under this is the fraction equation 2 divided by one fourth. Under this is the equation “two over one divided by one fourth.” Under this is two over one times four over one. Under this is the answer “8”.$

The numerators or denominators of some fractions contain fractions themselves. A fraction in which the numerator or the denominator is a fraction is called a complex fraction .

Complex fraction

A complex fraction is a fraction in which the numerator or the denominator contains a fraction.

Some examples of complex fractions are:

\frac{\frac{6}{7}}{3} \frac{\frac{3}{4}}{\frac{5}{8}} \frac{\frac{x}{2}}{\frac{5}{6}}

To simplify a complex fraction, we remember that the fraction bar means division . For example, the complex fraction $\frac{\frac{3}{4}}{\frac{5}{8}}$ means $\frac{3}{4} \div \frac{5}{8} .$

Simplify: $\frac{\frac{3}{4}}{\frac{5}{8}} .$

Solution

	$\frac{\frac{3}{4}}{\frac{5}{8}}$
Rewrite as division.	$\frac{3}{4} \div \frac{5}{8}$
Multiply the first fraction by the reciprocal of the second.	$\frac{3}{4} \cdot \frac{8}{5}$
Multiply.	$\frac{3 \cdot 8}{4 \cdot 5}$
Look for common factors.
Divide out common factors and simplify.	$\frac{6}{5}$

Got questions? Get instant answers now!

Simplify: $\frac{\frac{2}{3}}{\frac{5}{6}} .$

$\frac{4}{5}$

Got questions? Get instant answers now!

Simplify: $\frac{\frac{3}{7}}{\frac{6}{11}} .$

$\frac{11}{14}$

Got questions? Get instant answers now!

Simplify: $\frac{\frac{x}{2}}{\frac{x y}{6}} .$

Solution

	$\frac{\frac{x}{2}}{\frac{x y}{6}}$
Rewrite as division.	$\frac{x}{2} \div \frac{x y}{6}$
Multiply the first fraction by the reciprocal of the second.	$\frac{x}{2} \cdot \frac{6}{x y}$
Multiply.	$\frac{x \cdot 6}{2 \cdot x y}$
Look for common factors.
Divide out common factors and simplify.	$\frac{3}{y}$

Got questions? Get instant answers now!

Simplify: $\frac{\frac{a}{8}}{\frac{a b}{6}} .$

$\frac{3}{4 b}$

Got questions? Get instant answers now!

Simplify: $\frac{\frac{p}{2}}{\frac{p q}{8}} .$

$\frac{4}{2 q}$

Got questions? Get instant answers now!

Simplify expressions with a fraction bar

The line that separates the numerator from the denominator in a fraction is called a fraction bar. A fraction bar acts as grouping symbol. The order of operations then tells us to simplify the numerator and then the denominator. Then we divide.

To simplify the expression $\frac{5 - 3}{7 + 1},$ we first simplify the numerator and the denominator separately. Then we divide.

\frac{5 - 3}{7 + 1}

\frac{2}{8}

\frac{1}{4}

Simplify an expression with a fraction bar.

Simplify the expression in the numerator. Simplify the expression in the denominator.
Simplify the fraction.

Simplify: $\frac{4 - 2 (3)}{2^{2} + 2} .$

Solution

$\begin{matrix} \frac{4 - 2 (3)}{2^{2} + 2} \\ \begin{matrix} Use the order of operations to simplify the \\ numerator and the denominator. \end{matrix} & \frac{4 - 6}{4 + 2} \\ Simplify the numerator and the denominator. & \frac{−2}{6} \\ \begin{matrix} Simplify. A negative divided by a positive is \\ negative. \end{matrix} & - \frac{1}{3} \end{matrix}$

Got questions? Get instant answers now!

Simplify: $\frac{6 - 3 (5)}{3^{2} + 3} .$

$- \frac{3}{4}$

Got questions? Get instant answers now!

Simplify: $\frac{4 - 4 (6)}{3^{2} + 3} .$

$- \frac{2}{3}$

Got questions? Get instant answers now!

Where does the negative sign go in a fraction? Usually the negative sign is in front of the fraction, but you will sometimes see a fraction with a negative numerator, or sometimes with a negative denominator. Remember that fractions represent division. When the numerator and denominator have different signs, the quotient is negative.

\begin{matrix} \frac{−1}{3} = - \frac{1}{3} & \frac{negative}{positive} = negative \\ \frac{1}{−3} = - \frac{1}{3} & \frac{positive}{negative} = negative \end{matrix}

For any positive numbers a and b ,

\frac{− a}{b} = \frac{a}{− b} = - \frac{a}{b}

Simplify: $\frac{4 (−3) + 6 (−2)}{−3 (2) - 2} .$

Solution

The fraction bar acts like a grouping symbol. So completely simplify the numerator and the denominator separately.

$\begin{matrix} \frac{4 (−3) + 6 (−2)}{−3 (2) - 2} \\ Multiply. & \frac{−12 + (−12)}{−6 - 2} \\ Simplify. & \frac{−24}{−8} \\ Divide. & 3 \end{matrix}$

Got questions? Get instant answers now!

Simplify: $\frac{8 (−2) + 4 (−3)}{−5 (2) + 3} .$

Got questions? Get instant answers now!

Simplify: $\frac{7 (−1) + 9 (−3)}{−5 (3) - 2} .$

Got questions? Get instant answers now!

Translate phrases to expressions with fractions

Now that we have done some work with fractions, we are ready to translate phrases that would result in expressions with fractions.

Questions & Answers

what is microbiology

Agebe Reply

What is a cell

Odelana Reply

what is cell

Mohammed

how does Neisseria cause meningitis

Nyibol Reply

what is microbiologist

Muhammad Reply

what is errata

Muhammad

is the branch of biology that deals with the study of microorganisms.

Ntefuni Reply

What is microbiology

Mercy Reply

studies of microbes

Louisiaste

when we takee the specimen which lumbar,spin,

Ziyad Reply

How bacteria create energy to survive?

Muhamad Reply

Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments

_Adnan

But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?

Muhamad

they make spores

Louisiaste

what is sporadic nd endemic, epidemic

Aminu Reply

the significance of food webs for disease transmission

Abreham

food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.

Mark

explain assimilatory nitrate reduction

Esinniobiwa Reply

Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).

Elkana

This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products

Elkana

Examples of thermophilic organisms

Shu Reply

Give Examples of thermophilic organisms

Shu

advantages of normal Flora to the host

Micheal Reply

Prevent foreign microbes to the host

Abubakar

they provide healthier benefits to their hosts

ayesha

They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!

Mark

what is cell

faisal Reply

cell is the smallest unit of life

Fauziya

cell is the smallest unit of life

Akanni

Innocent

cell is the structural and functional unit of life

Hasan

is the fundamental units of Life

Musa

what are emergency diseases

Micheal Reply

There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️

_Adnan

define infection ,prevention and control

Innocent

I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life

Lubega

Heyy Lubega hussein where are u from?

_Adnan

en français

Adama

which site have a normal flora

ESTHER Reply

Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract

Safaa

skin

Asiina

skin,Oral,Nasal,GIt

Sadik

How can Commensal can Bacteria change into pathogen?

Sadik

How can Commensal Bacteria change into pathogen?

Sadik

all

Tesfaye

by fussion

Asiina

what are the advantages of normal Flora to the host

Micheal

what are the ways of control and prevention of nosocomial infection in the hospital

Micheal

Got questions? Join the online conversation and get instant answers!

Jobilize.com Reply

<< Chapter < Page Page > Chapter >>

Practice Key Terms 7

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask

	43 Biology 43 Animal Reproduction Development MCQ By OpenStax Start Quiz
	Real Estate Finance Exam 2006 By David Geltner Start Exam
	Social Organization Kinship By Richley Crapo Start Assignment
	NCE Ch 03 Human Growth and Develoment By Anh Dao Start Test
	2 AP Key Terms 02 Chemical Level of Organization By OpenStax Start Key Terms
	18 Sociology 18 Work and the Economy MCQ By OpenStax Start Quiz
	5 AP Key Terms 05 The Integumentary System By OpenStax Start Key Terms
	Interventionism Mixed Economy By Robert Murphy Start Test
	3 CDL Quiz - General Knowledge Part 1 By Jazzycazz Jackson Start Quiz
	3 Business Law MCQ 3 By Maureen Miller Start Exam

1.5 Visualize fractions (Page 4/12)

Complex fraction

Solution

Solution

Simplify expressions with a fraction bar

Simplify an expression with a fraction bar.

Solution

Placement of negative sign in a fraction

Solution

Translate phrases to expressions with fractions

Questions & Answers

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!