1.4 Fractions: multiplication (Page 2/2)

Page 2 / 2

Sample set b

Perform the following multiplications.

$\frac{4}{5} \cdot \frac{5}{6}$

$\frac{\overset{2}{4}}{\underset{1}{5}} \cdot \frac{\overset{1}{5}}{\underset{3}{6}} = \frac{2 \cdot 1}{1 \cdot 3} = \frac{2}{3}$

Divide 4 and 6 by 2
Divide 5 and 5 by 5

$\frac{8}{12} \cdot \frac{8}{10}$

$\frac{\overset{4}{8}}{\underset{3}{12}} \cdot \frac{\overset{2}{8}}{\underset{5}{10}} = \frac{4 \cdot 2}{3 \cdot 5} = \frac{8}{15}$

Divide 8 and 10 by 2.
Divide 8 and 12 by 4.

$8 \cdot \frac{5}{12} = \frac{\overset{2}{8}}{1} \cdot \frac{5}{\underset{3}{12}} = \frac{2 \cdot 5}{1 \cdot 3} = \frac{10}{3}$

$\frac{35}{18} \cdot \frac{63}{105}$

$\frac{\overset{\overset{1}{7}}{35}}{\underset{2}{18}} \frac{\overset{7}{63}}{\underset{\underset{3}{21}}{105}} = \frac{1 \cdot 7}{2 \cdot 3} = \frac{7}{6}$

$\frac{13}{9} \cdot \frac{6}{39} \cdot \frac{1}{12}$

$\frac{\overset{1}{13}}{9} \cdot \frac{\overset{\overset{1}{2}}{6}}{\underset{\underset{1}{3}}{39}} \cdot \frac{1}{\underset{6}{12}} = \frac{1 \cdot 1 \cdot 1}{9 \cdot 1 \cdot 6} = \frac{1}{54}$

Practice set b

Perform the following multiplications.

$\frac{2}{3} \cdot \frac{7}{8}$

$\frac{7}{12}$

$\frac{25}{12} \cdot \frac{10}{45}$

$\frac{25}{54}$

$\frac{40}{48} \cdot \frac{72}{90}$

$\frac{2}{3}$

$7 \cdot \frac{2}{49}$

$\frac{2}{7}$

$12 \cdot \frac{3}{8}$

$\frac{9}{2}$

$(\frac{13}{7}) (\frac{14}{26})$

$\frac{16}{10} \cdot \frac{22}{6} \cdot \frac{21}{44}$

$\frac{14}{5}$

Multiplication of mixed numbers

Multiplying mixed numbers

To perform a multiplication in which there are mixed numbers, it is convenient to first convert each mixed number to an improper fraction, then multiply.

Sample set c

Perform the following multiplications. Convert improper fractions to mixed numbers.

$1 \frac{1}{8} \cdot 4 \frac{2}{3}$

Convert each mixed number to an improper fraction.

$1 \frac{1}{8} = \frac{8 \cdot 1 + 1}{8} = \frac{9}{8}$

$4 \frac{2}{3} = \frac{4 \cdot 3 + 2}{3} = \frac{14}{3}$

$\frac{\overset{3}{9}}{\underset{4}{8}} \cdot \frac{\overset{7}{14}}{\underset{1}{3}} = \frac{3 \cdot 7}{4 \cdot 1} = \frac{21}{4} = 5 \frac{1}{4}$

$16 \cdot 8 \frac{1}{5}$

Convert $8 \frac{1}{5}$ to an improper fraction.

$8 \frac{1}{5} = \frac{5 \cdot 8 + 1}{5} = \frac{41}{5}$

$\frac{16}{1} \cdot \frac{41}{5}$ .

There are no common factors to divide out.

$\frac{16}{1} \cdot \frac{41}{5} = \frac{16 \cdot 41}{1 \cdot 5} = \frac{656}{5} = 131 \frac{1}{5}$

$9 \frac{1}{6} \cdot 12 \frac{3}{5}$

Convert to improper fractions.

$9 \frac{1}{6} = \frac{6 \cdot 9 + 1}{6} = \frac{55}{6}$

$12 \frac{3}{5} = \frac{5 \cdot 12 + 3}{5} = \frac{63}{5}$

$\frac{\overset{11}{55}}{\underset{2}{6}} \cdot \frac{\overset{21}{63}}{\underset{1}{5}} = \frac{11 \cdot 21}{2 \cdot 1} = \frac{231}{2} = 115 \frac{1}{2}$

$\begin{matrix} \frac{11}{8} \cdot 4 \frac{1}{2} \cdot 3 \frac{1}{8} & = & \frac{11}{8} \cdot \frac{\overset{3}{9}}{\underset{1}{2}} \cdot \frac{\overset{5}{10}}{\underset{1}{3}} \\ = & \frac{11 \cdot 3 \cdot 5}{8 \cdot 1 \cdot 1} = \frac{165}{8} = 20 \frac{5}{8} \end{matrix}$

Practice set c

Perform the following multiplications. Convert improper fractions to mixed numbers.

$2 \frac{2}{3} \cdot 2 \frac{1}{4}$

$6 \frac{2}{3} \cdot 3 \frac{3}{10}$

$7 \frac{1}{8} \cdot 12$

$85 \frac{1}{2}$

$2 \frac{2}{5} \cdot 3 \frac{3}{4} \cdot 3 \frac{1}{3}$

Powers and roots of fractions

Sample set d

Find the value of each of the following.

${(\frac{1}{6})}^{2} = \frac{1}{6} \cdot \frac{1}{6} = \frac{1 \cdot 1}{6 \cdot 6} = \frac{1}{36}$

$\sqrt{\frac{9}{100}}$ . We’re looking for a number, call it ?, such that when it is squared, $\frac{9}{100}$ is produced.

${(?)}^{2} = \frac{9}{100}$

We know that

$3^{2} = 9$ and $10^{2} = 100$

We’ll try $\frac{3}{10}$ . Since

${(\frac{3}{10})}^{2} = \frac{3}{10} \cdot \frac{3}{10} = \frac{3 \cdot 3}{10 \cdot 10} = \frac{9}{100}$

$\sqrt{\frac{9}{100}} = \frac{3}{10}$

$4 \frac{2}{5} \cdot \sqrt{\frac{100}{121}}$

$\frac{\overset{2}{22}}{\underset{1}{5}} \cdot \frac{\overset{2}{10}}{\underset{1}{11}} = \frac{2 \cdot 2}{1 \cdot 1} = \frac{4}{1} = 4$

$4 \frac{2}{5} \cdot \sqrt{\frac{100}{121}} = 4$

Practice set d

Find the value of each of the following.

${(\frac{1}{8})}^{2}$

$\frac{1}{64}$

${(\frac{3}{10})}^{2}$

$\frac{9}{100}$

$\sqrt{\frac{4}{9}}$

$\frac{2}{3}$

$\sqrt{\frac{1}{4}}$

$\frac{1}{2}$

$\frac{3}{8} \cdot \sqrt{\frac{1}{9}}$

$\frac{1}{8}$

$9 \frac{1}{3} \cdot \sqrt{\frac{81}{100}}$

$8 \frac{2}{5}$

$2 \frac{8}{13} \cdot \sqrt{\frac{169}{16}}$

$8 \frac{1}{2}$

Exercises

For the following six problems, use the diagrams to find each of the following parts. Use multiplication to verify your result.

$\frac{3}{4}$ of $\frac{1}{3}$

A rectangle divided into twelve parts in a pattern of four rows and three columns.

$\frac{1}{4}$

A rectangle divided into twelve parts in a pattern of four rows and three columns. Three of the parts are shaded.

$\frac{2}{3}$ of $\frac{3}{5}$

A rectangle divided into twelve parts in a pattern of three rows and four columns.

$\frac{2}{7}$ of $\frac{7}{8}$

A rectangle divided into fifty-six parts in a pattern of seven rows and eight columns.

$\frac{1}{4}$

A rectangle divided into fifty-six parts in a pattern of seven rows and eight columns. Fourteen of the parts are shaded.

$\frac{5}{6}$ of $\frac{3}{4}$

A rectangle divided into twenty-four parts in a pattern of six rows and four columns.

$\frac{1}{8}$ of $\frac{1}{8}$

A rectangle divided into sixty-four parts in a pattern of eight rows and eight columns.

$\frac{1}{64}$

A rectangle divided into sixty-four parts in a pattern of eight rows and eight columns. One part is shaded.

$\frac{7}{12}$ of $\frac{6}{7}$

A rectangle divided into eighty-four parts in a pattern of twelve rows and seven columns.

For the following problems, find each part without using a diagram.

$\frac{1}{2}$ of $\frac{4}{5}$

$\frac{2}{5}$

$\frac{3}{5}$ of $\frac{5}{12}$

$\frac{1}{4}$ of $\frac{8}{9}$

$\frac{2}{9}$

$\frac{3}{16}$ of $\frac{12}{15}$

$\frac{2}{9} of \frac{6}{5}$

$\frac{4}{15}$

$\frac{1}{8} of \frac{3}{8}$

$\frac{2}{3} of \frac{9}{10}$

$\frac{3}{5}$

$\frac{18}{19} of \frac{38}{54}$

$\frac{5}{6} of 2 \frac{2}{5}$

$2$

$\frac{3}{4} of 3 \frac{3}{5}$

$\frac{3}{2} of 2 \frac{2}{9}$

$\frac{10}{3} or 3 \frac{1}{3}$

$\frac{15}{4} of 4 \frac{4}{5}$

$5 \frac{1}{3} of 9 \frac{3}{4}$

$1 \frac{13}{15} of 8 \frac{3}{4}$

$\frac{8}{9} of \frac{3}{4} of \frac{2}{3}$

$\frac{4}{9}$

$\frac{1}{6} of \frac{12}{13} of \frac{26}{36}$

$\frac{1}{2} of \frac{1}{3} of \frac{1}{4}$

$\frac{1}{24}$

$1 \frac{3}{7} of 5 \frac{1}{5} of 8 \frac{1}{3}$

$2 \frac{4}{5} of 5 \frac{5}{6} of 7 \frac{5}{7}$

126

For the following problems, find the products. Be sure to reduce.

$\frac{1}{3} \cdot \frac{2}{3}$

$\frac{1}{2} \cdot \frac{1}{2}$

$\frac{1}{4}$

$\frac{3}{4} \cdot \frac{3}{8}$

$\frac{2}{5} \cdot \frac{5}{6}$

$\frac{1}{3}$

$\frac{3}{8} \cdot \frac{8}{9}$

$\frac{5}{6} \cdot \frac{14}{15}$

$\frac{7}{9}$

$\frac{4}{7} \cdot \frac{7}{4}$

$\frac{3}{11} \cdot \frac{11}{3}$

$\frac{9}{16} \cdot \frac{20}{27}$

$\frac{35}{36} \cdot \frac{48}{55}$

$\frac{28}{33}$

$\frac{21}{25} \cdot \frac{15}{14}$

$\frac{76}{99} \cdot \frac{66}{38}$

$\frac{4}{3}$

$\frac{3}{7} \cdot \frac{14}{18} \cdot \frac{6}{2}$

$\frac{4}{15} \cdot \frac{10}{3} \cdot \frac{27}{2}$

$\frac{14}{15} \cdot \frac{21}{28} \cdot \frac{45}{7}$

$\frac{8}{3} \cdot \frac{15}{4} \cdot \frac{16}{21}$

$7 \frac{13}{21} or \frac{160}{21}$

$\frac{18}{14} \cdot \frac{21}{35} \cdot \frac{36}{7}$

$\frac{3}{5} \cdot 20$

$\frac{8}{9} \cdot 18$

$\frac{6}{11} \cdot 33$

$\frac{18}{19} \cdot 38$

$\frac{5}{6} \cdot 10$

$\frac{25}{3} or 8 \frac{1}{3}$

$\frac{1}{9} \cdot 3$

$5 \cdot \frac{3}{8}$

$\frac{15}{8} =1 \frac{7}{8}$

$16 \cdot \frac{1}{4}$

$\frac{2}{3} \cdot 12 \cdot \frac{3}{4}$

$\frac{3}{8} \cdot 24 \cdot \frac{2}{3}$

$\frac{5}{18} \cdot 10 \cdot \frac{2}{5}$

$\frac{10}{9} =1 \frac{1}{9}$

$\frac{16}{15} \cdot 50 \cdot \frac{3}{10}$

$5 \frac{1}{3} \cdot \frac{27}{32}$

$\frac{9}{2} =4 \frac{1}{2}$

$2 \frac{6}{7} \cdot 5 \frac{3}{5}$

$6 \frac{1}{4} \cdot 2 \frac{4}{15}$

$\frac{85}{6} =14 \frac{1}{6}$

$9 \frac{1}{3} \cdot \frac{9}{16} \cdot 1 \frac{1}{3}$

$3 \frac{5}{9} \cdot 1 \frac{13}{14} \cdot 10 \frac{1}{2}$

$20 \frac{1}{4} \cdot 8 \frac{2}{3} \cdot 16 \frac{4}{5}$

${(\frac{2}{3})}^{2}$

$\frac{4}{9}$

${(\frac{3}{8})}^{2}$

${(\frac{2}{11})}^{2}$

$\frac{4}{121}$

${(\frac{8}{9})}^{2}$

${(\frac{1}{2})}^{2}$

$\frac{1}{4}$

${(\frac{3}{5})}^{2} \cdot \frac{20}{3}$

${(\frac{1}{4})}^{2} \cdot \frac{16}{15}$

$\frac{1}{15}$

${(\frac{1}{2})}^{2} \cdot \frac{8}{9}$

${(\frac{1}{2})}^{2} \cdot {(\frac{2}{5})}^{2}$

$\frac{1}{25}$

${(\frac{3}{7})}^{2} \cdot {(\frac{1}{9})}^{2}$

For the following problems, find each value. Reduce answers to lowest terms or convert to mixed numbers.

$\sqrt{\frac{4}{9}}$

$\frac{2}{3}$

$\sqrt{\frac{16}{25}}$

$\sqrt{\frac{81}{121}}$

$\frac{9}{11}$

$\sqrt{\frac{36}{49}}$

$\sqrt{\frac{144}{25}}$

$\frac{12}{5} = 2 \frac{2}{5}$

$\frac{2}{3} \cdot \sqrt{\frac{9}{16}}$

$\frac{3}{5} \cdot \sqrt{\frac{25}{81}}$

$\frac{1}{3}$

${(\frac{8}{5})}^{2} \cdot \sqrt{\frac{25}{64}}$

${(1 \frac{3}{4})}^{2} \cdot \sqrt{\frac{4}{49}}$

$\frac{7}{8}$

${(2 \frac{2}{3})}^{2} \cdot \sqrt{\frac{36}{49}} \cdot \sqrt{\frac{64}{81}}$

Exercises for review

( [link] ) How many thousands in 342,810?

( [link] ) Find the sum of 22, 42, and 101.

( [link] ) Is 634,281 divisible by 3?

yes

( [link] ) Is the whole number 51 prime or composite?

( [link] ) Reduce $\frac{36}{150}$ to lowest terms.

$\frac{6}{25}$

Questions & Answers

how did the oxygen help a human being

Achol Reply

how did the nutrition help the plants

Achol Reply

Biology is a branch of Natural science which deals/About living Organism.

Ahmedin Reply

what is phylogeny

Odigie Reply

evolutionary history and relationship of an organism or group of organisms

AI-Robot

Deng

what is biology

Hajah Reply

cell is the smallest unit of the humanity biologically

Abraham

what is biology

Victoria Reply

what is biology

Abraham

HOW CAN MAN ORGAN FUNCTION

Alfred Reply

the diagram of the digestive system

Assiatu Reply

allimentary cannel

Ogenrwot

How does twins formed

William Reply

They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together

Oluwatobi

what is genetics

Josephine Reply

Genetics is the study of heredity

Misack

how does twins formed?

Misack

What is manual

Hassan Reply

discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles

Joseph Reply

what is biology

Yousuf Reply

the study of living organisms and their interactions with one another and their environment.

Wine

discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form

Joseph Reply

what is the blood cells

Shaker Reply

list any five characteristics of the blood cells

Shaker

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

Jobilize.com Reply

<< Chapter < Page Page > Chapter >>

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, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6

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

Notification Switch

Would you like to follow the 'Contemporary math applications' conversation and receive update notifications?

Ask

	2 Microeconomics 02 Choice in a World of Scarcity By OpenStax Start Flashcards
	9 Neuroanatomy 09 The Auditory System By Stephen Voron Start Quiz
	Foundations of Software Engineering By Kevin Amaratunga Start Quiz
	2 SCEA Java Architect By JavaChamp Team Start Exam
	5 Biology 05 Plasma Membranes Structure Function By OpenStax Start Quiz
	1 Physiotherapy Flashcards Set 1 By Rhodes Start Flashcards
	19 AP 19 Cardiovascular System Heart MCQ By OpenStax Start Quiz
	2 Week 2 Social Psych By Yacoub Jayoghli Start Quiz
	16 AP Key Terms 16 Neurological Exam By OpenStax Start Key Terms
	4 AP 04 Tissue Level of Organization Essay By OpenStax Start Flashcards