The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.
(a) $ \frac{2}{12} $
(b) $ \frac{3}{15} $
(c) $ \frac{8}{50} $
(d) $ \frac{16}{100} $
(e) $ \frac{10}{60} $
(f) $ \frac{15}{75} $
(g) $ \frac{12}{60} $
(h) $ \frac{16}{96} $
(i) $ \frac{12}{75} $
(j) $ \frac{12}{72} $
(k) $ \frac{3}{18} $
(l) $ \frac{4}{25} $
To do:
We have to change the given fractions to their simplest form.
Solution:
(a) $\frac{2}{12}=\frac{2\times1}{2\times6}$
$=\frac{1}{6}$
Therefore,
The simplest form of \( \frac{2}{12} \) is $\frac{1}{6}$.
(b) $\frac{3}{15}=\frac{3\times1}{3\times5}$
$=\frac{1}{5}$
Therefore,
The simplest form of \( \frac{3}{15} \) is $\frac{1}{5}$.
(c) $\frac{8}{50}=\frac{2\times4}{2\times25}$
$=\frac{4}{25}$
Therefore,
The simplest form of \( \frac{8}{50} \) is $\frac{4}{25}$.
(d) $\frac{16}{100}=\frac{4\times4}{4\times25}$
$=\frac{4}{25}$
Therefore,
The simplest form of \( \frac{16}{100} \) is $\frac{4}{25}$.
(e) $\frac{10}{60}=\frac{10\times1}{10\times6}$
$=\frac{1}{6}$
Therefore,
The simplest form of \( \frac{10}{60} \) is $\frac{1}{6}$.
(f) $\frac{15}{75}=\frac{15\times1}{15\times5}$
$=\frac{1}{5}$
Therefore,
The simplest form of \( \frac{15}{75} \) is $\frac{1}{5}$.
(g) $\frac{12}{60}=\frac{12\times1}{12\times5}$
$=\frac{1}{5}$
Therefore,
The simplest form of \( \frac{12}{60} \) is $\frac{1}{5}$.
(h) $\frac{16}{96}=\frac{16\times1}{16\times6}$
$=\frac{1}{6}$
Therefore,
The simplest form of \( \frac{16}{96} \) is $\frac{1}{6}$.
(i) $\frac{12}{75}=\frac{3\times4}{3\times25}$
$=\frac{4}{25}$
Therefore,
The simplest form of \( \frac{12}{75} \) is $\frac{4}{25}$.
(j) $\frac{12}{72}=\frac{12\times1}{12\times6}$
$=\frac{1}{6}$
Therefore,
The simplest form of \( \frac{12}{72} \) is $\frac{1}{6}$.
(k) $\frac{3}{18}=\frac{3\times1}{3\times6}$
$=\frac{1}{6}$
Therefore,
The simplest form of \( \frac{3}{18} \) is $\frac{1}{6}$.
(l) $\frac{4}{25}$
4 and 25 are co-prime numbers.
This implies,
The simplest form of \( \frac{4}{25} \) is $\frac{4}{25}$.
Therefore,
The three groups of equivalent fractions are
$\frac{1}{6} = (a), (e), (h), (j), (k)$
$\frac{1}{5} = (b), (f), (g)$
$\frac{4}{25} = (c), (d), (i), (l)$
Related Articles
- Solve:(a) \( \frac{1}{18}+\frac{1}{18} \)(b) \( \frac{8}{15}+\frac{3}{15} \)(c) \( \frac{7}{7}-\frac{5}{7} \)(d) \( \frac{1}{22}+\frac{21}{22} \)(e) \( \frac{12}{15}-\frac{7}{15} \)(f) \( \frac{5}{8}+\frac{3}{8} \)(g) \( 1-\frac{2}{3}\left(1=\frac{3}{3}\right) \)(h) \( \frac{1}{4}+\frac{0}{4} \)(i) \( 3-\frac{12}{5} \)
- Write each of the following as decimals:(a) \( \frac{5}{10} \)(b) \( 3+\frac{7}{10} \)(c) \( 200+60+5+\frac{1}{10} \)(d) \( 70+\frac{8}{10} \)(e) \( \frac{88}{10} \)(f) \( 4 \frac{2}{10} \)(g) \( \frac{3}{2} \)(h) \( \frac{2}{5} \)(i) \( \frac{12}{5} \)(j) \( 3 \frac{3}{5} \)(k) \( 4 \frac{1}{2} \)
- Reduce the following fractions to simplest form:(a) \( \frac{48}{60} \)(b) \( \frac{150}{60} \)(c) \( \frac{84}{98} \)(d) \( \frac{12}{52} \)(e) \( \frac{7}{28} \)
- Write four more rational numbers in each of the following patterns:$(i)$. $\frac{-3}{5},\ \frac{-6}{10},\ \frac{-9}{15},\ \frac{-12}{20}$........$(ii)$. $\frac{-1}{4},\ \frac{-2}{8},\ \frac{-3}{12}$.....$(iii)$. $\frac{-1}{6},\ \frac{2}{-12},\ \frac{3}{-18},\ \frac{4}{-24}$......$(iv)$. $\frac{-2}{3},\ \frac{2}{-3},\ \frac{4}{-6},\ \frac{6}{-9}$.....
- Which of the following fractions is the greatest:$\frac{-3}{4} , \frac{5}{12} , \frac{-7}{16} , \frac{3}{24}$.
- Re-arrange suitably and find the sum in each of the following:(i) \( \frac{11}{12}+\frac{-17}{3}+\frac{11}{2}+\frac{-25}{2} \)(ii) \( \frac{-6}{7}+\frac{-5}{6}+\frac{-4}{9}+\frac{-15}{7} \)(iii) \( \frac{3}{5}+\frac{7}{3}+\frac{9}{5}+\frac{-13}{15}+\frac{-7}{3} \)(iv) \( \frac{4}{13}+\frac{-5}{8}+\frac{-8}{13}+\frac{9}{13} \)(v) \( \frac{2}{3}+\frac{-4}{5}+\frac{1}{3}+\frac{2}{5} \)(vi) \( \frac{1}{8}+\frac{5}{12}+\frac{2}{7}+\frac{7}{12}+\frac{9}{7}+\frac{-5}{16} \)
- Classify the following fractions:a)$\frac{3}{2}$b)$3\frac{4}{5}$c)$\frac{4}{2}$d)$\frac{13}{4}$e)$\frac{7}{3}$f)$\frac{21}{5}$g)$\frac{1}{9}$h)$12\frac{3}{7}$i)$3\frac{39}{56}$
- Write the following fractions in decimals:(i) $\frac{8}{10}$ (ii) $\frac{12}{15}$
- Solve(a) \( \frac{2}{3}+\frac{1}{7} \)(b) \( \frac{3}{10}+\frac{7}{15} \)(c) \( \frac{4}{9}+\frac{2}{7} \)(d) \( \frac{5}{7}+\frac{1}{3} \)(e) \( \frac{2}{5}+\frac{1}{6} \)(f) \( \frac{4}{5}+\frac{2}{3} \)(g) \( \frac{3}{4}-\frac{1}{3} \)(h) \( \frac{5}{6}-\frac{1}{3} \)(i) \( \frac{2}{3}+\frac{3}{4}+\frac{1}{2} \)(j) \( \frac{1}{2}+\frac{1}{3}+\frac{1}{6} \)(k) \( 1 \frac{1}{3}+3 \frac{2}{3} \)(l) \( 4 \frac{2}{3}+3 \frac{1}{4} \)(m) \( \frac{16}{5}-\frac{7}{5} \)(n) \( \frac{4}{3}-\frac{1}{2} \)
- Check whether the given fractions are equivalent. (a) \( \frac{5}{9}, \frac{30}{54} \)(b) \( \frac{3}{10}, \frac{12}{50} \)(c) \( \frac{7}{13}, \frac{5}{11} \)
- State the properties illustrated by these statement:$( i)$. $\frac{5}{6} \times 1=1 \times \frac{5}{6}$$( ii)$. $(\frac{-3}{7}) \times \frac{5}{8}=\frac{5}{8} \times(\frac{-3}{7})$$( iii)$. $\frac{-6}{11} \times( \frac{-1}{-18})=( \frac{-1}{-18}) \times \frac{-6}{11}$$( iv)$. $\frac{-4}{5} \times(\frac{5}{12}+\frac{7}{18})=\frac{-4}{5} \times \frac{5}{12}+\frac{-4}{5} \times \frac{7}{18}$$( v)$. $[\frac{3}{8} \times(\frac{-9}{16})] \times \frac{5}{6}=\frac{3}{8} \times[( \frac{-9}{16}) \times \frac{5}{6}]$$( vi)$. $\frac{8}{-13} \times(\frac{-13}{8})=1$$( vii)$. $\frac{12}{19} \times[\frac{-3}{18} \times(\frac{12}{-33})]=[\frac{12}{19} \times( \frac{-3}{18})] \times( \frac{12}{-33})$$( viii)$. $\frac{1}{3} \times(\frac{-7}{11}-\frac{2}{5})=\frac{1}{3} \times(\frac{-7}{11})-\frac{1}{3} \times \frac{2}{5}$
- Simplify:(i) \( \frac{8}{9}+\frac{-11}{5} \)(ii) \( 3+\frac{5}{-7} \)(iii) \( \frac{1}{-12} \) and \( \frac{2}{-15} \)(iv) \( \frac{-8}{19}+\frac{-4}{57} \)(v) \( \frac{7}{9}+\frac{3}{-4} \)(vi) \( \frac{5}{26}+\frac{11}{-39} \)(vii) \( \frac{-16}{9}+\frac{-5}{12} \)(viii) \( \frac{-13}{8}+\frac{5}{36} \)(ix) \( 0+\frac{-3}{5} \)(x) \( 1+\frac{-4}{5} \)(xi) \( \frac{-5}{16}+\frac{7}{24} \)
- Write the simplest form of:(i) \( \frac{15}{75} \)(ii) \( \frac{16}{72} \)(iii) \( \frac{17}{51} \)(iv) \( \frac{42}{28} \)(v) \( \frac{80}{24} \)
- Replace \( \square \) in each of the following by the correct number:(a) \( \frac{2}{7}=\frac{8}{\square} \)(b) \( \frac{5}{8}=\frac{10}{\square} \)(c) \( \frac{3}{5}=\frac{\square}{20} \)(d) \( \frac{45}{60}=\frac{15}{\square} \)(e) \( \frac{18}{24}=\frac{\square}{4} \)
- Write the following fractions as mixed fractions and arrange them in ascending order:$\frac{11}{8} , \frac{17}{12}, \frac{5}{3}, \frac{8}{6} $
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies