Write four more rational numbers in each of the following patterns:
$(i)$. $\frac{-3}{5},\ \frac{-6}{10},\ \frac{-9}{15},\ \frac{-12}{20}$........
$(ii)$. $\frac{-1}{4},\ \frac{-2}{8},\ \frac{-3}{12}$.....
$(iii)$. $\frac{-1}{6},\ \frac{2}{-12},\ \frac{3}{-18},\ \frac{4}{-24}$......
$(iv)$. $\frac{-2}{3},\ \frac{2}{-3},\ \frac{4}{-6},\ \frac{6}{-9}$.....
Given:
(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) $\frac{-2}{3},\ \frac{2}{-3},\ \frac{4}{-6},\ \frac{6}{-9}$.....
To do: To write four more rational numbers in each of the given patterns.
Solution:
(i) $\frac{-3}{5},\ \frac{-6}{10},\ \frac{-9}{15},\ \frac{-12}{20}$........
This given pattern of rational numbers can be written as below:
$\frac{-3}{5}\times\frac{1}{1},\ -\frac{3}{5}\times\frac{2}{2},\ -\frac{3}{5}\times\frac{3}{3},\ -\frac{3}{5}\times\frac{4}{4}......$
In this sequence, the next four rational numbers can be written as:
$-\frac{3}{5}\times\frac{5}{5},\ -\frac{3}{5}\times\frac{6}{6},\ -\frac{3}{5}\times\frac{7}{7},\ -\frac{3}{5}\times\frac{8}{8}$
Or $-\frac{15}{25},\ -\frac{18}{30},\ -\frac{21}{35},\ -\frac{24}{40}$
(ii) $\frac{-1}{4},\ \frac{-2}{8},\ \frac{-3}{12}.....$
This given pattern of rational numbers can be written as below:
$-\frac{1}{4}\times\frac{1}{1},\ -\frac{1}{4}\times\frac{2}{2},\ -\frac{1}{4}\times\frac{3.}{3}.....$
In this sequence, the next four rational numbers can be written as:
$\frac{-1}{4}\times\frac{4}{4},\ \frac{-1}{4}\times\frac{5}{5},\ \frac{-1}{4}\times\frac{6}{6},\ \frac{-1}{4}\times\frac{7}{7}$
$\frac{-4}{16},\ \frac{-5}{20},\ \frac{-6}{24},\ \frac{-7}{28}$
(iii) $\frac{-1}{6},\ \frac{2}{-12},\ \frac{3}{-18},\ \frac{4}{-24}......$
This given pattern of rational numbers can be written as below:
$\frac{-1}{6}\times\frac{1}{1},\ \frac{-1}{6}\times\frac{2}{2},\ \frac{-1}{6}\times\frac{3}{3},\ \frac{-1}{6}\times\frac{4}{4}$
In this sequence, the next four rational numbers can be written as:
$\frac{-1}{6}\times\frac{5}{5},\ \frac{-1}{6}\times\frac{6}{6},\ \frac{-1}{6}\times\frac{7}{7},\ \frac{-1}{6}\times\frac{8}{8}$
Or $\frac{-5}{30},\ \frac{-1}{36},\ \frac{-7}{42},\ \frac{-8}{48}$
(iv) $\frac{-2}{3},\ \frac{2}{-3},\ \frac{4}{-6},\ \frac{6}{-9}.....$
This given pattern of rational numbers can be written as below:
$\frac{-2}{3}\times\frac{1}{1},\ \frac{2}{-3}\times\frac{1}{1},\ \frac{2}{-3}\times\frac{2}{2},\ \frac{2}{-3}\times\frac{3}{3}......$
In this sequence, the next four rational numbers can be written as:
$\frac{2}{-3}\times\frac{4}{4},\ \frac{2}{-3}\times\frac{5}{5},\ \frac{2}{-3}\times\frac{6}{6},\ \frac{2}{-3}\times\frac{7}{7}$
Or $\frac{8}{-12},\ \frac{10}{-15},\ \frac{12}{-18},\ \frac{14}{-21}$
Related Articles
- Simplify:(i) \( \frac{-3}{2}+\frac{5}{4}-\frac{7}{4} \)(ii) \( \frac{5}{3}-\frac{7}{6}+\frac{-2}{3} \)(iii) \( \frac{5}{4}-\frac{7}{6}-\frac{-2}{3} \)(iv) \( \frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7} \)(v) \( \frac{5}{6}+\frac{-2}{5}-\frac{-2}{15} \)(vi) \( \frac{3}{8}-\frac{-2}{9}+\frac{-5}{36} \)
- 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) \( \frac{4}{3}-\frac{1}{2} \)
- Express each of the following as a rational number of the form $\frac{p}{q}$(i) \( -\frac{8}{3}+\frac{-1}{4}+\frac{-11}{6}+\frac{3}{8}-3 \)(ii) \( \frac{6}{7}+1+\frac{-7}{9}+\frac{19}{21}+\frac{-12}{7} \)(iii) \( \frac{15}{2}+\frac{9}{8}+\frac{-11}{3}+6+\frac{-7}{6} \)(iv) \( \frac{-7}{4}+0+\frac{-9}{5}+\frac{19}{10}+\frac{11}{14} \)(v) \( \frac{-7}{4}+\frac{5}{3}+\frac{-1}{2}+\frac{-5}{6}+2 \)
- 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) \( \frac{1}{8}+\frac{5}{12}+\frac{2}{7}+\frac{7}{12}+\frac{9}{7}+\frac{-5}{16} \)
- Simplify each of the following and write as a rational number of the form:(i) \( \frac{3}{4}+\frac{5}{6}+\frac{-7}{8} \)(ii) \( \frac{2}{3}+\frac{-5}{6}+\frac{-7}{9} \)(iii) \( \frac{-11}{2}+\frac{7}{6}+\frac{-5}{8} \)(iv) \( \frac{-4}{5}+\frac{-7}{10}+\frac{-8}{15} \)(v) \( \frac{-9}{10}+\frac{22}{15}+\frac{13}{-20} \)(vi) \( \frac{5}{3}+\frac{3}{-2}+\frac{-7}{3}+3 \)
- Which is greater in each of the following:$(i)$. $\frac{2}{3},\ \frac{5}{2}$$(ii)$. $-\frac{5}{6},\ -\frac{4}{3}$$(iii)$. $-\frac{3}{4},\ \frac{2}{-3}$$(iv)$. $-\frac{1}{4},\ \frac{1}{4}$$(v)$. $-3\frac{2}{7\ },\ -3\frac{4}{5}$
- Find: (a) $\frac{1}{2}$ of (i) $2\frac{3}{4}$ (ii) $4\frac{2}{9}$(b) $\frac{5}{8}$ of (i) $3\frac{5}{6}$ (ii) $9\frac{2}{3}$
- Write the following rational numbers in ascending order:$(i)$. $\frac{-3}{5},\ \frac{-2}{5},\ \frac{-1}{5}$$(ii)$. $\frac{1}{3},\ \frac{-2}{9},\ \frac{-4}{3}$$(iii)$. $\frac{-3}{7},\ \frac{-3}{2},\ \frac{-3}{4}$
- Solve:(i) $3-\frac{2}{5}$(ii) $4+\frac{7}{8}$(iii) $\frac{3}{5}+\frac{2}{7}$(iv) $\frac{9}{11}-\frac{4}{15}$(v) $\frac{7}{10}+\frac{2}{5}+\frac{3}{2}$(vi) $2\frac{2}{3}+3\frac{1}{2}$(vii) $8\frac{1}{2}-3\frac{5}{8}$
- 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)$. $\frac{1}{3} \times(\frac{-7}{11}-\frac{2}{5})=\frac{1}{3} \times(\frac{-7}{11})-\frac{1}{3} \times \frac{2}{5}$
- Multiply the following fractions:(i) $\frac{2}{5}\times5\frac{1}{4}$(ii) $6\frac{2}{5}\times\frac{7}{9}$(iii) $\frac{3}{2}\times5\frac{1}{3}$(iv) $\frac{5}{6}\times2\frac{3}{7}$(v) $3\frac{2}{5}\times\frac{4}{7}$(vi) $2\frac{3}{5}\times3$(vii) $3\frac{4}{7}\times\frac{3}{5}$
- Name the property used in the following:$[\frac{2}{3}+(\frac{-4}{5})]+\frac{1}{6}=\frac{2}{3}+[(\frac{-4}{5})+\frac{1}{6}]$
- How quickly can you do this? Fill appropriate sign. ( '')(a) \( \frac{1}{2} \square \frac{1}{5} \)(b) \( \frac{2}{4} \square \frac{3}{6} \)(c) \( \frac{3}{5} \square \frac{2}{3} \)(d) \( \frac{3}{4} \square \frac{2}{8} \)(e) \( \frac{3}{5} \square \frac{6}{5} \)(f) \( \frac{7}{9} \square \frac{3}{9} \)(g) \( \frac{1}{4} \square \frac{2}{8} \)(h) \( \frac{6}{10} \square \frac{4}{5} \)(i) \( \frac{3}{4} \square \frac{7}{8} \)(j) \( \frac{6}{10} \square \frac{3}{5} \)(k) \( \frac{5}{7} \square \frac{15}{21} \)
- Take away:(i) \( \frac{6}{5} x^{2}-\frac{4}{5} x^{3}+\frac{5}{6}+\frac{3}{2} x \) from \( \frac{x^{3}}{3}-\frac{5}{2} x^{2}+ \) \( \frac{3}{5} x+\frac{1}{4} \)(ii) \( \frac{5 a^{2}}{2}+\frac{3 a^{3}}{2}+\frac{a}{3}-\frac{6}{5} \) from \( \frac{1}{3} a^{3}-\frac{3}{4} a^{2}- \) \( \frac{5}{2} \)(iii) \( \frac{7}{4} x^{3}+\frac{3}{5} x^{2}+\frac{1}{2} x+\frac{9}{2} \) from \( \frac{7}{2}-\frac{x}{3}- \) \( \frac{x^{2}}{5} \)(iv) \( \frac{y^{3}}{3}+\frac{7}{3} y^{2}+\frac{1}{2} y+\frac{1}{2} \) from \( \frac{1}{3}-\frac{5}{3} y^{2} \)(v) \( \frac{2}{3} a c-\frac{5}{7} a b+\frac{2}{3} b c \) from \( \frac{3}{2} a b-\frac{7}{4} a c- \) \( \frac{5}{6} b c \)
- Multiply and reduce to lowest form (if\ possible):(i) $\frac{2}{3}\times2\frac{2}{3}$(ii) $\frac{2}{7}\times\frac{7}{9}$(iii) $\frac{3}{8}\times\frac{6}{4}$(iv) $\frac{9}{5}\times\frac{3}{5}$(v) $\frac{1}{3}\times\frac{15}{8}$(vi) $\frac{11}{2}\times\frac{3}{10}$(vii) $\frac{4}{5}\times\frac{12}{7}$
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