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MATHS 3 Marks Question

Simplification · Rajasthan Board (RBSE) STD 6 (Rajasthan - English Medium). 7 questions.

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3 Marks Question

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7 questions · self-marked practice — reveal the answer and mark yourself.

Question 13 Marks
Simplify: $4\frac{1}{10}-\Big[2\frac{1}{2}-\Big\{\frac{5}{6}-\Big(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\Big)\Big\}\Big]$
Answer
Given expression: $=4\frac{1}{10}-\Big[2\frac{1}{2}-\Big\{\frac{5}{6}-\Big(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\Big)\Big\}\Big]$
$=\frac{41}{10}-\Big[\frac{5}{2}-\Big\{\frac{5}{6}-\Big(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\Big)\Big\}\Big]$
$=\frac{41}{10}-\Big[\frac{5}{2}-\Big\{\frac{5}{6}-\Big(\frac{12+9-8}{30}\Big)\Big\}\Big]$
$=\frac{41}{10}-\Big[\frac{5}{2}-\Big\{\frac{5}{6}-\frac{13}{30}\Big\}\Big]$ (Removing parentheses)
$=\frac{41}{10}-\Big[\frac{5}{2}-\Big\{\frac{25-13}{30}\Big\}\Big]$
$=\frac{41}{10}-\Big[\frac{5}{2}-\frac{12}{30}\Big]$ (Removing braces)
$=\frac{41}{10}=\Big[\frac{75-12}{30}\Big]$
$=\frac{41}{10}-\frac{63}{30}$ (Removing square brackets)
$=\frac{123-63}{30}=\frac{60}{30}=2$
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Question 23 Marks
Simplify: $4\frac{4}{5}\div\frac{3}{5}\ \text{ of }5+\frac{4}{5}\times\frac{3}{10}-\frac{1}{5}$
Answer
Given expression: $4\frac{4}{5}\div\frac{3}{5}\ \text{ of }5+\frac{4}{5}\times\frac{3}{10}-\frac{1}{5}$
$=4\frac{4}{5}\div\frac{3}{5}\times\frac{5}{1}+\frac{4}{5}\times\frac{3}{10}-\frac{1}{5}$ (Removing 'of ')
$=\frac{24}{5}\div\frac{3}{1}+\frac{4}{5}\times\frac{3}{10}-\frac{1}{5}$
$=\frac{24}{5}\times\frac{1}{3}+\frac{4}{5}\times\frac{3}{10}-\frac{1}{5}$ (Removing $'÷')$
$=\frac{8}{5}+\frac{4}{5}\times\frac{3}{10}-\frac{1}{5}$ (Removing $'\times ')$
$=\frac{8}{5}+\frac{6}{25}-\frac{1}{5}$ (Removing $'\times ')$
$=\frac{40+6-5}{25}=\frac{41}{25}=1\frac{16}{25}$
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Question 33 Marks
Simplify: $\Big(\frac{2}{3}+\frac{4}{9}\Big)\text{ of }\frac{3}{5}\div1\frac{2}{3}\times1\frac{1}{4}-\frac{1}{3}$
Answer
Given expression: $\Big(\frac{2}{3}+\frac{4}{9}\Big)\text{ of }\frac{3}{5}\div1\frac{2}{3}\times1\frac{1}{4}-\frac{1}{3}$
$=\Big(\frac{6+4}{9}\Big)\ \text{ of }\frac{3}{5}\div1\frac{2}{3}\times1\frac{}{4}-\frac{1}{3}$ (Removing parentheses)
$=\frac{10}{9}\times\frac{3}{5}\div1\frac{2}{3}\times1\frac{1}{4}-\frac{1}{3}$ (Removing 'of ')
$=\frac{2}{3}\div\frac{5}{3}\times1\frac{1}{4}-\frac{1}{3}$
$=\frac{2}{3}\times\frac{3}{5}\times\frac{5}{4}-\frac{1}{3}$ (Removing $'÷')$
$=\frac{1}{2}-\frac{1}{3}$(Removing $'\times ')$
$=\frac{(3-2)}{6}=\frac{1}{6}$
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Question 43 Marks
Simplify: $7\frac{1}{3}\div\frac{2}{3}\text{ of }2\frac{1}{5}+1\frac{3}{8}\div2\frac{3}{4}-1\frac{1}{2}$
Answer
Given expression: $7\frac{1}{3}\div\frac{2}{3}\text{ of }2\frac{1}{5}+1\frac{3}{8}\div2\frac{3}{4}-1\frac{1}{2}$
$=\frac{22}{3}\div\frac{2}{3}\text{ of }\frac{11}{5}+\frac{11}{8}\div\frac{11}{4}-\frac{3}{2}$
$=\frac{22}{3}\div\frac{2}{3}\times\frac{11}{5}+\frac{11}{8}\div\frac{11}{4}-\frac{3}{2}$ (Removing 'of')
$=\frac{22}{3}\div\frac{22}{15}+\frac{11}{8}\div\frac{11}{4}-\frac{3}{2}$
$=\frac{22}{3}\times\frac{15}{22}+\frac{11}{8}\div\frac{11}{4}-\frac{3}{2}$ (Removing $'÷')$
$=5+\frac{11}{8}\times\frac{4}{11}-\frac{3}{2}$ (Removing $'÷')$
$=5+\frac{1}{2}-\frac{3}{2}$ (On simplifying)
$=\frac{10+1-3}{2}=\frac{8}{2}=4$
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Question 53 Marks
Simplify: $9\frac{3}{4}\div\Big[2\frac{1}{6}+\Big\{4\frac{1}{3}-\Big(1\frac{1}{2}+1\frac{3}4{}\Big)\Big\}\Big]$
Answer
Given expression: $=9\frac{3}{4}\div\Big[2\frac{1}{6}+\Big\{4\frac{1}{3}-\Big(1\frac{1}{2}+1\frac{3}4{}\Big)\Big\}\Big]$
$=\frac{39}{4}\div\Big[\frac{13}{6}+\Big\{\frac{13}{3}-\Big(\frac{3}{2}+\frac{7}{4}\Big)\Big\}\Big]$
$=\frac{39}{4}\div\Big[\frac{13}{6}+\Big\{\frac{13}{3}-\Big(\frac{6+7}{4}\Big)\Big\}\Big]$
$=\frac{39}{4}\div\Big[\frac{13}{6}+\Big\{\frac{13}{3}-\frac{13}{4}\Big\}\Big]$(Removing parentheses)
$=\frac{39}{4}\div\Big[\frac{13}{6}+\Big\{\frac{52-39}{12}\Big\}\Big]$
$=\frac{39}{4}\div\Big[\frac{13}{6}+\frac{13}{12}\Big]$(Removing braces)
$=\frac{39}{4}\div\Big[\frac{26+13}{12}\Big]$
$=\frac{39}{4}\div\frac{39}{12}$ (Removing square brackets)
$=\frac{39}{4}\times\frac{12}{39}=3$ (Removing $'÷')$
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Question 63 Marks
Simplify: $5\frac{1}{7}-\Big\{3\frac{3}{10}\div\Big(2\frac{4}{5}-\frac{7}{10}\Big)\Big\}$
Answer
Given expression: $5\frac{1}{7}-\Big\{3\frac{3}{10}\div\Big(2\frac{4}{5}-\frac{7}{10}\Big)\Big\}$
$=\frac{36}{7}-\Big\{\frac{33}{10}\div\Big(\frac{14}{5}-\frac{7}{10}\Big)\Big\}$
$=\frac{36}{7}-\Big\{\frac{33}{10}\div\Big(\frac{28-7}{10}\Big)\Big\}$
$=\frac{36}{7}-\Big\{\frac{33}{10}\div\frac{21}{10}\Big\}$ (Removing parentheses)
$=\frac{36}{7}-\Big\{\frac{33}{10}\div\frac{10}{21}\Big\}$ (Removing $'÷')$
$=\frac{36}{7}-\frac{11}{7}$ (Removing braces)
$=\frac{36-11}{7}=\frac{25}{7}=3\frac{4}{7}$ (Simplifying)
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Question 73 Marks
Simplify: $1\frac{5}{6}+\Big[2\frac{2}{3}-\Big\{3\frac{3}{4}\Big(3\frac{4}{5}\div9\frac{1}{2}\Big)\Big\}\Big]$
Answer
Given expression: $=1\frac{5}{6}+\Big[2\frac{2}{3}-\Big\{3\frac{3}{4}\Big(3\frac{4}{5}\div9\frac{1}{2}\Big)\Big\}\Big]$
$=\frac{11}{6}+\Big[\frac{8}{3}-\Big\{\frac{15}{4}\Big(\frac{19}{5}\div\frac{19}{2}\Big)\Big\}\Big]$
$=\frac{11}{6}+\Big[\frac{8}{3}-\Big\{\frac{15}{4}\Big(\frac{19}{5}\times\frac{2}{9}\Big)\Big\}\Big]$
$=\frac{11}{6}+\Big[\frac{8}3{}-\Big\{\frac{15}{4}\times\frac{2}{5}\Big\}\Big]$
$=\frac{11}{6}+\Big[\frac{8}{3}-\frac{3}{2}\Big]$
$=\frac{11}{6}+\Big[\frac{16-9}{6}\Big]$
$=\frac{11}{6}+\frac{7}{6}$
$=\frac{18}{6}=3$
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