Question 12 Marks
Find the product: $7\frac{1}{2}\times2\frac{4}{15}$
Answer
View full question & answer→We have, $7\frac{1}{2}\times2\frac{4}{15}$ $=\frac{15}{2}\times\frac{34}{15}$ $=\frac{15\times34}{2\times15}$ $=\frac{510}{30}$ $=17$
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Question 22 Marks
Compare the following fractions by using the symbo $>$ or $<$ or = $\frac{11}{9}\text{ and }\frac{5}{9}$
Answer
View full question & answer→We have, $\frac{11}{9}\text{ and }\frac{5}{9}$
The given fractions are equivalent fractions as the denominators are equal, And we know that, $11 > 5$
Therefore, $119 > 59$
The given fractions are equivalent fractions as the denominators are equal, And we know that, $11 > 5$
Therefore, $119 > 59$
Question 32 Marks
Simplify: $7\frac{5}{6}-4\frac{3}{8}+2\frac{7}{12}$
Answer
View full question & answer→We have, $7\frac{5}{6}-4\frac{3}{8}+2\frac{7}{12}$
$=\frac{47}{6}-\frac{35}{8}+\frac{31}{12}$
Taking out the $LCM$ of $6, 8$ and $12$ we get, $2 \times 2 \times 2 \times 3 = 48$
Now, we convert the given fractions to equivalent fraction by making the denominators $48$
we get, $\frac{47\times8}{6\times8}-\frac{35\times6}{8\times6}+\frac{31\times4}{12\times4}$
$=\frac{376}{48}-\frac{210}{48}+\frac{124}{48}$
$=\frac{376-210+124}{48}$
$=\frac{290}{48}$
$=\frac{145}{24}$
$=\frac{47}{6}-\frac{35}{8}+\frac{31}{12}$
Taking out the $LCM$ of $6, 8$ and $12$ we get, $2 \times 2 \times 2 \times 3 = 48$
Now, we convert the given fractions to equivalent fraction by making the denominators $48$
we get, $\frac{47\times8}{6\times8}-\frac{35\times6}{8\times6}+\frac{31\times4}{12\times4}$
$=\frac{376}{48}-\frac{210}{48}+\frac{124}{48}$
$=\frac{376-210+124}{48}$
$=\frac{290}{48}$
$=\frac{145}{24}$
Question 42 Marks
Multiply: $\frac{3}{5}\text{ by }{25}$
Answer
View full question & answer→We have, $\frac{3}{5}\text{ by }{25}$ $=\frac{3}{5}\times25$ $=15$
Question 52 Marks
By selling oranges at the rate of $₹\ 5\frac{1}{4}$ per orange, a fruit-seller gets $₹ 630$. How many dozens of oranges does he sell?
Answer
View full question & answer→By selling oranges at the rate of $₹\ 5\frac{1}{4}$ per orange, a fruit-seller gets $₹ 630.$
$5\Big(\frac{1}{4}\Big)=2\Big(\frac{1}{4}\Big)$ Number of oranges for $₹\ \frac{21}{4}=1$
Number of oranges for $₹\ 1=\frac{4}{21}$
Number of oranges for $₹ 630$ $=\frac{4}{21}\times630=120\text{ apples}$
$12$ apples $= 1$ dozen Therefore, $120$ apples $= 10$ dozen
$5\Big(\frac{1}{4}\Big)=2\Big(\frac{1}{4}\Big)$ Number of oranges for $₹\ \frac{21}{4}=1$
Number of oranges for $₹\ 1=\frac{4}{21}$
Number of oranges for $₹ 630$ $=\frac{4}{21}\times630=120\text{ apples}$
$12$ apples $= 1$ dozen Therefore, $120$ apples $= 10$ dozen
Question 62 Marks
Find:$\frac{3}{7}\text{ of }42\text{ litres}$
Answer
View full question & answer→We have, $\frac{3}{7}\text{ of }42\text{ litres}$ $=\frac{3}{7}\times42\text{ litres}$ $=3\times6\text{ litres}$ $=18\text{ litres}$
Question 72 Marks
Divide:
$3\frac{1}{4}\text{ by }\frac{2}{3}$
$3\frac{1}{4}\text{ by }\frac{2}{3}$
Answer
View full question & answer→ $3\frac{1}{4}\text{ by }\frac{2}{3}$
$=\frac{3\frac{1}{4}}{\frac{2}{3}}$
$=\frac{\frac{13}{4}}{\frac{2}{3}}$
$=\frac{13\times3}{4\times2}$
$=\frac{39}{8}$
$=4\frac{7}{8}$
$=\frac{3\frac{1}{4}}{\frac{2}{3}}$
$=\frac{\frac{13}{4}}{\frac{2}{3}}$
$=\frac{13\times3}{4\times2}$
$=\frac{39}{8}$
$=4\frac{7}{8}$
Question 82 Marks
Find:$\frac{7}{11}\text{ of }₹\ 330$
Answer
View full question & answer→We have, $\frac{7}{11}\text{ of }330$ $=\frac{7}{11}\times330$ $=7\times30$ $=210$
Question 92 Marks
A sugar bag contains $30\ kg$ of sugar. After consuming $\frac{2}{3}$ of it, how much sugar is left in the bag?
Answer
View full question & answer→Given, A sugar bag contains $30\ kg$ of sugar After consuming $23$ of it, the amount of sugar left in the bag,
$=30\text{kg}-\frac{2}{3}\times30\text{kg}$
$=30\text{kg}-20\text{kg}$
$=10\text{kg}$
$=30\text{kg}-\frac{2}{3}\times30\text{kg}$
$=30\text{kg}-20\text{kg}$
$=10\text{kg}$
Question 102 Marks
Find the difference:
$8-\frac{5}{9}$
$8-\frac{5}{9}$
Answer
View full question & answer→ We have,
$8-\frac{5}{9}$
$=\frac{8\times9-5}{9}$
$=\frac{72-5}{9}$
$=\frac{67}{9}$
$8-\frac{5}{9}$
$=\frac{8\times9-5}{9}$
$=\frac{72-5}{9}$
$=\frac{67}{9}$
Question 112 Marks
In mid-day meal scheme $\frac{3}{10}$ litre of milk is given to each student of a primary school. If $30$ litres of milk is distributed every day in the school, how many students are there in the school?
Answer
View full question & answer→Number of students in the school $=\frac{\text{Total amount of milk distributed per day}}{\text{Amount of milk given to one student}}$ $=30\div\frac{3}{10}$ $=30\times\frac{10}{3}$ $=100$
Question 122 Marks
Simplify:
$\frac{10}{27}\times\frac{39}{56}\times\frac{28}{65}$
$\frac{10}{27}\times\frac{39}{56}\times\frac{28}{65}$
Answer
View full question & answer→ We have,
$\frac{10}{27}\times\frac{39}{56}\times\frac{28}{65}$
$=\frac{10\times39\times28}{27\times56\times65}$
$=\frac{10920}{98280}$
$=\frac{1}{9}$
$\frac{10}{27}\times\frac{39}{56}\times\frac{28}{65}$
$=\frac{10\times39\times28}{27\times56\times65}$
$=\frac{10920}{98280}$
$=\frac{1}{9}$
Question 132 Marks
Find:$\frac{1}{2}\text{ of }4\frac{2}{9}$
Answer
View full question & answer→We have, $\frac{1}{2}\text{ of }4\frac{2}{9}$ $=\frac{1}{2}\times\frac{38}{9}$ $=\frac{38}{18}$ $=2\frac{1}{9}$
Question 142 Marks
Find the difference:
$9-5\frac{2}{3}$
$9-5\frac{2}{3}$
Answer
View full question & answer→ We have,
$9-5\frac{2}{3}$
$=9-\frac{17}{3}$
$=\frac{9\times3-17}{3}$
$=\frac{27-17}{3}$
$=\frac{10}{3}$
$9-5\frac{2}{3}$
$=9-\frac{17}{3}$
$=\frac{9\times3-17}{3}$
$=\frac{27-17}{3}$
$=\frac{10}{3}$
Question 152 Marks
Simplify: $5\frac{4}{7}\div1\frac{3}{10}$
Answer
View full question & answer→$5\frac{4}{7}\div1\frac{3}{10}$ $=\frac{39}{7}\div\frac{13}{10}$ $=\frac{39\times10}{7\times13}$ $=\frac{390}{91}$ $=4\frac{2}{7}$
Question 162 Marks
Find the difference:
$4\frac{3}{10}-1\frac{2}{15}$
$4\frac{3}{10}-1\frac{2}{15}$
Answer
View full question & answer→We have,
$4\frac{3}{10}-1\frac{2}{15}$
$=\frac{43}{10}-\frac{17}{15}$
Taking out the $LCM$ of $10$ and $15,$ we get
$2 \times 3 \times 5 = 30$
Now, we convert the given fractions to equivalent fractions by marking the denominators $30$
$=\frac{43\times3}{10\times3}-\frac{17\times2}{15\times2}$
$=\frac{129-34}{30}$
$=\frac{129-34}{30}$
$=\frac{95}{30}$
$=\frac{19}{6}$
$4\frac{3}{10}-1\frac{2}{15}$
$=\frac{43}{10}-\frac{17}{15}$
Taking out the $LCM$ of $10$ and $15,$ we get
$2 \times 3 \times 5 = 30$
Now, we convert the given fractions to equivalent fractions by marking the denominators $30$
$=\frac{43\times3}{10\times3}-\frac{17\times2}{15\times2}$
$=\frac{129-34}{30}$
$=\frac{129-34}{30}$
$=\frac{95}{30}$
$=\frac{19}{6}$
Question 172 Marks
Write five equivalent fractions of $\frac{3}{5}$
Answer
View full question & answer→Multiplying or dividing both the numerator and denominator by the same number,
So, that the fraction keeps its value.
So, the equivalent fractions of $\frac{3}{5}$ are $\frac{3\times2}{5\times2},\frac{3\times3}{5\times3},\frac{3\times4}{5\times4},\frac{3\times5}{5\times5},\frac{3\times5}{5\times6}$
$\frac{6}{10},\frac{9}{15},\frac{12}{20},\frac{15}{25},\frac{18}{30}$ Are the five equivalent fractions of $\frac{3}{5}$
So, that the fraction keeps its value.
So, the equivalent fractions of $\frac{3}{5}$ are $\frac{3\times2}{5\times2},\frac{3\times3}{5\times3},\frac{3\times4}{5\times4},\frac{3\times5}{5\times5},\frac{3\times5}{5\times6}$
$\frac{6}{10},\frac{9}{15},\frac{12}{20},\frac{15}{25},\frac{18}{30}$ Are the five equivalent fractions of $\frac{3}{5}$
Question 182 Marks
Lipika reads a books for $1\frac{3}{4}$ hours everyday. She reads the entire book in $6$ days. How many hours in all were required by her to read the book?
Answer
View full question & answer→Given, Time taken by Lipika to read a book per day $=13\Big(\frac{3}{4}\Big)=\frac{7}{4}$ hours Time taken by Lipika to read a book for $6$ days. $=\frac{7}{4}\times6=\frac{42}{4}=10\frac{1}{2}\text{ hours}$
Question 192 Marks
A wire of length $12\frac{1}{2}\text{m}$ is cut into $10$ pieces of equal length. find the length. Find the length of each piece.
Answer
View full question & answer→Given, $12\frac{1}{2}\text{m}=\frac{25}{2}\text{m}$
$10$ pieces of wire $=\frac{25}{2}\text{m}$
$1$ piece of wire $=\frac{\frac{25}{2}}{10}$
$=\frac{25}{20}$
$=\frac{5}{4}$
$=1\frac{1}{4}$
$10$ pieces of wire $=\frac{25}{2}\text{m}$
$1$ piece of wire $=\frac{\frac{25}{2}}{10}$
$=\frac{25}{20}$
$=\frac{5}{4}$
$=1\frac{1}{4}$
Question 202 Marks
Find:$\frac{1}{12}\text{ of an hour}$
Answer
View full question & answer→We have, $\frac{1}{12}\text{ of an hour}$ An hour $= 60$
minutes $\therefore\ \frac{1}{12}\times60\text{ minutes}$
$=5\text{ minutes}$
minutes $\therefore\ \frac{1}{12}\times60\text{ minutes}$
$=5\text{ minutes}$
Question 212 Marks
Simplify: $\frac{3}{10}\div\frac{10}{3}$
Answer
View full question & answer→$\frac{3}{10}\div\frac{10}{3}$ $=\frac{3\times3}{10\times10}$ $=\frac{9}{100}$
Question 222 Marks
Each side of a square is $6\frac{2}{3}\text{m}$ long. Find its area.
Answer
View full question & answer→Given, Each side $=6\frac{2}{3}\text{m}=\frac{20}{3}\text{m}$ $\text{Area}=\text{side}^2=\Big(\frac{20}{3}\Big)^2\text{m}^2$ $=\frac{400}{9}\text{m}^2$ $=44\frac{4}{9}\text{m}^2$
Question 232 Marks
Find:$\frac{7}{20}\text{of a litre}$
Answer
View full question & answer→We have, $\frac{7}{20}\text{of a litre}$ 1litre $= 1000ml$
$\therefore\ \frac{7}{20}\times1000\text{ml}$
$=7\times50\text{ml}$
$=350\text{ml}$
$\therefore\ \frac{7}{20}\times1000\text{ml}$
$=7\times50\text{ml}$
$=350\text{ml}$
Question 242 Marks
Find the difference of: $\frac{13}{24}\text{ and }\frac{7}{16}$
Answer
View full question & answer→We have, $\frac{13}{24}\text{ and }\frac{7}{16}$ Taking out the $LCM$ of $24$ and $16$,
we get $2 \times 2 \times 2 \times 2 \times 3 = 48$
Now, we convert the given fractions to equivalent fractions by making the denominators $48$
$=\frac{26}{48}-\frac{21}{48}$
$=\frac{36-21}{48}$
$=\frac{5}{48}$
we get $2 \times 2 \times 2 \times 2 \times 3 = 48$
Now, we convert the given fractions to equivalent fractions by making the denominators $48$
$=\frac{26}{48}-\frac{21}{48}$
$=\frac{36-21}{48}$
$=\frac{5}{48}$
Question 252 Marks
Find:$\frac{5}{8}\text{ of }9\frac{2}{3}$
Answer
View full question & answer→We have, $\frac{5}{8}\text{ of }9\frac{2}{3}$ $=\frac{5}{8}\times\frac{29}{3}$ $=\frac{145}{24}$ $=6\frac{1}{24}$
Question 262 Marks
Divide: $10\text{ by }\frac{100}{3}$
Answer
View full question & answer→$10\text{ by }\frac{100}{3}$ $=\frac{10}{\frac{100}{3}}$ $=\frac{10\times3}{100}$ $=\frac{3}{10}$
Question 272 Marks
Divide: $\frac{9}{16}\text{ by }6$
Answer
View full question & answer→$\frac{9}{16}\text{ by }6$ $\frac{\frac{9}{16}}{6}$ $=\frac{9}{16\times6}$ $=\frac{9}{96}$ $=\frac{3}{32}$
Question 282 Marks
Simplify: $\frac{2}{3}+\frac{1}{6}-\frac{2}{9}$
Answer
View full question & answer→We have, $\frac{2}{3}+\frac{1}{6}-\frac{2}{9}$
Taking out the $LCM$ of $3, 6$ and $9,$
we get, $3 \times 3 \times 2 = 18$
Now, we convert the given fractions to equivalent by making the denominators $18,$
we get $=\frac{12}{18}+\frac{3}{18}-\frac{4}{18}$ $=\frac{12+3-4}{18}$ $=\frac{11}{18}$
Taking out the $LCM$ of $3, 6$ and $9,$
we get, $3 \times 3 \times 2 = 18$
Now, we convert the given fractions to equivalent by making the denominators $18,$
we get $=\frac{12}{18}+\frac{3}{18}-\frac{4}{18}$ $=\frac{12+3-4}{18}$ $=\frac{11}{18}$
Question 292 Marks
Simplify: $4\frac{3}{5}\div\frac{4}{5}$
Answer
View full question & answer→$4\frac{3}{5}\div\frac{4}{5}$ $=\frac{23}{5}\div\frac{4}{5}$ $=\frac{23\times5}{5\times4}$ $=\frac{23}{4}$ $=5\frac{3}{4}$
Question 302 Marks
The product of two numbers is $25\frac{5}{6}.$ If one of the numbers is $6\frac{2}{3},$ find the other.
Answer
View full question & answer→The product of two numbers is $25\Big(\frac{5}{6}\Big).$ If one of the numbers is $6\Big(\frac{2}{3}\Big),$
$6\frac{2}{3}=\frac{20}{3}$ And, $25\frac{5}{6}=\frac{155}{6}$
Let the other number be $x$. $\frac{20}{3}\times\text{x}=\frac{155}{6}$
$\text{x}=\frac{3}{20}\times\frac{155}{6}$
$\text{x}=\frac{3\times155}{20\times6}$
$\text{x}=\frac{31}{8}$
$\text{x}=3\frac{7}{8}$
$6\frac{2}{3}=\frac{20}{3}$ And, $25\frac{5}{6}=\frac{155}{6}$
Let the other number be $x$. $\frac{20}{3}\times\text{x}=\frac{155}{6}$
$\text{x}=\frac{3}{20}\times\frac{155}{6}$
$\text{x}=\frac{3\times155}{20\times6}$
$\text{x}=\frac{31}{8}$
$\text{x}=3\frac{7}{8}$
Question 312 Marks
Simplify: $2\frac{2}{17}\times7\frac{2}{9}\times1\frac{33}{52}$
Answer
View full question & answer→We have, $2\frac{2}{17}\times7\frac{2}{9}\times1\frac{33}{52}$
$=\frac{36}{17}\times\frac{65}{9}\times\frac{85}{52}$
$=\frac{36\times65\times85}{17\times9\times52}$
$=\frac{198900}{7956}$
$=25$
$=\frac{36}{17}\times\frac{65}{9}\times\frac{85}{52}$
$=\frac{36\times65\times85}{17\times9\times52}$
$=\frac{198900}{7956}$
$=25$
Question 322 Marks
Simplify: $4\div2\frac{2}{5}$
Answer
View full question & answer→$4\div2\frac{2}{5}$ $=4\div\frac{12}{5}$ $=\frac{4}{\frac{12}{5}}$ $=\frac{20}{12}$ $=1\frac{2}{3}$
Question 332 Marks
Simplify: $12-3\frac{1}{2}$
Answer
View full question & answer→We have, $12-3\frac{1}{2}$ $=12-\frac{7}{2}$
$=\frac{12\times2-7}{2}$
$=\frac{24-7}{2}$
$=\frac{17}{2}$
$=\frac{12\times2-7}{2}$
$=\frac{24-7}{2}$
$=\frac{17}{2}$
Question 342 Marks
Divide: $\frac{3}{8}\text{ by }4$
Answer
View full question & answer→$\frac{3}{8}\text{ by }4$ $=\frac{\frac{3}{8}}{4}$ $=\frac{3}{8\times4}$ $=\frac{3}{32}$
Question 352 Marks
Shikha plants $5$ saplings in a row in her garden. The distance between two adjacent saplings is $\frac{3}{4}\text{m}.$ Find the distance between the first and the last sapling.
Answer
View full question & answer→There are $4$ adjacent spacing for $5$ saplings.
Given, the distance between two adjacent saplings is $\frac{3}{4}\text{m}$ $4$ adjacent spacing for $5$ saplings $\frac{3}{4}\times4=3\text{m}$ Therefore, the distance between first and last sapling is $3m$.
Given, the distance between two adjacent saplings is $\frac{3}{4}\text{m}$ $4$ adjacent spacing for $5$ saplings $\frac{3}{4}\times4=3\text{m}$ Therefore, the distance between first and last sapling is $3m$.
Question 362 Marks
The length of a rectangular plot of area $65\frac{1}{3}\text{m}^2$ is $12\frac{1}{4}\text{m}.$ What is the width of the plot?
Answer
View full question & answer→Area of rectangle = Length of rectangle $\times $ Width of rectangle $65\frac{1}{3}=12\frac{1}{4}\times\text{Width of the rectangle}$ $\frac{(65\times3)+1}{3}=\Big[\frac{(12\times4)+1}{4}\Big]\times\text{Width of the rectangle}$ $\frac{196}{3}=\frac{49}{4}\times\text{Width of the rectangle}$ $\text{Width of the rectangle}=\frac{196}{3}\times\frac{4}{49}=\frac{16}{3}\text{m}$
Question 372 Marks
Find:$\frac{5}{6}\text{ of an year}$
Answer
View full question & answer→We have, $\frac{5}{6}\text{ of an year}$
$1$ year $= 12$ months
$\therefore\ \frac{5}{6}\times12\text{ months}$
$=5\times2\text{ months}$
$=10\text{ months}$
$1$ year $= 12$ months
$\therefore\ \frac{5}{6}\times12\text{ months}$
$=5\times2\text{ months}$
$=10\text{ months}$
Question 382 Marks
Multiply: $\frac{7}{11}\text{ by }\frac{3}{5}$
Answer
View full question & answer→We have, $\frac{7}{11}\text{ by }\frac{3}{5}$ $=\frac{7}{11}\times\frac{3}{5}$ $=\frac{21}{55}$
Question 392 Marks
Simplify: $\frac{12}{25}\times\frac{15}{28}\times\frac{35}{36}$
Answer
View full question & answer→We have, $\frac{12}{25}\times\frac{15}{28}\times\frac{35}{36}$ $=\frac{12\times15\times35}{25\times28\times36}$ $=\frac{6300}{25200}$ $=\frac{1}{4}$
Question 402 Marks
Find the product:
$3\frac{6}{7}\times4\frac{2}{3}$
$3\frac{6}{7}\times4\frac{2}{3}$
Answer
View full question & answer→ $3\frac{6}{7}\times4\frac{2}{3}\Leftrightarrow\frac{(3\times7)+6}{7}\times\frac{(4\times3)+2}{3}$
$\Rightarrow\frac{27}{7}\times\frac{14}{3}=\frac{9}{1}\times\frac{2}{1}\Leftrightarrow\frac{18}{1}$
$\Rightarrow\frac{27}{7}\times\frac{14}{3}=\frac{9}{1}\times\frac{2}{1}\Leftrightarrow\frac{18}{1}$
Question 412 Marks
Find:$\frac{5}{9}\text{ of }108\text{ metres}$
Answer
View full question & answer→We have, $\frac{5}{9}\text{ of }108\text{ metres}$ $\frac{5}{9}\times108\text{ metres}$ $=5\times12\text{ meters}$ $=60\text{ meters}$
Question 422 Marks
Find:$\frac{2}{7}\text{ of a week}$
Answer
View full question & answer→We have, $\frac{2}{7}\text{ of a week}$ $1$
week $= 7$ days
$\therefore\ \frac{2}{7}\times7\text{ days}$
$=2\text{ days}$
week $= 7$ days
$\therefore\ \frac{2}{7}\times7\text{ days}$
$=2\text{ days}$
Question 432 Marks
Find:$\frac{2}{3}\text{ of }\frac{9}{16}$
Answer
View full question & answer→We have, $\frac{2}{3}\text{ of }\frac{9}{16}$ $=\frac{2}{3}\times\frac{9}{16}$ $=\frac{2\times9}{3\times16}$ $=\frac{18}{48}$ $=\frac{3}{8}$
Question 442 Marks
Sharda can walk $8\frac{1}{3}\text{km}$ in one hour. How much distance will she cover in $2\frac{2}{5}$ hours?
Answer
View full question & answer→Given, $8\frac{1}{3}\text{km}=\frac{25}{3}\text{km}$
$2\frac{2}{5}\text{ hours}=\frac{12}{5}\text{ hours}$
Distance covered by Sharda in one hour $=\frac{25}{3}\text{km}$
Distance covered by Sharda in $\frac{12}{5}\text{hours}$
$=2\frac{2}{5}\times\frac{25}{3}=20\text{ km}$
$2\frac{2}{5}\text{ hours}=\frac{12}{5}\text{ hours}$
Distance covered by Sharda in one hour $=\frac{25}{3}\text{km}$
Distance covered by Sharda in $\frac{12}{5}\text{hours}$
$=2\frac{2}{5}\times\frac{25}{3}=20\text{ km}$
Question 452 Marks
Divide: $\frac{7}{8}\text{ by }4\frac{1}{2}$
Answer
View full question & answer→$\frac{7}{8}\text{ by }4\frac{1}{2}$ $=\frac{\frac{7}{8}}{\frac{9}{2}}$ $=\frac{7\times2}{9\times8}$ $=\frac{14}{72}$ $=\frac{7}{36}$
Question 462 Marks
Find the product: $6\frac{11}{14}\times3\frac{1}{2}$
Answer
View full question & answer→$6\frac{11}{14}\times3\frac{1}{2}\Leftrightarrow\frac{(14\times6)+11}{14}\times\frac{(3\times2)+1}{2}$ $\Rightarrow\frac{95}{14}\times\frac{7}{2}\Leftrightarrow\frac{95}{4}$
Question 472 Marks
In a charity show $₹ 6496$ were collected by selling some tickets. If the price of each ticket was $₹\ 50\frac{3}{4},$ how many tickets were sold?
Answer
View full question & answer→Given, $₹ 6496$ were collected by selling some tickets.
If the price of each ticket was $₹\ 50\Big(\frac{3}{4}\Big)$
$50\frac{3}{4}=\frac{203}{4}$
Number of tickets bought at $₹\ \frac{203}{4}=1$
Number of trickets bought at $₹\ 1=\frac{4}{203}$
Number of tickets bought at $₹ 6496$ $=\frac{4}{203}\times6496$
$=4\times32=128$
If the price of each ticket was $₹\ 50\Big(\frac{3}{4}\Big)$
$50\frac{3}{4}=\frac{203}{4}$
Number of tickets bought at $₹\ \frac{203}{4}=1$
Number of trickets bought at $₹\ 1=\frac{4}{203}$
Number of tickets bought at $₹ 6496$ $=\frac{4}{203}\times6496$
$=4\times32=128$
Question 482 Marks
Divide: $9\text{ by }\frac{3}{16}$
Answer
View full question & answer→$9\text{ by }\frac{3}{16}$ $=\frac{9}{\frac{3}{16}}$ $=\frac{9\times16}{3}$ $=3\times16$ $=48$
Question 492 Marks
Compare the following fractions by using the symbo $>$ or $<$ or = $\frac{37}{41}\text{ and }\frac{19}{30}$
Answer
View full question & answer→We have, $\frac{37}{41}\text{ and }\frac{19}{30}$
Taking the $LCM$ of $41$ and $30$, we get $41 \times 30 = 1230$
Now, we convert the given fractions to equivalent fractions by making the denominators $1230$
$\frac{37\times30}{41\times30}\text{ and }\frac{19\times41}{30\times41}$
$\frac{1110}{1230}\text{ and }\frac{779}{1230}$
Now, we clearly know $1110 > 779$ Therefore, $3741 > 1930$
Taking the $LCM$ of $41$ and $30$, we get $41 \times 30 = 1230$
Now, we convert the given fractions to equivalent fractions by making the denominators $1230$
$\frac{37\times30}{41\times30}\text{ and }\frac{19\times41}{30\times41}$
$\frac{1110}{1230}\text{ and }\frac{779}{1230}$
Now, we clearly know $1110 > 779$ Therefore, $3741 > 1930$
Question 502 Marks
Which is greater? $\frac{1}{2}\text{ of }\frac{6}{7}\text{ or }\frac{2}{3}\text{ of }\frac{3}{7}$
Answer
View full question & answer→Given, $\frac{1}{2}\text{ of }\frac{6}{7}\text{ or }\frac{2}{3}\text{ of }\frac{3}{7}$
$=\frac{1}{2}\times\frac{6}{7}\text{ or }\frac{2}{3}\times\frac{3}{7}$
$=\frac{1\times6}{2\times7}\times\frac{2\times3}{3\times7}$
$=\frac{6}{14}\text{ or }\frac{6}{21}$
While comparing two fractions, when the numerators of both the fractions are same,
then the denominator having higher value shows the fraction has lower value.
So, $\frac{6}{14}$ is greater.
$\therefore\ \frac{1}{2}\text{ of }\frac{6}{7}$ is greater.
$=\frac{1}{2}\times\frac{6}{7}\text{ or }\frac{2}{3}\times\frac{3}{7}$
$=\frac{1\times6}{2\times7}\times\frac{2\times3}{3\times7}$
$=\frac{6}{14}\text{ or }\frac{6}{21}$
While comparing two fractions, when the numerators of both the fractions are same,
then the denominator having higher value shows the fraction has lower value.
So, $\frac{6}{14}$ is greater.
$\therefore\ \frac{1}{2}\text{ of }\frac{6}{7}$ is greater.
Question 512 Marks
The cost of $6\frac{1}{4}\text{kg}$ of apples is $₹ 400$. At what rate per kg are the apples being sold?
Answer
View full question & answer→Given, The cost of $6\frac{1}{4}\text{kg}$ of apples is $₹ 400$ $6\frac{1}{4}=\frac{25}{4}$
Cost of $\frac{25}{4}\text{kg}$ of apple $= ₹ 400$
Cost of $1\ kg$ of apple $=₹\ \frac{4}{25}\times400=₹\ 64$
Cost of $\frac{25}{4}\text{kg}$ of apple $= ₹ 400$
Cost of $1\ kg$ of apple $=₹\ \frac{4}{25}\times400=₹\ 64$
Question 522 Marks
Find:$\frac{5}{6}\text{ of a day}$
Answer
View full question & answer→We have, $\frac{5}{6}\text{ of a day}$ $1$ day $= 24$ hours
$\therefore\ \frac{5}{6}\times24\text{ hours}$
$=5\times4\text{ hours}$
$=20\text{ hours}$
$\therefore\ \frac{5}{6}\times24\text{ hours}$
$=5\times4\text{ hours}$
$=20\text{ hours}$
Question 532 Marks
Divide: $6\frac{1}{4}\text{ by }2\frac{3}{5}$
Answer
View full question & answer→$6\frac{1}{4}\text{ by }2\frac{3}{5}$ $=\frac{6\frac{1}{4}}{2\frac{3}{5}}$ $=\frac{\frac{25}{4}}{\frac{13}{5}}$ $=\frac{25\times5}{4\times13}$ $=\frac{75}{52}$ $=2\frac{21}{52}$
Question 542 Marks
Ravish reads $\frac{1}{3}$ part of a books in $1$ hour. How much part of the book will he read in $2\frac{1}{5}$ hours?
Answer
View full question & answer→Let $x$ be the full part of book.
Given, Ravish reads $\frac{1}{3}$ part of a book in one hour $1\text{ hour}=\Big(\frac{1}{3}\Big)\text{x}$
Part of the book will he read in $2\Big(\frac{1}{5}\Big)$ hours $2\frac{1}{5}=\frac{11}{5}\text{ hours}$
$=\frac{1}{3}\times\text{x}\times\frac{11}{5}$
$\frac{11}{5}\text{x}=\frac{11}{15}$ part of book
Given, Ravish reads $\frac{1}{3}$ part of a book in one hour $1\text{ hour}=\Big(\frac{1}{3}\Big)\text{x}$
Part of the book will he read in $2\Big(\frac{1}{5}\Big)$ hours $2\frac{1}{5}=\frac{11}{5}\text{ hours}$
$=\frac{1}{3}\times\text{x}\times\frac{11}{5}$
$\frac{11}{5}\text{x}=\frac{11}{15}$ part of book
Question 552 Marks
There are $45$ students in a class and $\frac{3}{5}$ of them are boys. How many girls are there in the class?
Answer
View full question & answer→Given,
There are $45$ students in a class,
And $\frac{3}{5}$ of them are boys.
Therefore, no of girls in the class $=45-\frac{3}{5}\times45$
$=45-27$
$=18$
There are $45$ students in a class,
And $\frac{3}{5}$ of them are boys.
Therefore, no of girls in the class $=45-\frac{3}{5}\times45$
$=45-27$
$=18$
Question 562 Marks
By what number should $6\frac{2}{9}$ be multiplied to get $4\frac{4}{9}?$
Answer
View full question & answer→Let the required number be $x$.
According to the question, $6\frac{2}{9}\times\text{x}=4\frac{4}{9}$
$\frac{(6\times9+2)}{9}\times\text{x}=\frac{(4\times9)+4}{9}$
$\frac{56}{9}\times\text{x}=\frac{40}{9}$
$\text{x}=\frac{40}{9}\times\frac{9}{56}$
$\text{x}=\frac{40}{56}$
$\text{x}=\frac{5}{7}$
According to the question, $6\frac{2}{9}\times\text{x}=4\frac{4}{9}$
$\frac{(6\times9+2)}{9}\times\text{x}=\frac{(4\times9)+4}{9}$
$\frac{56}{9}\times\text{x}=\frac{40}{9}$
$\text{x}=\frac{40}{9}\times\frac{9}{56}$
$\text{x}=\frac{40}{56}$
$\text{x}=\frac{5}{7}$
Question 572 Marks
Multiply: $3\frac{4}{15}\text{ by }{24}$
Answer
View full question & answer→We have, $3\frac{4}{15}\text{ by }{24}$ $=\frac{49}{15}\times24$ $=\frac{1176}{24}$ $=78\frac{2}{5}$
Question 582 Marks
Divide: $\frac{3}{8}\text{ by }\frac{5}{9}$
Answer
View full question & answer→$\frac{3}{8}\text{ by }\frac{5}{9}$ $=\frac{\frac{3}{8}}{\frac{5}{9}}$ $=\frac{3\times9}{8\times5}$ $=\frac{27}{40}$
Question 592 Marks
Find:$\frac{3}{20}\text{ of a kg}$
Answer
View full question & answer→We have, $\frac{3}{20}\text{ of a kg}$
$1kg = 1000gms$
$\therefore\ \frac{3}{20}\times1000\text{gms}$
$=3\times50\text{gms}$
$=150\text{gms}$
$1kg = 1000gms$
$\therefore\ \frac{3}{20}\times1000\text{gms}$
$=3\times50\text{gms}$
$=150\text{gms}$
Question 602 Marks
Multiply: $3\frac{1}{8}\text{ by }4\frac{10}{11}$
Answer
View full question & answer→We have, $3\frac{1}{8}\text{ by }4\frac{10}{11}$ $=\frac{25}{8}\times\frac{54}{11}$ $=\frac{25\times54}{88}$ $=15\frac{15}{44}$
Question 612 Marks
Evaluate: $\frac{12}{17}$ of $\frac{68}{3}$
Answer
View full question & answer→16
Question 622 Marks
Multiply the following fractions: $7 \frac{5}{9} \times 1 \frac{1}{2}$
Answer
View full question & answer→$11 \frac{1}{3}$
Question 632 Marks
Evaluate: $\frac{2}{11}$ of $\frac{121}{10}$
Answer
View full question & answer→$2 \frac{1}{5}$
Question 642 Marks
Multiply the following fractions: $6 \frac{11}{14} \times 3 \frac{1}{2}$
Answer
View full question & answer→$23 \frac{3}{4}$
Question 652 Marks
Evaluate: $\frac{1}{7}$ of $\frac{6}{5}$
Answer
View full question & answer→$\frac{6}{35}$
Question 662 Marks
Multiply the following fractions: $6 \frac{2}{5} \times \frac{7}{9}$
Answer
View full question & answer→$\frac{224}{45}$
Question 672 Marks
Evaluate: $\frac{1}{4}$ of $\frac{3}{5}$
Answer
View full question & answer→$\frac{3}{20}$
Question 682 Marks
Multiply the following fractions: $\frac{2}{3} \times 2 \frac{2}{3}$
Answer
View full question & answer→$\frac{16}{9}$
Question 692 Marks
(i) Write the number in the box $\square$ such that $\frac{3}{5} \times \square=\frac{24}{75}$.
(ii) What is the simplest form of the number written in the box $\square$ in (i)?
(ii) What is the simplest form of the number written in the box $\square$ in (i)?
Answer
View full question & answer→(i) $\frac{8}{15}$
(ii) $\frac{8}{15}$
(ii) $\frac{8}{15}$
Question 702 Marks
(i) Write the number in the box $\square$, such that $\frac{2}{3} \times \square=\frac{10}{30}$.
(ii) What is the simplest form of the number written in the box $\square$ in (i)?
(ii) What is the simplest form of the number written in the box $\square$ in (i)?
Answer
View full question & answer→(i) $\frac{5}{10}$
(ii) $\frac{1}{2}$
(ii) $\frac{1}{2}$
Question 712 Marks
Aarush used $1 \frac{2}{5}$ bag of soil fertilizer for his garden and Aayush used $\frac{2}{7}$ of the fertilizer uset: by Aarush for his garden. How much soil fertilizer will Aayush require for his garden.
Answer
View full question & answer→$\frac{2}{5} bag$
Question 722 Marks
Find: $\frac{5}{6}$ of a day
Answer
View full question & answer→20 hours
Question 732 Marks
Find: $\frac{7}{20}$ of a litre
Answer
View full question & answer→350 ml
Question 742 Marks
Find: $\frac{3}{20}$ of a kg
Answer
View full question & answer→150 gms
Question 752 Marks
Evaluate: $\frac{3}{14}$ of 70 metre
Answer
View full question & answer→15 metre
Question 762 Marks
Find: $\frac{5}{6}$ of an year
Answer
View full question & answer→10 months
Question 772 Marks
Find: $\frac{2}{7}$ of a week
Answer
View full question & answer→2 days
Question 782 Marks
Simplify: $4 \div 2 \frac{2}{5}$
Answer
View full question & answer→$1 \frac{2}{3}$
Question 792 Marks
Divide: 10 by $\frac{100}{3}$
Answer
View full question & answer→$\frac{3}{10}$
Question 802 Marks
Divide: $6 \frac{1}{4}$ by $2 \frac{3}{5}$
Answer
View full question & answer→$2 \frac{21}{52}$
Question 812 Marks
Find: $\frac{1}{12}$ of an hour
Answer
View full question & answer→5 minutes
Question 822 Marks
Simplify: $5 \frac{4}{7} \div 1 \frac{3}{10}$
Answer
View full question & answer→$4 \frac{2}{7}$
Question 832 Marks
Divide: 9 by $\frac{3}{16}$
Answer
View full question & answer→48
Question 842 Marks
Divide: $\frac{7}{8}$ by $4 \frac{1}{2}$
Answer
View full question & answer→$\frac{7}{36}$
Question 852 Marks
Find: $\frac{3}{7}$ of 42 litres
Answer
View full question & answer→18 litres
Question 862 Marks
Simplify: $4 \frac{3}{5} \div \frac{4}{5}$
Answer
View full question & answer→$5 \frac{3}{4}$
Question 872 Marks
Divide: $\frac{9}{16}$ by 6
Answer
View full question & answer→$\frac{3}{32}$
Question 882 Marks
Divide: $3 \frac{1}{4}$ by $\frac{2}{3}$
Answer
View full question & answer→$4 \frac{7}{8}$
Question 892 Marks
Find: $\frac{5}{9}$ of 108 metres
Answer
View full question & answer→60 metres
Question 902 Marks
Simplify: $\frac{3}{10} \div \frac{10}{3}$
Answer
View full question & answer→$\frac{9}{100}$
Question 912 Marks
Divide: $\frac{3}{8}$ by 4
Answer
View full question & answer→$\frac{3}{32}$
Question 922 Marks
Divide: $\frac{3}{8}$ by $\frac{5}{9}$
Answer
View full question & answer→$\frac{27}{40}$
Question 932 Marks
Find:$\frac{7}{11}$ of ₹330
Answer
View full question & answer→₹210
Question 942 Marks
Evaluate product, reduce it to the lowest form, and convert it into a mixed fraction if possible. $20 \times \frac{4}{5}$
Answer
View full question & answer→16
Question 952 Marks
Evaluate product, reduce it to the lowest form, and convert it into a mixed fraction if possible. $12 \times 1 \frac{1}{6}$
Answer
View full question & answer→14
Question 962 Marks
Evaluate product, reduce it to the lowest form, and convert it into a mixed fraction if possible. $6 \times 2 \frac{3}{7}$
Answer
View full question & answer→$14 \frac{4}{7}$
Question 972 Marks
Evaluate product, reduce it to the lowest form, and convert it into a mixed fraction if possible.$15 \times \frac{3}{5}$
Answer
View full question & answer→9
Question 982 Marks
Evaluate product, reduce it to the lowest form, and convert it into a mixed fraction if possible. $5 \times \frac{4}{9}$
Answer
View full question & answer→$5 \frac{4}{9}$
Question 992 Marks
Evaluate product, reduce it to the lowest form, and convert it into a mixed fraction if possible. $7 \times \frac{3}{5}$
Answer
View full question & answer→$7 \frac{3}{5}$
Question 1002 Marks
In pictures shown in Fig. determine which of them represents:$3 \times \frac{3}{4}=2 \frac{1}{4}$
Answer
View full question & answer→(ii)
Question 1012 Marks
Evaluate product, reduce it to the lowest form, and convert it into a mixed fraction if possible. $3 \times \frac{1}{24}$
Answer
View full question & answer→$\frac{1}{8}$
Question 1022 Marks
Answer
View full question & answer→(i)
Question 1032 Marks
Evaluate product, reduce it to the lowest form, and convert it into a mixed fraction if possible. $5 \times \frac{3}{10}$
Answer
View full question & answer→$\frac{3}{2}$
Question 1042 Marks
In pictures shown in Fig. determine which of them represents: $2 \times \frac{1}{3}=\frac{2}{3}$
Answer
View full question & answer→(iii)
Question 1052 Marks
One tin holds $12 \frac{3}{4} kg$. litres of oil. How many litres of oil can 26 such tins hold?
Answer
View full question & answer→$331 \frac{1}{2}$ litres
Question 1062 Marks
Simplify: $7 \frac{5}{6}-4 \frac{3}{8}+2 \frac{7}{12}$
Answer
View full question & answer→$\frac{145}{24}$
Question 1072 Marks
Find the sum:$2 \frac{3}{5}+4 \frac{7}{10}+2 \frac{4}{15}$
Answer
View full question & answer→$\frac{287}{30}$
Question 1082 Marks
Find the sum:$\frac{5}{6}+3+\frac{3}{4}$
Answer
View full question & answer→$\frac{55}{12}$
Question 1092 Marks
Simplify: $12-3 \frac{1}{2}$
Answer
View full question & answer→$\frac{17}{2}$
Question 1102 Marks
Find the sum:$4 \frac{3}{4}+9 \frac{2}{5}$
Answer
View full question & answer→$\frac{283}{20}$
Question 1112 Marks
Simplify: $\frac{2}{3}+\frac{1}{6}-\frac{2}{9}$
Answer
View full question & answer→$\frac{11}{18}$
Question 1122 Marks
Find the sum:$\frac{5}{8}+\frac{3}{10}$
Answer
View full question & answer→$\frac{37}{40}$
Question 1132 Marks
Write five equivalent fractions e ${ }^{\prime}$
Answer
View full question & answer→$\frac{6}{10}, \frac{9}{15}, \frac{1}{20}, \frac{15}{25}, \frac{13}{30}$
Question 1142 Marks
By what number should $6 \frac{2}{9}$ be multiplied to get 40 ?
Answer
View full question & answer→$6 \frac{3}{7}$
Question 1152 Marks
By what number should $6 \frac{2}{9}$ be divided to obtain $4 \frac{2}{3}$ ?
Answer
View full question & answer→$1 \frac{1}{3}$
Question 1162 Marks
What should be subtracted from $17 \frac{3}{4}$ to get $11 \frac{2}{3}$ ?
Answer
View full question & answer→$6 \frac{1}{12}$
Question 1172 Marks
What should be added to $15 \frac{2}{3}$ to get $18 \frac{5}{6}$ ?
Answer
View full question & answer→ $3 \frac{1}{6}$
Question 1182 Marks
Evaluate: $1 \frac{7}{12}+13 \frac{11}{16}-2 \frac{1}{48}$
Answer
View full question & answer→ $13 \frac{1}{4}$