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Question 12 Marks
Find the product:
$7\frac{1}{2}\times2\frac{4}{15}$
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
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
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Question 32 Marks
Simplify:
$7\frac{5}{6}-4\frac{3}{8}+2\frac{7}{12}$
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 × 2 × 2 × 3 = 48
Now, we convert the given fractions to equivalent fraction by making the denominators 48 we get,
$\frac{47\times8}{6\times8}-\frac{35\times6}{8\times6}+\frac{31\times4}{12\times4}$
$=\frac{376}{48}-\frac{210}{48}+\frac{124}{48}$
$=\frac{376-210+124}{48}$
$=\frac{290}{48}$
$=\frac{145}{24}$
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Question 42 Marks
Multiply:
$\frac{3}{5}\text{ by }{25}$
Answer
We have, $\frac{3}{5}\text{ by }{25}$
$=\frac{3}{5}\times25$
$=15$
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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
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
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Question 62 Marks
Find:$\frac{3}{7}\text{ of }42\text{ litres}$
Answer
We have,
$\frac{3}{7}\text{ of }42\text{ litres}$
$=\frac{3}{7}\times42\text{ litres}$
$=3\times6\text{ litres}$
$=18\text{ litres}$
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Question 72 Marks
Divide:
$3\frac{1}{4}\text{ by }\frac{2}{3}$
Answer
$3\frac{1}{4}\text{ by }\frac{2}{3}$
$=\frac{3\frac{1}{4}}{\frac{2}{3}}$
$=\frac{\frac{13}{4}}{\frac{2}{3}}$
$=\frac{13\times3}{4\times2}$
$=\frac{39}{8}$
$=4\frac{7}{8}$
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Question 82 Marks
Find:$\frac{7}{11}\text{ of }₹\ 330$
Answer
We have,
$\frac{7}{11}\text{ of }330$
$=\frac{7}{11}\times330$
$=7\times30$
$=210$
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Question 92 Marks
A sugar bag contains 30kg of sugar. After consuming $\frac{2}{3}$ of it, how much sugar is left in the bag?
Answer
Given, A sugar bag contains 30kg of sugar
After consuming 23 of it, the amount of sugar left in the bag,
$=30\text{kg}-\frac{2}{3}\times30\text{kg}$
$=30\text{kg}-20\text{kg}$
$=10\text{kg}$
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Question 102 Marks
Find the difference:
$8-\frac{5}{9}$
Answer
We have,
$8-\frac{5}{9}$
$=\frac{8\times9-5}{9}$
$=\frac{72-5}{9}$
$=\frac{67}{9}$
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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
Number of students in the school $=\frac{\text{Total amount of milk distributed per day}}{\text{Amount of milk given to one student}}$
$=30\div\frac{3}{10}$
$=30\times\frac{10}{3}$
$=100$
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Question 122 Marks
Simplify:
$\frac{10}{27}\times\frac{39}{56}\times\frac{28}{65}$
Answer
We have,
$\frac{10}{27}\times\frac{39}{56}\times\frac{28}{65}$
$=\frac{10\times39\times28}{27\times56\times65}$
$=\frac{10920}{98280}$
$=\frac{1}{9}$
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Question 132 Marks
Find:$\frac{1}{2}\text{ of }4\frac{2}{9}$
Answer
We have,
$\frac{1}{2}\text{ of }4\frac{2}{9}$
$=\frac{1}{2}\times\frac{38}{9}$
$=\frac{38}{18}$
$=2\frac{1}{9}$
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Question 142 Marks
Find the difference:
$9-5\frac{2}{3}$
Answer
We have,
$9-5\frac{2}{3}$
$=9-\frac{17}{3}$
$=\frac{9\times3-17}{3}$
$=\frac{27-17}{3}$
$=\frac{10}{3}$
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Question 152 Marks
Simplify:
$5\frac{4}{7}\div1\frac{3}{10}$
Answer
$5\frac{4}{7}\div1\frac{3}{10}$
$=\frac{39}{7}\div\frac{13}{10}$
$=\frac{39\times10}{7\times13}$
$=\frac{390}{91}$
$=4\frac{2}{7}$
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Question 162 Marks
Find the difference:
$4\frac{3}{10}-1\frac{2}{15}$
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 × 3 × 5 = 30
Now, we convert the given fractions to equivalent fractions by marking the denominators 30
$=\frac{43\times3}{10\times3}-\frac{17\times2}{15\times2}$
$=\frac{129-34}{30}$
$=\frac{129-34}{30}$
$=\frac{95}{30}$
$=\frac{19}{6}$
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Question 172 Marks
Write five equivalent fractions of $\frac{3}{5}$
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 $\frac{3}{5}$
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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
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.
$=\frac{7}{4}\times6=\frac{42}{4}=10\frac{1}{2}\text{ hours}$
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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
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 $=\frac{\frac{25}{2}}{10}$
$=\frac{25}{20}$
$=\frac{5}{4}$
$=1\frac{1}{4}$
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Question 202 Marks
Find:$\frac{1}{12}\text{ of an hour}$
Answer
We have,
$\frac{1}{12}\text{ of an hour}$
An hour = 60 minutes
$\therefore\ \frac{1}{12}\times60\text{ minutes}$
$=5\text{ minutes}$
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Question 212 Marks
Simplify:
$\frac{3}{10}\div\frac{10}{3}$
Answer
$\frac{3}{10}\div\frac{10}{3}$
$=\frac{3\times3}{10\times10}$
$=\frac{9}{100}$
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Question 222 Marks
Each side of a square is $6\frac{2}{3}\text{m}$ long. Find its area.
Answer
Given,
Each side $=6\frac{2}{3}\text{m}=\frac{20}{3}\text{m}$
$\text{Area}=\text{side}^2=\Big(\frac{20}{3}\Big)^2\text{m}^2$
$=\frac{400}{9}\text{m}^2$
$=44\frac{4}{9}\text{m}^2$
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Question 232 Marks
Find:$\frac{7}{20}\text{of a litre}$
Answer
We have,
$\frac{7}{20}\text{of a litre}$
1litre = 1000ml
$\therefore\ \frac{7}{20}\times1000\text{ml}$
$=7\times50\text{ml}$
$=350\text{ml}$
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Question 242 Marks
Find the difference of:
$\frac{13}{24}\text{ and }\frac{7}{16}$
Answer
We have,
$\frac{13}{24}\text{ and }\frac{7}{16}$
Taking out the LCM of 24 and 16, we get
2 × 2 × 2 × 2 × 3 = 48
Now, we convert the given fractions to equivalent fractions by making the denominators 48
$=\frac{26}{48}-\frac{21}{48}$
$=\frac{36-21}{48}$
$=\frac{5}{48}$
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Question 252 Marks
Find:$\frac{5}{8}\text{ of }9\frac{2}{3}$
Answer
We have,
$\frac{5}{8}\text{ of }9\frac{2}{3}$
$=\frac{5}{8}\times\frac{29}{3}$
$=\frac{145}{24}$
$=6\frac{1}{24}$
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Question 262 Marks
Divide:
$10\text{ by }\frac{100}{3}$
Answer
$10\text{ by }\frac{100}{3}$
$=\frac{10}{\frac{100}{3}}$
$=\frac{10\times3}{100}$
$=\frac{3}{10}$
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Question 272 Marks
Divide:
$\frac{9}{16}\text{ by }6$
Answer
$\frac{9}{16}\text{ by }6$
$\frac{\frac{9}{16}}{6}$
$=\frac{9}{16\times6}$
$=\frac{9}{96}$
$=\frac{3}{32}$
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Question 282 Marks
Simplify:
$\frac{2}{3}+\frac{1}{6}-\frac{2}{9}$
Answer
We have,
$\frac{2}{3}+\frac{1}{6}-\frac{2}{9}$
Taking out the LCM of 3, 6 and 9, we get,
3 × 3 × 2 = 18
Now, we convert the given fractions to equivalent by making the denominators 18, we get
$=\frac{12}{18}+\frac{3}{18}-\frac{4}{18}$
$=\frac{12+3-4}{18}$
$=\frac{11}{18}$
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Question 292 Marks
Simplify:
$4\frac{3}{5}\div\frac{4}{5}$
Answer
$4\frac{3}{5}\div\frac{4}{5}$
$=\frac{23}{5}\div\frac{4}{5}$
$=\frac{23\times5}{5\times4}$
$=\frac{23}{4}$
$=5\frac{3}{4}$
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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
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.
$\frac{20}{3}\times\text{x}=\frac{155}{6}$
$\text{x}=\frac{3}{20}\times\frac{155}{6}$
$\text{x}=\frac{3\times155}{20\times6}$
$\text{x}=\frac{31}{8}$
$\text{x}=3\frac{7}{8}$
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Question 312 Marks
Simplify:
$2\frac{2}{17}\times7\frac{2}{9}\times1\frac{33}{52}$
Answer
We have,
$2\frac{2}{17}\times7\frac{2}{9}\times1\frac{33}{52}$
$=\frac{36}{17}\times\frac{65}{9}\times\frac{85}{52}$
$=\frac{36\times65\times85}{17\times9\times52}$
$=\frac{198900}{7956}$
$=25$
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Question 322 Marks
Simplify:
$4\div2\frac{2}{5}$
Answer
$4\div2\frac{2}{5}$
$=4\div\frac{12}{5}$
$=\frac{4}{\frac{12}{5}}$
$=\frac{20}{12}$
$=1\frac{2}{3}$
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Question 332 Marks
Simplify:
$12-3\frac{1}{2}$
Answer
We have,
$12-3\frac{1}{2}$
$=12-\frac{7}{2}$
$=\frac{12\times2-7}{2}$
$=\frac{24-7}{2}$
$=\frac{17}{2}$
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Question 342 Marks
Divide:
$\frac{3}{8}\text{ by }4$
Answer
$\frac{3}{8}\text{ by }4$
$=\frac{\frac{3}{8}}{4}$
$=\frac{3}{8\times4}$
$=\frac{3}{32}$
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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
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.
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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
Area of rectangle = Length of rectangle × Width of rectangle
$65\frac{1}{3}=12\frac{1}{4}\times\text{Width of the rectangle}$
$\frac{(65\times3)+1}{3}=\Big[\frac{(12\times4)+1}{4}\Big]\times\text{Width of the rectangle}$
$\frac{196}{3}=\frac{49}{4}\times\text{Width of the rectangle}$
$\text{Width of the rectangle}=\frac{196}{3}\times\frac{4}{49}=\frac{16}{3}\text{m}$
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Question 372 Marks
Find:$\frac{5}{6}\text{ of an year}$
Answer
We have,
$\frac{5}{6}\text{ of an year}$
1 year = 12 months
$\therefore\ \frac{5}{6}\times12\text{ months}$
$=5\times2\text{ months}$
$=10\text{ months}$
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Question 382 Marks
Multiply:
$\frac{7}{11}\text{ by }\frac{3}{5}$
Answer
We have, $\frac{7}{11}\text{ by }\frac{3}{5}$
$=\frac{7}{11}\times\frac{3}{5}$
$=\frac{21}{55}$
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Question 392 Marks
Simplify:
$\frac{12}{25}\times\frac{15}{28}\times\frac{35}{36}$
Answer
We have,
$\frac{12}{25}\times\frac{15}{28}\times\frac{35}{36}$
$=\frac{12\times15\times35}{25\times28\times36}$
$=\frac{6300}{25200}$
$=\frac{1}{4}$
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Question 402 Marks
Find the product:
$3\frac{6}{7}\times4\frac{2}{3}$
Answer
$3\frac{6}{7}\times4\frac{2}{3}\Leftrightarrow\frac{(3\times7)+6}{7}\times\frac{(4\times3)+2}{3}$
$\Rightarrow\frac{27}{7}\times\frac{14}{3}=\frac{9}{1}\times\frac{2}{1}\Leftrightarrow\frac{18}{1}$
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Question 412 Marks
Find:$\frac{5}{9}\text{ of }108\text{ metres}$
Answer
We have,
$\frac{5}{9}\text{ of }108\text{ metres}$
$\frac{5}{9}\times108\text{ metres}$
$=5\times12\text{ meters}$
$=60\text{ meters}$
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Question 422 Marks
Find:$\frac{2}{7}\text{ of a week}$
Answer
We have,
$\frac{2}{7}\text{ of a week}$
1 week = 7 days
$\therefore\ \frac{2}{7}\times7\text{ days}$
$=2\text{ days}$
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Question 432 Marks
Find:$\frac{2}{3}\text{ of }\frac{9}{16}$
Answer
We have,
$\frac{2}{3}\text{ of }\frac{9}{16}$
$=\frac{2}{3}\times\frac{9}{16}$
$=\frac{2\times9}{3\times16}$
$=\frac{18}{48}$
$=\frac{3}{8}$
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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
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 $\frac{12}{5}\text{hours}$
$=2\frac{2}{5}\times\frac{25}{3}=20\text{ km}$
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Question 452 Marks
Divide:
$\frac{7}{8}\text{ by }4\frac{1}{2}$
Answer
$\frac{7}{8}\text{ by }4\frac{1}{2}$
$=\frac{\frac{7}{8}}{\frac{9}{2}}$
$=\frac{7\times2}{9\times8}$
$=\frac{14}{72}$
$=\frac{7}{36}$
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Question 462 Marks
Find the product:
$6\frac{11}{14}\times3\frac{1}{2}$
Answer
$6\frac{11}{14}\times3\frac{1}{2}\Leftrightarrow\frac{(14\times6)+11}{14}\times\frac{(3\times2)+1}{2}$
$\Rightarrow\frac{95}{14}\times\frac{7}{2}\Leftrightarrow\frac{95}{4}$
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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
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 $=\frac{4}{203}\times6496$
$=4\times32=128$
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Question 482 Marks
Divide:
$9\text{ by }\frac{3}{16}$
Answer
$9\text{ by }\frac{3}{16}$
$=\frac{9}{\frac{3}{16}}$
$=\frac{9\times16}{3}$
$=3\times16$
$=48$
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Question 492 Marks
Compare the following fractions by using the symbo > or < or =
$\frac{37}{41}\text{ and }\frac{19}{30}$
Answer
We have,
$\frac{37}{41}\text{ and }\frac{19}{30}$
Taking the LCM of 41 and 30, we get
41 × 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
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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
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.
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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
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 $=₹\ \frac{4}{25}\times400=₹\ 64$
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Question 522 Marks
Find:$\frac{5}{6}\text{ of a day}$
Answer
We have,
$\frac{5}{6}\text{ of a day}$
1 day = 24 hours
$\therefore\ \frac{5}{6}\times24\text{ hours}$
$=5\times4\text{ hours}$
$=20\text{ hours}$
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Question 532 Marks
Divide:
$6\frac{1}{4}\text{ by }2\frac{3}{5}$
Answer
$6\frac{1}{4}\text{ by }2\frac{3}{5}$
$=\frac{6\frac{1}{4}}{2\frac{3}{5}}$
$=\frac{\frac{25}{4}}{\frac{13}{5}}$
$=\frac{25\times5}{4\times13}$
$=\frac{75}{52}$
$=2\frac{21}{52}$
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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
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
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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
Given,
There are 45 students in a class,
And $\frac{3}{5}$ of them are boys.
Therefore, no of girls in the class $=45-\frac{3}{5}\times45$
$=45-27$
$=18$
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Question 562 Marks
By what number should $6\frac{2}{9}$ be multiplied to get $4\frac{4}{9}?$
Answer
Let the required number be x.
According to the question,
$6\frac{2}{9}\times\text{x}=4\frac{4}{9}$
$\frac{(6\times9+2)}{9}\times\text{x}=\frac{(4\times9)+4}{9}$
$\frac{56}{9}\times\text{x}=\frac{40}{9}$
$\text{x}=\frac{40}{9}\times\frac{9}{56}$
$\text{x}=\frac{40}{56}$
$\text{x}=\frac{5}{7}$
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Question 572 Marks
Multiply:
$3\frac{4}{15}\text{ by }{24}$
Answer
We have, $3\frac{4}{15}\text{ by }{24}$
$=\frac{49}{15}\times24$
$=\frac{1176}{24}$
$=78\frac{2}{5}$
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Question 582 Marks
Divide:
$\frac{3}{8}\text{ by }\frac{5}{9}$
Answer
$\frac{3}{8}\text{ by }\frac{5}{9}$
$=\frac{\frac{3}{8}}{\frac{5}{9}}$
$=\frac{3\times9}{8\times5}$
$=\frac{27}{40}$
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Question 592 Marks
Find:$\frac{3}{20}\text{ of a kg}$
Answer
We have,
$\frac{3}{20}\text{ of a kg}$
1kg = 1000gms
$\therefore\ \frac{3}{20}\times1000\text{gms}$
$=3\times50\text{gms}$
$=150\text{gms}$
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Question 602 Marks
Multiply:
$3\frac{1}{8}\text{ by }4\frac{10}{11}$
Answer
We have, $3\frac{1}{8}\text{ by }4\frac{10}{11}$
$=\frac{25}{8}\times\frac{54}{11}$
$=\frac{25\times54}{88}$
$=15\frac{15}{44}$
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