Question 15 Marks
A piece of wire is of length $12\frac{3}{4}\text{m}.$ If it is cut into two pieces in such a way that the length of one piece is $5\frac{1}{4}\text{m},$ what is the length of the other piece?
AnswerA piece of wire of length $12\frac{3}{4}\text{m}.$ one piece is $5\frac{1}{4}\text{m},$
$12\frac{3}{4}=\frac{51}{4}\text{ and }5\frac{1}{4}=\frac{21}{4}$
Let the length of other piece be x m. $\frac{51}{4}=\text{x}+\frac{21}{4}$
$\Rightarrow\text{x}=\frac{51}{4}-\frac{21}{4}$
$\Rightarrow\text{x}=\frac{51-21}{4}$
$\Rightarrow\text{x}=\frac{30}{4}$
$\Rightarrow\text{x}=\frac{15}{2}$
$\Rightarrow\text{x}=7\frac{1}{2}$
View full question & answer→Question 25 Marks
A rectangular sheet of paper is $12\frac{1}{2}\text{cm}$ long and $10\frac{2}{3}\text{cm}$ wide. Find its perimeter.
Answer A rectangular piece of paper is $12\frac{1}{2}\text{cm}$ long and $10\frac{2}{3}\text{cm}$ wide,
$12\frac{1}{2}=\frac{25}{2}\text{ and }10\frac{2}{3}=\frac{32}{3}$
Perimeter = 2(length + width)
Perimeter $=2\Big(\frac{25}{2}\text{cm}+\frac{32}{3}\text{cm}\Big)$
Perimeter $=2\Big(\frac{75}{6}+\frac{64}{6}\Big)\text{cm}$
Perimeter $=2\Big(\frac{139}{6}\Big)\text{cm}$
Perimeter $=\frac{139}{3}$
Perimeter $=46\frac{1}{3}$
View full question & answer→Question 35 Marks
Waht should be added to $5\frac{4}{15}$ to get $12\frac{3}{5}?$
AnswerWe have, $5\frac{4}{15}=\frac{79}{15}$
$12\frac{3}{5}=\frac{63}{5}$ Let x be the number added to $\frac{79}{15}$ to get $\frac{63}{5}$
$=\frac{79}{15}+\text{x}=\frac{63}{5}$
$\Rightarrow\text{x}=\frac{63}{5}-\frac{79}{15}$
Taking out the $LCM$ of $5$ and $15$
we get, $3 \times 5 = 15$
Now, we convert the given fraction to equivalent fractions by making the denominators $15$,
we get, $\Rightarrow\text{x}=\frac{63\times3}{5\times3}-\frac{79}{15}$
$\Rightarrow\text{x}=\frac{189}{15}-\frac{79}{15}$
$\Rightarrow\text{x}=\frac{189-79}{15}$
$\Rightarrow\text{x}=\frac{110}{15}$
$\Rightarrow\text{x}=\frac{22}{3}$
View full question & answer→Question 45 Marks
Arrange the following fraction in descending order: $\frac{2}{7},\frac{11}{35},\frac{9}{14},\frac{13}{28}$
AnswerWe have, $\frac{2}{7},\frac{11}{35},\frac{9}{14},\frac{13}{28}$
Taking the $LCM$ of $7, 35, 14$ and $28,$
we get $7 × 5 × 2 × 2 = 140$
Now, we convert the given fractions to equivalent fractions by making the denominators $140 \frac{2\times20}{7\times20},\frac{11\times4}{35\times4},\frac{9\times10}{14\times10},\frac{13\times5}{28\times5}$
$\frac{40}{140},\frac{44}{140},\frac{90}{140},\frac{65}{140}$
As we know $40 > 44 > 65 > 90$
Therefore, $\frac{90}{140}<\frac{65}{140}<\frac{44}{140}<\frac{40}{140}$
Hence, $\frac{9}{14}<\frac{13}{28}<\frac{11}{35}<\frac{2}{7}$
View full question & answer→Question 55 Marks
Arrange the following fractions in ascending order: $\frac{4}{6},\frac{3}{8},\frac{6}{12},\frac{5}{16}$
AnswerWe have, $\frac{4}{6},\frac{3}{8},\frac{6}{12},\frac{5}{16}$
Taking the $LCM$ of $6, 8, 12$ 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
$48$, $\frac{4\times8}{6\times8},\frac{3\times6}{8\times6},\frac{6\times2}{12\times2},\frac{5\times3}{16\times3}$
$=\frac{32}{48},\frac{18}{48},\frac{12}{48},\frac{15}{48}$
We know that $12 < 15 < 18 < 32$
Therefore, $\frac{12}{48}<\frac{15}{48}<\frac{18}{48}<\frac{32}{148}$
Hence, $\frac{6}{12}<\frac{5}{16}<\frac{3}{8}<\frac{4}{6}$
View full question & answer→Question 65 Marks
Arrange the following fraction in descending order: $\frac{4}{5},\frac{7}{10},\frac{11}{15},\frac{17}{20}$
AnswerWe have, $\frac{4}{5},\frac{7}{10},\frac{11}{15},\frac{17}{20}$
Taking the $LCM$ of $5, 10, 15$ and $20$,
we get $5 \times 2 \times 2 \times 3 = 60$
Now, we convert the given fractions to equivalent fractions by making the denominators $48,$
$\frac{4\times12}{5\times12},\frac{7\times6}{10\times6},\frac{11\times4}{15\times4},\frac{17\times3}{20\times3}$
$\frac{48}{60},\frac{42}{60},\frac{44}{60},\frac{51}{60}$
As we know $51 > 48 > 44 > 42$
Therefore, $\frac{51}{60}<\frac{48}{60}<\frac{44}{60}<\frac{42}{60}$
Hence, $\frac{17}{20}<\frac{4}{5}<\frac{11}{15}<\frac{7}{10}$
View full question & answer→Question 75 Marks
Suman studies for $5\frac{2}{3}$ hours daily. She devotes $2\frac{4}{5}$ hours of her time lor Science and Mathematics. How much time does she devote for other subjects?
AnswerGiven, Suman studies for $5\frac{2}{3}$ i.e., $\frac{17}{3}$
hours daily She devotes $5\frac{2}{3}$ i.e., $\frac{17}{3}$
hours of her time for science and Mathematics.
Let x be time she devotes for other subject. $\frac{17}{3}=\text{x}+\frac{14}{5}$
$\Rightarrow\text{x}=\frac{17}{3}-\frac{14}{5}$
Taking out the $LCM$ of $3$ and $5$ we get, $3 × 5 = 15$
Now, we convert the given fractions to equivalent fractions by making the denominators $48$, we get, $\Rightarrow\text{x}=\frac{17\times5}{3\times5}-\frac{14\times3}{5\times3}$
$\Rightarrow\text{x}=\frac{85}{15}-\frac{42}{15}$
$\Rightarrow\text{x}=\frac{85-42}{15}\text{hours}$
$\Rightarrow\text{x}=\frac{43}{15}\text{hours}$
$\Rightarrow\text{x}=2\frac{13}{15}\text{hours}$
View full question & answer→Question 85 Marks
Arrange the following fractions in ascending order: $\frac{3}{8},\frac{5}{6},\frac{6}{8},\frac{2}{4},\frac{1}{3}$
Answer$\frac{3}{8},\frac{5}{6},\frac{6}{8},\frac{2}{4},\frac{1}{3}$
Taking the $LCM$ of $8, 6, 8, 4$ and $3,$
we get $2 \times 4 \times 3 = 24$
Now, we convert the given fractions to equivalent fractions by making the denominators $24$, $\frac{3\times3}{8\times3},\frac{5\times4}{6\times4},\frac{6\times3}{8\times3},\frac{2\times6}{4\times6},\frac{1\times8}{3\times8}$
$=\frac{9}{24},\frac{20}{24},\frac{18}{24},\frac{12}{24},\frac{8}{24}$
We know that, $8 < 9 < 12 < 18 < 20$
Therefore, $\frac{8}{24}<\frac{9}{24}<\frac{12}{24}<\frac{18}{24}<\frac{20}{24}$
Hence, $13 < 38 < 24 < 68 < 56$
View full question & answer→Question 95 Marks
Compare the following fractions by using the symbo $> or < or = \frac{17}{15}\text{ and }\frac{119}{105}$
AnswerWe have, $\frac{17}{15}\text{ and }\frac{119}{105}$
Taking the $LCM$ of $15$ and $105$,
we get $5 \times 3 \times 7 = 105$
Now, we convert the given fractions to equivalent fractions by making the denominators $105$,
$\frac{17\times7}{15\times7}\text{ and }\frac{119}{105}$
$\frac{119}{105}\text{ and }\frac{119}{105}$
View full question & answer→Question 105 Marks
In a "magic square", the sum of the numbers in each row, in each column and along the diagonal is the same. Is this a magic square?
| $\frac{4}{11}$ |
$\frac{9}{11}$ |
$\frac{2}{11}$ |
| $\frac{3}{11}$ |
$\frac{5}{11}$ |
$\frac{7}{11}$ |
| $\frac{8}{11}$ |
$\frac{1}{11}$ |
$\frac{6}{11}$ |
AnswerGiven,
| $\frac{4}{11}$ |
$\frac{9}{11}$ |
$\frac{2}{11}$ |
| $\frac{3}{11}$ |
$\frac{5}{11}$ |
$\frac{7}{11}$ |
| $\frac{8}{11}$ |
$\frac{1}{11}$ |
$\frac{6}{11}$ |
Along the $1^{\text {st }}$ column $=\frac{4}{11}+\frac{3}{11}+\frac{8}{11}=\frac{15}{11}$
Along the $2^{\text {nd }}$ column $=\frac{9}{11}+\frac{5}{11}+\frac{1}{11}=\frac{15}{11}$
Along the $3^{\text {rd }}$ column $=\frac{2}{11}+\frac{7}{11}+\frac{6}{11}=\frac{15}{11}$
Along the $1^{\text {st }}$ column $=\frac{4}{11}+\frac{9}{11}+\frac{2}{11}=\frac{15}{11}$
Along the $2^{\text {nd }}$ row $=\frac{3}{11}+\frac{5}{11}+\frac{7}{11}=\frac{15}{11}$
Along the $3^{\text {rd }}$ row $=\frac{8}{11}+\frac{1}{11}+\frac{6}{11}=\frac{15}{11}$
Diagonally $=\frac{4}{11}+\frac{5}{11}+\frac{6}{11}=\frac{15}{11}$
And $\frac{2}{11}+\frac{5}{11}+\frac{8}{11}=\frac{15}{11}$
Therefore, the sum of numbers in each row, in row column and along the diagonal is same and the sum is $\frac{15}{11}$ View full question & answer→Question 115 Marks
Each side of a square is $6 \frac{2}{3} m$ long. Find its area.
Answer$44 \frac{4}{9} m^2$
View full question & answer→Question 125 Marks
Sharda can walk $8 \frac{1}{3} km$ in one hour. How much distance will she cover in $2 \frac{2}{5}$ hours?
View full question & answer→Question 135 Marks
If milk is available at ₹ $17 \frac{3}{4}$ per litre, find the cost of $7 \frac{2}{5}$ litres of milk.
Answer₹$131 \frac{7}{20}$
View full question & answer→Question 145 Marks
In a charity show ₹ 6496 were collected by selling some tickets. If the price of each ticket wis ₹$ 50 \frac{3}{4}$ how many tickets were sold?
View full question & answer→Question 155 Marks
In mid-day meal scheme $\frac{3}{10}$ litre of milk is given to each student of a primary school. If 30 litre of milk is distributed every day in the school, how many students are there in the school?
View full question & answer→Question 165 Marks
By selling oranges at the rate of ₹$ 5 \frac{1}{4}$ per orange, a fruit-seller gets ₹ $630$. How many dozens oranges does he sell?
View full question & answer→Question 175 Marks
The cost of $6 \frac{1}{4} kg$ of apples is ₹ 400 . At what rate per kg are the apples being sold?
View full question & answer→Question 185 Marks
The product of two numbers is $25 \frac{5}{6}$. If one of the numbers is $6 \frac{2}{3}$, find the other,
View full question & answer→Question 195 Marks
The length of a rectangular plot of area $65 \frac{1}{3} m^2$ is $12 \frac{1}{4} m$. What is the width of the plot?
View full question & answer→Question 205 Marks
There are 45 students in a class and $\frac{3}{5}$ of them are boys. How many girls are there in the class?
View full question & answer→Question 215 Marks
A sugar bag contains 30 kg of sugar. After consuming $\frac{2}{3}$ of it , how much sugar is left in the bag?
View full question & answer→Question 225 Marks
Ravish and Ravi went for a picnic. Their grandmother gave them a water bottle that contained 5 litres of water. Ravish consumed $\frac{2}{5}$ of the water. Ravi consumed the remaining water.
(i) How much water did Ravish drink?
(ii) What fraction of the total quantity of water did Ravi drink?
Answer(i) 2 litres
(ii) $\frac{3}{5}$
View full question & answer→Question 235 Marks
In the school annual day function, $\frac{2}{7}$ of the total seats in the auditorium are occupied by class VII students. If there are 175 seats in the auditorium, find the number of students in class VII.
View full question & answer→Question 245 Marks
A total of 25 ply-boards are stacked on the top of each other. If each board is $2 \frac{3}{5} cm$ thick. How high is the stack?
View full question & answer→Question 255 Marks
A car runs 18 km in one litre of petrol. How much distance will it cover in $3 \frac{4}{9}$ litres of petrol?
View full question & answer→Question 265 Marks
Lipika reads a book 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$10 \frac{1}{2}$ hours
View full question & answer→Question 275 Marks
Shikha plants 5 saplings in a row in her garden. The distance between two adjacent saplings is $\frac{3}{4} m$. Find the distance between the first and the last sapling.
View full question & answer→Question 285 Marks
Arrange the following fraction in descending order:
$\frac{2}{7}, \frac{11}{35}, \frac{9}{14}, \frac{13}{28}$
Answer$\frac{9}{14}>\frac{13}{28}>\frac{11}{35}>\frac{2}{7}$
View full question & answer→Question 295 Marks
Arrange the following fraction in ascending order:
$\frac{4}{6}, \frac{3}{8}, \frac{6}{12}, \frac{5}{16}$
Answer$\frac{5}{16}<\frac{3}{8}<\frac{6}{12}<\frac{4}{6}$
View full question & answer→Question 305 Marks
Arrange the following fraction in ascending order:
$\frac{3}{8}, \frac{5}{6}, \frac{6}{8}, \frac{2}{4}, \frac{1}{3}$
Answer$\frac{1}{3}<\frac{3}{8}<\frac{2}{4}<\frac{6}{8}<\frac{5}{6}$
View full question & answer→Question 315 Marks
In a "magic square", the sum of the numbers in each row, in each column and along the diagonal is the same. Is this a magic square?| $\frac{4}{11}$ | $\frac{9}{11}$ | $\frac{2}{11}$ |
| $\frac{3}{11}$ | $\frac{5}{11}$ | $\frac{7}{11}$ |
| $\frac{8}{11}$ | $\frac{1}{11}$ | $\frac{6}{11}$ |
View full question & answer→Question 325 Marks
A rectangular sheet of paper is $12 \frac{1}{2} cm$ long and $10 \frac{2}{3} cm$ wide. Find its perimeter.
Answer$46 \frac{1}{3} cm$
View full question & answer→Question 335 Marks
A piece of wire is of length $12 \frac{3}{4} m$. If it is cut into two pieces in such a way that the length of one piece is $5 \frac{1}{4} m$, what is the length of the other piece?
View full question & answer→Question 345 Marks
Suman studies for $5 \frac{2}{3}$ hours daily. She devotes $2 \frac{4}{5}$ hours of her time for Science and Mathematics. How much time does she devote for other subjects?
Answer$2 \frac{13}{15}$ hours
View full question & answer→Question 355 Marks
What should be added to $5 \frac{4}{15}$ to get $12 \frac{3}{5}$ ?
View full question & answer→Question 365 Marks
What should be added to $5 \frac{3}{7}$ to get $12 ?$
View full question & answer→