Question 13 Marks
Jeevika takes $\frac{10}{3}$ minutes to take a complete round of the park and her friend Namit takes $\frac{13}{4}$ minutes to do the same. Who takes less time and by how much?
AnswerTime taken by Jeevika = $\frac{10}{3}$ minutes
and time taken by Narnit = $\frac{13}{4}$ minutes
Now, $\frac{10}{3} \times \frac{4}{4}=\frac{40}{12}$ and $\frac{13}{4} \times \frac{3}{3}=\frac{39}{12}$
Clearly, $\frac{10}{3}>\frac{13}{4}$
∴ Jeevika takes less ti me by $\left(\frac{10}{3}-\frac{13}{4}\right)$ minutes
$=\left(\frac{40}{12}-\frac{39}{12}\right)$ minutes
$=\frac{1}{12}$ minutes.
View full question & answer→Question 23 Marks
Jaya’s school is $\frac{7}{10}$ km from her home. She takes an auto for $\frac{1}{2}$ km from her home daily, and then walks the remaining distance to reach her school. How much does she walk daily to reach the school?
AnswerTotal distance between school and home = $\frac{7}{10} km$
Distance travelled in Auto = $\frac{1}{2} km$.
∴ Distance she walks daily to reach the school
$\begin{array}{l}=\left(\frac{7}{10}-\frac{1}{2}\right) km \\ =\left(\frac{7}{10}-\frac{1}{2} \times \frac{5}{5}\right) km \\ =\left(\frac{7}{10}-\frac{5}{10}\right) km \\ =\frac{2}{10} km \\ =\frac{1}{5} km\end{array}$
View full question & answer→Question 33 Marks
Geeta bought $\frac{2}{5}$ meter of lace and Shamim bought $\frac{3}{4}$ meter of the same lace to put a complete border on a table cloth whose perimeter is 1 meter long. Find the total length of the lace they both have bought. Will the lace be sufficient to cover the whole border?
AnswerLength of lace bought by Geeta = $\frac{2}{5} m$
Length of lace bought by Shamim = $\frac{3}{4} m$
Total length of lace bought = $\frac{2}{5}+\frac{3}{4}$
LCM of 5 and 4 is 20.
$\begin{array}{l}\frac{2}{5}=\frac{2}{5} \times \frac{4}{4}=\frac{8}{20} \\ \frac{3}{4}=\frac{3}{4} \times \frac{5}{5}=\frac{15}{20} \\ \frac{8}{20}+\frac{15}{20}=\frac{23}{20}=1 \frac{3}{20}\end{array}$
This length is more than 1 m. So, lace is more than sufficient or will be left extra after covering the border.
View full question & answer→Question 43 Marks
Rahim mixes $\frac{2}{3}$ liters of yellow paint with $\frac{3}{4}$ liters of blue paint to make green paint What is the volume of green paint he has made?
AnswerQuantity of yellow paint added = $\frac{2}{3}$ litres
Quantity of blue paint added = $\frac{3}{4}$ litres
Total quantity of green paint made = $\frac{2}{3}+\frac{3}{4}$
LCM of 3 and 4 is 12.
$\begin{array}{l}\frac{2}{3}=\frac{2}{3} \times \frac{4}{4}=\frac{8}{12} \\ \frac{3}{4}=\frac{3}{4} \times \frac{3}{3}=\frac{9}{12} \\ \frac{8}{12}+\frac{9}{12}=\frac{8+9}{12}=\frac{17}{12}\end{array}$
So, the total quantity of paint made is $\frac{17}{12}$ liters.
View full question & answer→Question 53 Marks
Write the fractions in descending order.
$\frac{3}{4}, \frac{12}{5}, \frac{7}{12}, \frac{5}{4}$
Answer$\frac{3}{4}=\frac{3 \times 15}{4 \times 15}=\frac{45}{60}, \frac{12}{5}=\frac{12 \times 12}{5 \times 12}=\frac{144}{60}$
$\frac{7}{12}=\frac{7 \times 5}{12 \times 5}=\frac{35}{60}, \frac{5}{4}=\frac{5 \times 15}{4 \times 15}=\frac{75}{60}$
As $\frac{144}{60}>\frac{75}{60}>\frac{45}{60}>\frac{35}{60}$. So, $\frac{12}{5}>\frac{5}{4}>\frac{3}{4}>\frac{7}{12}$
View full question & answer→Question 63 Marks
Write the fractions in descending order.
$\frac{25}{16}, \frac{7}{8}, \frac{13}{4}, \frac{17}{32}$
Answer$\frac{25}{16}=\frac{25 \times 2}{16 \times 2}=\frac{50}{32}, \frac{7}{8}=\frac{7 \times 4}{8 \times 4}=\frac{28}{32}$
$\frac{13}{4}=\frac{13 \times 8}{4 \times 8}=\frac{104}{32}, \frac{17}{32}=\frac{17 \times 1}{32 \times 1}=\frac{17}{32}$
As $\frac{104}{32}>\frac{50}{32}>\frac{28}{32}>\frac{17}{32}$. So, $\frac{13}{4}>\frac{25}{16}>\frac{7}{8}>\frac{17}{32}$
View full question & answer→Question 73 Marks
Write fractions ascending order.
$\frac{19}{24}, \frac{5}{6}, \frac{7}{12}$
AnswerThe given fractions are $\frac{19}{24}, \frac{5}{6}, \frac{7}{12}$
Here LCM of 24, 6, 12 is 24.
$\therefore \frac{19 \times 1}{24 \times 1}, \frac{5 \times 4}{6 \times 4}, \frac{7 \times 2}{12 \times 2}$
Thus $\frac{19}{24}<\frac{20}{24}>\frac{14}{24}$
On arranging in ascending Order, we get
$\begin{array}{l}\frac{14}{24}, \frac{19}{24}, \frac{20}{24} \\ \Rightarrow \frac{7}{12}, \frac{19}{24}, \frac{5}{6}\end{array}$
View full question & answer→Question 83 Marks
Write fractions ascending order.
$\frac{7}{10}, \frac{11}{15}, \frac{2}{5}$
AnswerThe given fractions are $\frac{7}{10}, \frac{11}{15}, \frac{2}{5}$
Let us find LCM of denominator 10, 15, 5
∴ LCM of 10, 15 and 5 = 2 × 3 × 5 = 30
Now let us make denominator of each fractions as LCM
$\frac{7 \times 3}{10 \times 3}, \frac{11 \times 2}{15 \times 2}, \frac{2 \times 6}{5 \times 6}$
$\frac{21}{30}, \frac{22}{30}, \frac{12}{30}$
Clearly $\frac{12}{30}<\frac{21}{30}<\frac{22}{30}$
$\Rightarrow \frac{2}{5}<\frac{7}{10}<\frac{11}{5}$
Hence given fractions in ascending order are: $\frac{2}{5}, \frac{7}{10} \frac{11}{5}$ View full question & answer→Question 93 Marks
Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.
$\frac{13}{6}$ and $\frac{1}{9}$
AnswerGiven fractions are $\frac{13}{6}$ and $\frac{1}{9}$
Here, the denominators are 6 and 9.
And least common multiple of 6 and 9 is 18.
Now for $\frac{13}{6}$ multiply both the numerator and the denominator by 3.
$\frac{13}{6}=\frac{13 \times 3}{6 \times 3}=\frac{39}{18}$
And for $\frac{1}{9}$ multiply both the numerator and the denominator by 2, we get
$\frac{1}{9}=\frac{1 \times 2}{9 \times 2}=\frac{2}{18}$
So, the equivalent fractions with the same denominator are:
$\frac{39}{18}$ and $\frac{2}{18}$
View full question & answer→Question 103 Marks
Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.
$\frac{8}{3}$ and $\frac{11}{4}$
AnswerGiven fractions are $\frac{8}{3}$ and $\frac{11}{4}$
Here, the denominators are 3 and 4.
And least common multiple of 3 and 4 is 12.
Now for $\frac{8}{3}$ multiply both the numerator and the denominator by 4.
$\frac{8}{3}=\frac{8 \times 4}{3 \times 4}=\frac{32}{12}$
And for $\frac{11}{4}$ multiply both the numerator and the denominator by 3, we get
$\frac{11}{4}=\frac{11 \times 3}{4 \times 3}=\frac{33}{12}$
So, the equivalent fractions with the same denominator are:
$\frac{32}{12}$ and $\frac{33}{12}$
View full question & answer→Question 113 Marks
Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.
$\frac{1}{10}$ and $\frac{2}{9}$
AnswerGiven fractions are $\frac{1}{10}$ and $\frac{2}{9}$
Here, the denominators are 10 and 9.
And least common multiple of 10 and 9 is 90.
Now for $\frac{1}{10}$ multiply both the numerator and the denominator by 9.
$\frac{1}{10}=\frac{1 \times 9}{10 \times 9}=\frac{9}{90}$
And for 2 multiply both the numerator and the denominator by 10, we get
$\frac{2}{9}=\frac{2 \times 10}{9 \times 10}=\frac{20}{90}$
So, the equivalent fractions with the same denominator are:
$\frac{9}{90}$ and $\frac{20}{90}$
View full question & answer→Question 123 Marks
Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.
$\frac{9}{4}$ and $\frac{5}{2}$
AnswerGiven fractions are $\frac{9}{4}$ and $\frac{5}{2}$
Here, the denominators are 4 and 2.
And least common multiple of 4 and 2 is 4.
Now for $\frac{5}{2}$ multiply both the numerator and the denominator by 2.
$\frac{5}{2}=\frac{5 \times 2}{2 \times 2}=\frac{10}{4}$
and $\frac{9}{4}$ already have a denominator 4
So, the equivalent fractions with the same denominator are:
$\frac{9}{4}$ and $\frac{10}{4}$
View full question & answer→Question 133 Marks
Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.
$\frac{6}{7}$ and $\frac{8}{5}$
AnswerGiven fractions are $\frac{6}{7}$ and $\frac{8}{5}$
Here, the denominators are 7 and 5.
And least common multiple of 7 and 5 is 35.
Now for $\frac{6}{7}$ multiply both the numerator and the denominator by 5.
$\frac{6}{7}=\frac{6 \times 5}{7 \times 5}=\frac{30}{35}$
And for $\frac{8}{5}$ multiply both the numerator and the denominator by 7, we get
$\frac{8}{5}=\frac{8 \times 7}{5 \times 7}=\frac{56}{35}$
So, the equivalent fractions with the same denominator are:
$\frac{30}{35}$ and $\frac{56}{35}$
View full question & answer→Question 143 Marks
Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.
$\frac{3}{4}$ and $\frac{3}{5}$
AnswerGiven fractions are $\frac{3}{4}$ and $\frac{3}{5}$
Here, the denominators are 4 and 5.
And least common multiple of 4 and 5 is 20.
Now for $\frac{3}{4}$ multiply both the numerator and the denominator by 5.
$\frac{3}{4}=\frac{3 \times 5}{4 \times 5}=\frac{15}{20}$
And for $\frac{3}{5}$ multiply both the numerator and the denominator by 4, we get
$\frac{3}{5}=\frac{3 \times 4}{5 \times 4}=\frac{12}{20}$
So, the equivalent fractions with the same denominator are:
$\frac{15}{20}$ and $\frac{12}{20}$
View full question & answer→Question 153 Marks
Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.
$\frac{8}{3}$ and $\frac{5}{6}$
AnswerGiven fractions are $\frac{8}{3}$ and $\frac{5}{6}$
Here, the denominators are 3 and 6.
And least common multiple of 3 and 6 is 6.
Now for $\frac{8}{3}$ multiply both the numerator and the denominator by 2.
$\frac{8}{3}=\frac{8 \times 2}{3 \times 2}=\frac{16}{6}$
$\frac{5}{6}$ already have a denominator 6.
Hence, the equivalent fractions with the same denominator are:
$\frac{16}{6}$ and $\frac{5}{6}$
View full question & answer→Question 163 Marks
Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.
$\frac{7}{2}$ and $\frac{3}{5}$
AnswerGiven fractions are $\frac{7}{2}$ and $\frac{3}{5}$
Here, the denominators are 2 and 5.
And least common multiple of 2 and 5 is 10.
Hence for both fractions let’s have same denominator of 10.
Now for $\frac{7}{2}$ multiply both the numerator and the denominator by 5.
$\frac{7}{2}=\frac{7 \times 5}{2 \times 5}=\frac{35}{10}$
And for $\frac{3}{5}$ multiply both the numerator and the denominator by 2, we get,
$\frac{3 \times 2}{5 \times 2}=\frac{6}{10}$
Hence, the equivalent fractions with the same denominator are:
$\frac{35}{10}$ and $\frac{6}{10}$
View full question & answer→Question 173 Marks
Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.
AnswerOne roti is shared as shown in the figure below:
The four shares must be equal to each other!
A similar distribution will be done for the second roti also.
So, each child will get $\frac{1}{4}$ part from a rod.
So, the total fraction of roti received by each child from 2 rotis = $\frac{2}{4}=\frac{1}{2}$
The division fact is $2 \div 4=\frac{ 2 }{ 4 }$
The addition fact is $=\frac{2}{4}+\frac{2}{4}+\frac{2}{4}+\frac{2}{4}$
The multiplication fact is $2=4 \times \frac{2}{4}$ View full question & answer→Question 183 Marks
Three rotis are shared equally by four children, show the division in the picture and write a fraction of how much each child gets. Also, write the corresponding division facts, addition facts, and, multiplication facts.
The fraction of roti each child gets is ___________
Division fact:
Addition fact:
Multiplication fact:
Compare your picture and answer with your classmates!
Question 193 Marks
Figure out the number of whole units in each of the following fractions:
(a) $\frac{8}{3}$
(b) $\frac{11}{5}$
(C) $\frac{9}{4}$
View full question & answer→Question 203 Marks
On a number line, draw lines of length $\frac{1}{10}, \frac{3}{10}$, and $\frac{4}{5}$.
Answer
Divide the unit into 10 equal parts and point A represents $\frac{1}{10}$.
Divide a unit into 10 equal parts and point B represents $\frac{3}{10}$.
Divide a unit into 5 equal parts and point C represents $\frac{4}{5}$. View full question & answer→Question 213 Marks
Match each fractional unit with the correct picture:
Question 223 Marks
Draw a picture and write an addition statement as above to show:
(a) 5 times $\frac{1}{4}$ of a roti
(b) 9 times $\frac{1}{4}$ of a roti
Answer(a)
5 times $\frac{1}{4}$ of a roti
$=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}$
(b)
9 times $\frac{1}{4}$ of a roti
$=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}$ View full question & answer→Question 233 Marks
Make $\frac{1}{3}$ using a paper strip. Can you use this to also make $\frac{1}{6} ?$
AnswerTake a strip of paper.
Fold the strip into three equal parts and then open up.
Yes, we can also make $\frac{1}{6}$ using a paper strip by folding 6 again the above strip. View full question & answer→Question 243 Marks
Continue this table of $\frac{1}{2}$ for 2 more steps.
Answer |  |
$\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$
$=6$ times half | $\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$
= 7 times half |
View full question & answer→Question 253 Marks
Arrange these fraction words in order of size from the smallest to the biggest in the empty box below: One and a half, three quarters, one and a quarter, half, quarter, two and a half.
Answer
∴ The fractions from smallest to the biggest are as follows: quarter, half, three quarters one and a quarter, one and a half, two and a half.
View full question & answer→Question 263 Marks
Are $\frac{3}{6}, \frac{4}{8}, \frac{5}{10}$ equivalent fractions? Why?
AnswerHere, simplest form of $\frac{ 3 }{ 6 }=\frac{3 \div 3}{6 \div 3}=\frac{1}{2}$ [HCF of 3 and 6 is 3]
and simplest form of $\frac{4}{8}$ is $\frac{4 \div 4}{8 \div 4}=\frac{1}{2}$ [HCF of 4 and 8 is 4]
and simplest form of $\frac{5}{10}$ is $\frac{5 \div 5}{10 \div 5}=\frac{1}{2}$ [HCF of 5 and 10 is 5]
Hence, $\frac{3}{6}, \frac{4}{8}, \frac{5}{10}$ are equivalent fractions.
View full question & answer→