Important Questions for CBSE Class 6 Maths Chapter 7 - Fractions

Very Short Answer Questions                                                1 Mark

1. Write fraction representing the shaded portion

Ans: Given- A figure with some shaded squares in it.

We have to find fractions for the shaded portion.

Total number of squares $=12$

Number of shaded boxes $=6$

$\therefore $ the shaded portion $=\dfrac{6}{12}$

2. Shade in the given figure: $\dfrac{5}{9}$

Ans: Given: A figure having $9$ boxes.

We have to shade 5 boxes out of a total 9 boxes.

Therefore,

3. Write in fraction form of eight-ninths.

Ans: We are given eight-ninths

To find: the fraction form of eight-ninths

Eight - ninths means eight parts out of nine

So, the fraction will be $\dfrac{8}{9}$

4. Write down the fraction with numerator 3, denominator 9

Ans: Given, numerator =3

Denominator =9

We have to find the fraction.

We know that the numerator is the above part of a fraction and the denominator is the below part of the fraction.

$\therefore$ The fraction is $\dfrac{3}{9}$.

5. Fill up the blanks

1. $\mathbf{\dfrac{1}{12}\square 1}$

Ans: Given: $\dfrac{1}{12}\square 1$

We have to put a sign between the terms like $<,>,=$

Solve, $\dfrac{1}{12}$

$=0.83$

We can see that the value is less than one.

$\therefore \dfrac{1}{12}<1$

2. $\mathbf{\dfrac{6512}{6512}\square 1}$

Ans: Given: $\dfrac{6512}{6512}\square 1$

We have to put a sign between the terms like $<,>,=$

Solve, $\dfrac{6512}{6512}$

$=1$

Therefore,

$\dfrac{6512}{6512}=1$

6. Compare $\mathbf{\dfrac{4}{5}}$ and $\mathbf{\dfrac{3}{5}}$

Ans: Given: two terms $\dfrac{4}{5},\,\dfrac{3}{5}$

We have to compare the given terms.

We can see that the denominator of both the terms is the same. So we will compare the numerators only.

Here, 

4>3

 $\therefore \dfrac{4}{5}>\dfrac{3}{5}$

Short Answer Questions                                                           2 Marks

1. Find $\mathbf{\dfrac{3}{4}}$ of $\mathbf{12.}$

Ans: Given, two terms $\dfrac{3}{4},12$

We have to find $\dfrac{3}{4}$ of $12.$

We know that $x$ of $y$ means $x\times y$

$\therefore \dfrac{3}{4}$ of $12$\[\]

$ =\dfrac{3}{4}\times 12 $

$ =9 $

2. What fraction of an hour is 35 minutes?

Ans: Given, a time

We have to find $35$ minutes will be what fraction of an hour.

We know that $1$ hour $=60$ minutes

$\therefore $ fraction will be $\dfrac{35}{60}.$

3. The figure given can be written in the fraction form as $\mathbf{\dfrac{2}{3}.}$ Say true or false.

Ans: Given: figure

We have to find if the figure shows fraction $\dfrac{2}{3}.$

As we can see that all parts of the figure are not similar. Therefore, it cannot be represented as a fraction. So, the statement is False.

4. Name the numerator and denominator in the $\mathbf{\dfrac{16}{20}}$

Ans: Given: $\dfrac{16}{20}$

To find: numerator and denominator

We know that the numerator is the above part of the fraction and the denominator is the below part.

$\therefore $ Numerator $=16$

Denominator $=20$

5. Convert $\mathbf{\dfrac{30}{8}}$ into a mixed fraction

Ans: Given: $\dfrac{30}{8}$

To find: mixed fraction of the given expression.

We got mixed fraction by dividing the fraction

We know if  $\dfrac{x}{y}=z$ then mixed fraction is $z\dfrac{x}{y}$

$\therefore $ $\dfrac{30}{8}$

$ =3\dfrac{6}{8} $

$ =3\dfrac{3}{4}$

6. Convert $\mathbf{6\dfrac{7}{9}}$ into improper fraction.

Ans: Given: $6\dfrac{7}{9}$

To find the improper form of the given expression

We know that \[z\dfrac{x}{y}=\dfrac{y\times z+x}{y}\]

So, $6\dfrac{7}{9}=9\times 6+7$ as numerator

Therefore, the improper fraction will be $\dfrac{61}{9}.$

7. Fill in the blanks $\mathbf{\dfrac{54}{63}=\dfrac{6}{\square }}$

Ans:  Given: $\dfrac{54}{63}=\dfrac{6}{\square }$

We need to fill the blank

On Left Hand Side, divide numerator and denominator y by $9$

Thus, $\dfrac{54}{63}\div \dfrac{9}{9}$

$=\dfrac{6}{7}$

Thus, the number which has to be filled at blank is $7.$

8. Simplify:

1. $\mathbf{\dfrac{3}{8}+\dfrac{4}{8}+\dfrac{2}{8}}$

Ans: Given: $\dfrac{3}{8}+\dfrac{4}{8}+\dfrac{2}{8}$

We have to simplify the fractions by adding them

As the denominator of each fraction is same then the $\text{L}\text{.C}\text{.M}$ will be $8.$

Now, simply add the numerator of each fraction, we get

$=\dfrac{3+4+2}{8}$
$=\dfrac{9}{8}.$

2. $\mathbf{\dfrac{8}{9}-\dfrac{6}{9}}$

Ans: We have to find the difference between the fractions.

We can see that the denominator of both fractions is same then the $\text{L}\text{.C}\text{.M}$will be $9.$

Now, simply subtract the numerators, we get

$ \dfrac{8-6}{9} $

$ =\dfrac{2}{9} $

Short Answer Questions                                                           3 Marks

1. Seema has 28 books. She gave $\mathbf{\dfrac{4}{10}}$ to Meera. How many books does Meena has? How much is left with Seema?

Ans: Given: Total books Seema has $=28$

Seema gave books to Meera $\dfrac{4}{10}$ of $28$

$\therefore $ Books with Meena $=\dfrac{4}{10}\times 28$

$=11$ Books

Now, books left with Seema $=28-11$

$=17$ Books

2. Represent $\mathbf{3\dfrac{2}{5}}$ on the number line.

Ans: Given: $3\dfrac{2}{5}$

We have to represent the fraction on the number line.

We can write the fraction as,

$3\dfrac{2}{5}=3+\dfrac{2}{5}$

Therefore, we represent it on the number line as 

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3. Write a fraction equivalent to $\mathbf{\dfrac{4}{5}}$ with numerator 16.

Ans: Given: $\dfrac{4}{5}$

We have to find a fraction so that the numerator of fraction is $16.$

Multiply the numerator and denominator of the given fraction with $4$to get the required fraction.

$ \dfrac{4}{5}\times \dfrac{4}{4} $ 

$ =\dfrac{16}{20} $

4. Write a fraction equivalent to $\mathbf{\dfrac{42}{60}}$ with denominator 10.

Ans: Given: $\dfrac{42}{60}$

We have to find a fraction so that the denominator of fraction is $10.$

Divide the numerator and denominator of the given fraction with $6$ to get the required fraction.

$ \therefore \dfrac{42}{60}\div \dfrac{6}{6} $

$ =\dfrac{7}{10} $

5. Simplify $\mathbf{\dfrac{7}{10}}$ into the simplest form.

Ans: Given: $\dfrac{7}{10}$

We have to find the simplest form of the fraction.

The HCF of the terms \[7\text{ }\!\!\And\!\!\text{ }10\] is \[1.\]

Thus, the fraction $\dfrac{7}{10}$ is already in its simplest form.

6. Simplify \[\mathbf{2\dfrac{7}{9}+\dfrac{11}{15}+\dfrac{9}{24}-3\dfrac{1}{4}}\]

Ans: Given: \[2\dfrac{7}{9}+\dfrac{11}{15}+\dfrac{9}{24}-3\dfrac{1}{4}\]

We need to simplify the given expression. So we’ll find \[\text{LCM}\]and then simplify the expression.

\[\text{LCM}\]of numbers \[9,15,24,4=360\]

$ 2\dfrac{7}{9}+\dfrac{11}{15}+\dfrac{9}{24}-3\dfrac{1}{4} $ 

$ =\dfrac{25}{9}+\dfrac{11}{15}+\dfrac{9}{24}-\dfrac{13}{4} $

$ =\dfrac{1000+264+135-1170}{360} $

$ =\dfrac{1399-1170}{360} $

$ =\dfrac{229}{360} $

7. Subtract $\mathbf{3\dfrac{7}{8}-5\dfrac{1}{6}}$

Ans: Given: $3\dfrac{7}{8}-5\dfrac{1}{6}$

We need to simplify the given expression. So we’ll find \[\text{LCM}\]and then simplify the expression.

\[\text{LCM}\] of the numbers $6,8=24$

$ 3\dfrac{7}{8}-5\dfrac{1}{6} $

$ =\dfrac{31}{6}-\dfrac{31}{8}$ 

$ =\dfrac{31\times 4-31\times 3}{24} $

$ =\dfrac{124-93}{24} $

$ =\dfrac{31}{24} $

Long  Answer Questions                                                           4 Marks

1. Write four equivalent fraction for each of the following:

1. $\mathbf{\dfrac{3}{7}}$

 Ans: Given: $\dfrac{3}{7}$

To find: four equivalent fraction

Multiply and divide numerator and denominator with four different numbers

$ \dfrac{3}{7}\times \dfrac{2}{2}=\dfrac{6}{14} $

$ \dfrac{3}{7}\times \dfrac{3}{3}=\dfrac{9}{21} $

$ \dfrac{3}{7}\times \dfrac{4}{4}=\dfrac{12}{28} $

$ \dfrac{3}{7}\times \dfrac{5}{5}=\dfrac{15}{35} $

2. $\mathbf{\dfrac{300}{900}}$

Ans: To find four equivalent fraction

Multiply and divide numerator and denominator with four different numbers

$ \dfrac{300}{900}\div \dfrac{2}{2}=\dfrac{150}{450}$ 

$ \dfrac{300}{900}\div \dfrac{3}{3}=\dfrac{100}{300} $

$ \dfrac{300}{900}\div \dfrac{5}{5}=\dfrac{60}{180} $

$ \dfrac{300}{900}\div \dfrac{10}{10}=\dfrac{30}{90} $ 

2. Show that $\mathbf{\dfrac{6}{7}}$ and $\mathbf{\dfrac{42}{49}}$ are equivalent fractions.

Ans: Given: Fractions, $\dfrac{6}{7}$, $\dfrac{42}{49}$

We need to show that both the fractions are equivalent.

Thus, $\dfrac{6}{7}=\dfrac{42}{49}$

Cross multiply, we get

$ 6\times 49=249........(1) $

$ 7\times 42=294........(2) $

$ \Rightarrow (1)=(2) $

Therefore, we can say that the given fractions are equivalent.

3. Reduce into simplest form: $\mathbf{\dfrac{225}{500}}$

Ans: Given: $\dfrac{225}{500}$

We need to find the simplest form of the given fraction.

Divide by \[5,\] we get

$\dfrac{225}{500}\div \dfrac{5}{5}=\dfrac{45}{100}$

Again, divide by \[5,\] we get

$\dfrac{45}{100}\div \dfrac{5}{5}=\dfrac{9}{20}$

We can see that the HCF of the terms of the fraction is $1$

$\therefore \dfrac{9}{20}$ is the simplest form of the given fraction.

4. Convert \[\mathbf{\dfrac{1}{4},\dfrac{5}{8},\dfrac{13}{24}}\] into like fractions.

Ans: Given: \[\dfrac{1}{4},\dfrac{5}{8},\dfrac{13}{24}\]

We need to convert the given fractions into like fractions.

The LCM of the denominators will be

\[\begin{align} & 4\left| \!{\underline {\, 4,8,24 \,}} \right.  \\ & 2\left| \!{\underline {\, 1,2,6 \,}} \right.  \\ & \left| \!{\underline {\, 1,1,3 \,}} \right.  \\ \end{align}\]

Therefore, LCM = $4\times 2\times 3$ 

$\quad\quad\quad\quad\quad\quad=24$ 

$=\dfrac{\left( 6\times 1 \right),\left( 5\times 3 \right),\left( 13 \right)}{24}$ 

$=\dfrac{6,15,13}{24}$

So, the required like fractions are $\dfrac{6}{24},\dfrac{15}{24},\dfrac{13}{24}$

5. Compare $\mathbf{\dfrac{8}{13}\text{and}\dfrac{8}{7}}$

Ans: Given: fractions $\dfrac{8}{13}\text{and}\dfrac{8}{7}$

We need to compare the fractions.

To compare the fractions the denominator of the fractions must be the same.

To convert into like terms, take LCM then we get

$ =13\times 7 $

$ =91 $

$ \therefore \dfrac{8\times 7,8\times 13}{91} $

$ =\dfrac{56,104}{91} $

$ \therefore \dfrac{56}{91}<\dfrac{104}{91} $

6. Roshni bought a material of length $\mathbf{3\dfrac{2}{5}\text{m}}$ and one more piece of length $\mathbf{2\dfrac{7}{10}\text{m}\text{.}}$ How much material did she purchase in all?

Ans: Given: Length of first material bought by Roshni $=3\dfrac{2}{5}\text{m}$

Length of second material bought by Roshni $=2\dfrac{7}{10}\text{m}$

Total length of material purchased by Roshni will be

$ =3\dfrac{2}{5}+2\dfrac{7}{10} $

$ =3+\dfrac{2}{5}+2+\dfrac{7}{10} $

$ =5+\dfrac{2\times 2+7}{10} $

$ =5+\dfrac{4+7}{10} $

$ =5+\dfrac{11}{10} $

$ =\dfrac{61}{10} $

$ =6\dfrac{1}{10}\text{m} $

7. Ram bought $\mathbf{6\dfrac{1}{2}}$ litres of milk. Out of this $\mathbf{5\dfrac{1}{4}}$ litres was used. How much is the remaining milk?

Ans: Total milk bought by Ram $=6\dfrac{1}{2}\text{litres}$

Milk Used $=5\dfrac{1}{4}\text{litres}$

Remaining milk with Ram will be

$ =6\dfrac{1}{2}-5\dfrac{1}{4} $

$ =6+\dfrac{1}{2}-\left[ 5+\dfrac{1}{4} \right] $

$ =6-5+\left[ \dfrac{1}{2}-\dfrac{1}{4} \right] $

$ =1+\dfrac{1}{4} $

$ =1\dfrac{1}{4}\text{litres} $

Very Long  Answer Questions                                             6 Marks

1.  Classify each of the following into proper, improper and mixed fractions.

1. $\mathbf{\dfrac{1}{5}}$

 Ans: Proper fraction

2. $\mathbf{12}$

Ans: Improper fraction

3. $\mathbf{3\dfrac{1}{5}}$

Ans: Proper fraction

4. $\mathbf{\dfrac{15}{6}}$

Ans: Improper fraction

5. $\mathbf{\dfrac{15}{20}}$

Ans: Proper fraction

2. Compare $\mathbf{\dfrac{5}{8}}$ and $\mathbf{\dfrac{4}{9}}$

Ans: Given: $\dfrac{5}{8}$ and $\dfrac{4}{9}$

We need to compare the given fractions so we will convert both fractions into like fractions by taking LCM.

$ \text{LCM = 72} $

$ \text{=}\dfrac{5\times 9,4\times 8}{72} $

$ =\dfrac{45,32}{72} $

$ =\dfrac{5}{8}>\dfrac{4}{9} $

3. Arrange the following in ascending and descending order $\mathbf{\dfrac{2}{3},\dfrac{3}{4},\dfrac{7}{10},\dfrac{8}{15},\dfrac{5}{8}}$

Ans: Given: fractions $\dfrac{2}{3},\dfrac{3}{4},\dfrac{7}{10},\dfrac{8}{15},\dfrac{5}{8}$

We need to find the ascending and descending order of the fractions.

We will first convert the fractions in like terms and then find the order.

To convert into like terms. LCM will be

$\begin{align} & 4\left| \!{\underline {\, 3,4,10,15,8 \,}} \right.  \\ & 5\left| \!{\underline {\, 3,1,10,15,2 \,}} \right.  \\ & 3\left| \!{\underline {\, 3,1,2,3,2 \,}} \right.  \\ & 2\left| \!{\underline {\, 1,1,2,1,2 \,}} \right.  \\ & \left| \!{\underline {\, 1,1,1,1,1 \,}} \right.  \\ & \text{LCM = 4}\times \text{5}\times \text{3}\times \text{2} \\ & \text{=120} \\ \end{align}$

Then the fractions will be

$ \dfrac{2\times 20,3\times 30,7\times 12,8\times 8,5\times 15}{120} $

$ =\dfrac{80,90,84,64,75}{120}$

$=\dfrac{80}{120},\dfrac{90}{120},\dfrac{84}{120},\dfrac{64}{120},\dfrac{75}{120} $

Ascending order will be

$=\dfrac{64}{120},\dfrac{75}{120},\dfrac{80}{120},\dfrac{84}{120},\dfrac{90}{120} $

$ =\dfrac{8}{15},\dfrac{5}{8},\dfrac{2}{5},\dfrac{7}{10},\dfrac{3}{4} $

Descending order will be

$=\dfrac{90}{120},\dfrac{84}{120},\dfrac{80}{120},\dfrac{75}{120},\dfrac{64}{120} $

$ =\dfrac{3}{4},\dfrac{7}{10},\dfrac{2}{3},\dfrac{5}{8},\dfrac{8}{15} $

Definition of Fraction:

A fraction is a number that represents a part of a whole number. Fractions represent equal parts of a whole or a collection.

Representation of Fraction:

A fraction is represented by two parts separated by the “/” symbol. The number written above the line is called the numerator. It helps us to know how many equal parts of the whole or collection are taken. The number written below the line is known as the denominator. With the help of fraction, we can know the total number of equal parts which are there in a collection.

Types of Fractions

• Proper fractions

• Improper fractions

• Mixed fractions

• Like fractions

• Unlike fractions

• Equivalent fractions

Proper Fractions

The proper fractions are those fractions where the numerator is less than the denominator.

Example: 5/9 will be a proper fraction since “numerator < denominator”.

Improper Fractions

The improper fraction is a fraction where the numerator is greater than the denominator.

Example: 9/5 will be an improper fraction since “denominator < numerator”.

Mixed Fractions

The combination of the integer part and a proper fraction is called a mixed fraction also known as a mixed number.

Example: \[3\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}\]

Like Fractions

Like fractions are a fraction that has two or more fractions that have the same denominator. Example- Take ½ and 2/4, they are alike fractions since if we simplify it mathematically, we will get the same fraction.

Unlike Fractions

Unlike fractions are fractions that have different denominators.

Example: ½ and ⅓ are unlike fractions.

Equivalent Fractions

Two fractions are said to be equivalent to each other if after simplification either of two fractions is equal to the other one.

Example: ⅔ and 4/6 are equivalent fractions.

Since, 4/6 = (2 × 2)/(2 × 3) = ⅔

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There are some basic rules we should know before solving the problems based on fractions.

1. Before performing addition or subtraction on fractions, we must make sure that the denominators are equal. Hence, addition and subtraction of fractions are possible only when the denominator is common.

2. If we have multiplied two fractions, then the numerators are multiplied as well as the denominators are multiplied. Later, simplify the fraction.

3. When we divide a fraction from another fraction, we need to find the reciprocal of the other fraction and then multiply it to the first one to get the answer.

Addition of Fractions

The addition of fractions is easy when they have a common denominator, we need to just add the numerators here.

Example: ⅔ + 8/3 = (2 + 8)/3 = 10/3

If the denominators of the two fractions are different then we have to simplify them by finding the LCM of denominators and then making it common for both fractions.

Example: ⅔ + ¾

Here, the denominators are 3 and 4.

Hence, LCM of 3 and 4 is 12.

Therefore, we multiply  ⅔ by 4/4 and ¾ by 3/3, we get,

= 8/12 + 9/12

= (8 + 9)/12

= 17/12

Subtraction of Fractions

The rule for subtracting two or more fractions is the same as for addition. We should make denominators common to subtract two fractions.

Example: 9/2 – 7/2 = (9-7)/2 = 2/2 = 1

If the denominators of the two fractions are different, then we have to simplify them by finding the LCM of denominators after that making it common for both fractions.

For example ⅔ – ¾

Here, the denominators are 3 and 4.

Hence, LCM of 3 and 4 is 12.

Therefore, we multiply  ⅔ by 4/4 and ¾ by 3/3, we get,

8/12 – 9/12

= (8 – 9)/12

= –1/12

Multiplication of Fractions

As per rule 2, when two fractions are multiplied, then the top part (numerators) and the bottom part (denominators) are multiplied together.

Suppose a/b and c/d are two different fractions, then the multiplication of a/b and c/d will be:

(a/b) × (c/d) = (a × c)/(b × d) = (ac/bd)

Example: Multiply ⅔ and 3/7.

= (⅔) × (3/7) = (2 × 3)/(3 × 7) = 2/7

Division of Fractions

As per rule 3, if we have to divide any two fractions where we need to multiply the first fraction to the reciprocal of the second fraction.

Suppose, a/b and c/d are two different fractions, then the division a/b by c/d can be expressed as:

(a/b) ÷ (c/d) = (a/b) × (d/c) = (ad/bc)

Example: Divide ⅔ by 3/7.

(⅔) ÷ (3/7) = (⅔) × (7/3) = (2 × 7)/(3 × 3) = 14/9

What are the Benefits of Important Questions from Vedantu for Class 7 Math Chapter 7 - Fractions

• Focus on key topics for efficient studying.

• Prepares students for exams and reduces anxiety.

• Reinforces understanding of fundamental concepts.

• Teaches effective time management.

• Enables self-assessment and progress tracking.

• Strategic approach for higher scores.

• Covers a wide range of topics for comprehensive understanding.

• Supports exam preparation and boosts confidence.

Conclusion:

Fractions are a part of our day-to-day life. Fractions make the calculations easier. Also, fractions can be converted into decimals which are heavily used in our monetary system.

After going through the above-given summary, students are advised to attempt the questions provided in Class 6 maths chapter 7 important questions. Students can easily understand the concept behind the question and solve it easily.

Important Related Links for CBSE Class 6 Maths