## NCERT Solutions for Class 6 Maths Chapter 11 Algebra (Ex 11.3) Exercise 11.3

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## Access NCERT Solution for Class 6 Maths Chapter 11- Algebra

### Exercise 11.3

1. Make up as many expressions with numbers (no variables) as you can from three numbers 5, 7 and 8. Every number should be used not more than once. Use only addition, subtraction and multiplication.

Ans: Since there are only three numbers 5, 7 and 8, only two signs from $ + $, $ - $ and $ \times $ can be used at once.

The expressions that can be formed by using $ + $ and $ - $ are as follows.

$5 + \left( {8 - 7} \right)$

$5 + \left( {7 - 8} \right)$

$7 + \left( {8 - 5} \right)$

$7 + \left( {5 - 8} \right)$

$8 + \left( {7 - 5} \right)$

$8 + \left( {5 - 7} \right)$

$5 - \left( {7 + 8} \right)$

$7 - \left( {5 + 8} \right)$

$8 - \left( {5 + 7} \right)$

The expressions that can be formed by using $ + $ and $ \times $ are as follows.

$5 + \left( {8 \times 7} \right)$

$7 + \left( {8 \times 5} \right)$

$8 + \left( {5 \times 7} \right)$

$5 \times \left( {8 + 7} \right)$

$7 \times \left( {8 + 5} \right)$

$8 \times \left( {7 + 5} \right)$

The expressions that can be formed by using $ - $ and $ \times $ are as follows.

$5 - \left( {8 \times 7} \right)$

$7 - \left( {8 \times 5} \right)$

$8 - \left( {7 \times 5} \right)$

$5 \times \left( {8 - 7} \right)$

$5 \times \left( {7 - 8} \right)$

$7 \times \left( {8 - 5} \right)$

$7 \times \left( {5 - 8} \right)$

$8 \times \left( {7 - 5} \right)$

$8 \times \left( {5 - 7} \right)$

2. Which out of the following are expressions with numbers only?

\[\mathbf{y + 3}\]

Ans: The given expression \[y + 3\] contains the variable $y$, which is not a number.

Hence, \[y + 3\] is not an expression with numbers only.

$\mathbf{\left( {7 \times 20} \right) - 8}z$

Ans: The given expression $\left( {7 \times 20} \right) - 8z$ contains the variable $z$, which is not a number.

Hence, $\left( {7 \times 20} \right) - 8z$ is not an expression with numbers only.

$\mathbf{5\left( {21 - 7} \right) + 7 \times 2}$

Ans: The given expression $5\left( {21 - 7} \right) + 7 \times 2$ does not contain variable.

Hence, $5\left( {21 - 7} \right) + 7 \times 2$ is an expression with numbers only.

5

Ans: The given expression 5 does not contain variable.

Hence, it is an expression with numbers only.

$\mathbf{3x}$

Ans: The given expression $3x$ contains a variable $x$, which is not a number.

Hence, $3x$ is not an expression with numbers only.

$\mathbf{5 - 5n}$

Ans: The given expression $5 - 5n$ contains a variable $n$, which is not a number.

Hence, $5 - 5n$ is not an expression with numbers only.

$\mathbf{\left( {7 \times 20} \right) - \left( {5 \times 10} \right) - 45 + p}$

Ans: The given expression $\left( {7 \times 20} \right) - \left( {5 \times 10} \right) - 45 + p$ contains variable $p$, which is not a number.

Hence, $\left( {7 \times 20} \right) - \left( {5 \times 10} \right) - 45 + p$ is not an expression with numbers only.

3. Identify the operations (addition, subtraction, division, multiplication) in forming the following expressions and tell how the expressions have been formed.

\[\mathbf{z + 1,{\text{ }}z--1,{\text{ }}y + 17,\,{\text{ }}y--17}\]

Ans: $z + 1$ is an expression where $z$ and 1 are added.

Therefore, the required operation is addition.

$z - 1$ is an expression where 1 is subtracted from $z$.

Therefore, the required operation is subtraction.

$y + 17$ is an expression where 17 is added to $y$.

Therefore, the required operation is addition.

$y - 17$ is an expression where 17 is subtracted from $y$.

Therefore, the required operation is subtraction.

$\mathbf{17y,{\text{ }}\dfrac{y}{{17}},{\text{ }}5z}$

Ans: $17y$ is an expression where $y$ is multiplied by 17.

Therefore, the required operation is multiplication.

$\dfrac{y}{{17}}$ is an expression where $y$ is divided by 17.

Therefore, the required operation is division.

$5z$ is an expression where $z$ and 5 are to be uploaded.

Therefore, the required operation is multiplication.

$\mathbf{2y + 17,{\text{ }}2y - 17}$

Ans: $2y + 17$ is an expression where first $y$ is multiplied by 2. Then 17 is added to the obtained result.

Therefore, the required operation is multiplication and addition.

$2y - 17$ is an expression where the first $y$ is multiplied by 2. Then 17 is subtracted from the obtained result.

Therefore, the required operation is multiplication and subtraction.

\[7m,{\text{ }} - 7m + 3,{\text{ }} - 7m--3\]

Ans: \[7m\]is an expression where $m$ is multiplied by 7.

Therefore, the required operation is multiplication.

\[ - 7m + 3\] is an expression where the first $m$ is multiplied by $ - 7$. Then 3 is added to the obtained result.

Therefore, the required operation is multiplication and addition.

\[ - 7m - 3\] is an expression where the first $m$ is multiplied by $ - 7$. Then 3 is subtracted from the obtained result.

Therefore, the required operation is multiplication and subtraction.

4. Give expressions for the following cases.

7 added to $p$

Ans: In order to add 7 to $p$, use the addition operation as follows.

$ \Rightarrow p + 7$

7 subtracted from $p$

Ans: In order to subtract 7 from $p$, use the subtraction operation as follows.

$ \Rightarrow p - 7$

$p$ multiplied by 7

Ans: In order to multiply $p$ by 7, use the multiplication operation as follows.

$\Rightarrow p \times 7 $

$\Rightarrow 7p $

$p$ divided by 7

Ans: In order to divide$p$ by 7, use division operation as follows.

$ \Rightarrow \dfrac{p}{7}$

7 subtracted from $ - m$

Ans: In order to subtract 7 from $ - m$, use the subtraction operation as follows.

$ \Rightarrow - m - 7$

# -p multiplied by 5

Ans: In order to multiply $ - p$ by 5, use the multiplication operation as follows.

$\Rightarrow - p \times 5$

$\Rightarrow - 5p$

$ - p$ divided by 5

Ans: In order to divide $ - p$ by 5, use division operation as follows.

$ \Rightarrow \dfrac{{ - p}}{5}$

$ \Rightarrow - \dfrac{p}{5}$

p multiplied by $ - 5$

Ans: In order to multiply $p$ by $ - 5$, use the multiplication operation as follows.

$ \Rightarrow p \times \left( { - 5} \right) $

$ \Rightarrow - p \times 5 $

$\Rightarrow - 5p $

5. Give expressions in the following cases.

11 added to $2m$

Ans: In order to add 11 to $2m$, use addition operation as follows.

$ \Rightarrow 2m + 11$

11 subtracted from $2m$

Ans: In order to subtract 11 from $2m$, use the subtraction operation as follows.

$ \Rightarrow 2m - 11$

5 times $y$ to which 3 is added

Ans: In order to multiply $y$ by 5, use the multiplication operation as follows.

$\Rightarrow y \times 5 $

$\Rightarrow 5y $

In order to add 3 to $5y$, use the addition operation as follows.

$ \Rightarrow 5y + 3$

5 times $y$ from which 3 is subtracted

Ans: In order to multiply $y$ by 5, use the multiplication operation as follows.

$\Rightarrow y \times 5 $

$\Rightarrow 5y $

In order to subtract 3 from$5y$, use the subtraction operation as follows.

$ \Rightarrow 5y - 3$

$y$ is multiplied by $ - 8$

Ans: In order to multiply $y$ by $ - 8$, use the multiplication operation as follows.

$\Rightarrow y \times \left( { - 8} \right) $

$\Rightarrow - y \times 8 $

$\Rightarrow - 8y $

$y$ is multiplied by $ - 8$ and then 5 is added to the result

Ans: In order to multiply $y$ by $ - 8$, use the multiplication operation as follows.

$\Rightarrow y \times \left( { - 8} \right) $

$\Rightarrow - y \times 8 $

$ \Rightarrow - 8y $

In order to add 5 to $ - 8y$, use the addition operation as follows.

$ \Rightarrow - 8y + 5$

$y$ is multiplied by 5 and the result is subtracted from 16

Ans: In order to multiply $y$ by 5, use the multiplication operation as follows.

$\Rightarrow y \times 5 $

$\Rightarrow 5y $

In order to subtract$5y$ from16, use the subtraction operation as follows.

$ \Rightarrow 16 - 5y$

$y$ is multiplied by $ - 5$ and the result is added to 16.

Ans: In order to multiply $y$ by $ - 5$, use the multiplication operation as follows.

$\Rightarrow y \times \left( { - 5} \right) $

$\Rightarrow - y \times 5 $

$ \Rightarrow - 5y $

In order to add $ - 5y$ to 16, use the addition operation as follows.

$ \Rightarrow - 5y + 16$

6.

Form expressions using $t$ and 4. Use not more than one number operation. Every expression must have $t$ in it.

Ans: The expressions that can be formed by using $ + $ are as follows.

$t + 4$

$4 + t$

The expressions that can be formed by using $ - $ are as follows.

$t - 4$

$4 - t$

The expression that can be formed by using $ \times $ is as follows.

$\Rightarrow t \times 4 $

$\Rightarrow 4t $

The expressions that can be formed by using $/$ are as follows.

$\dfrac{t}{4}$

$\dfrac{4}{t}$

Form expressions using $y$, 2 and 7. Every expression must have $y$ in it. Use only two number operations. These should be different.

Ans: The expression that can be formed by using $ + $ and only two numbers are as follows.

$2y + 7$

$7y + 2$

The expressions that can be formed by using $ - $ and only two numbers are as follows.

$2y - 7$

$7y - 2$

### NCERT Solutions for Class 6 Maths Chapter 11 Algebra Exercise 11.3

Opting for the NCERT solutions for Ex 11.3 Class 6 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 11.3 Class 6 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

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