NCERT Solutions Class 7 Maths Chapter 10 Algebraic Expressions

Exercise 10.1

Class 7 Maths Ch 12 focuses on introducing algebraic expressions by explaining their core components, such as variables, constants, and coefficients. It helps students identify different terms in expressions and distinguish between monomials, binomials, and polynomials. The exercise includes practice questions that require students to recognize and classify various algebraic expressions.

Exercise 10.2

Class 7 Math Chapter 10 deals with operations on algebraic expressions, including the addition and subtraction of like terms. It involves simplifying expressions by combining like terms and using the distributive property. The problems in this exercise guide students through the steps needed to simplify complex expressions, ensuring a solid understanding of the operations involved.

Access NCERT Solutions for Class 7 Maths Chapter 10 – Algebraic Expressions

Exercise  10.1

1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:

(i) Subtraction of $z$ from $y$.

Ans: $y-z$

(ii) One-half of the sum of numbers $x$ and $y$.

Ans: $\frac{x+y}{2}$

(iii) The number $z$ multiplied by  itself.

Ans: ${{z}^{2}}$

(iv) One-fourth of the product of numbers $p$ and $q$.

Ans: $\frac{pq}{4}$

(v) Numbers $x$ and $y$ both squared and added.

Ans: ${{x}^{2}}+{{y}^{2}}$

(vi) Number $5$ added to three times the product of $m$ and $n$.

Ans: $3mn+5$

(vii) Product of numbers $y$ and $z$ subtracted from $10$.

Ans: $10-yz$

(viii) Sum of numbers $a$ and $b$ subtracted from their product.

Ans: $ab-\left( a+b \right)$

 2.

(i) Identify the terms and their factors in the following expressions, show the term and factors by tree diagram:

(a) $x-3$ 

Ans: Terms: $x,-3$

(b) $1+x+{{x}^{2}}$

Ans: Terms: $1,x,{{x}^{2}}$

(c) $y-{{y}^{3}}$

Ans: Terms: $y,-{{y}^{3}}$

(d) $5x{{y}^{2}}+7{{x}^{2}}y$

Ans: Terms: $5x{{y}^{2}},7{{x}^{2}}y$

(e) $-ab+2{{b}^{2}}-3{{a}^{2}}$

Ans: Terms: $-ab,2{{b}^{2}},-3{{a}^{2}}$

(ii) Identify the terms and factors in the given expressions given below:

(a) $-4x+5$

Ans: Terms: $-4x,5$ and factors: $-4,x;5$

(b) $-4x+5y$

Ans: Terms: $-4x,5y$ and factors: $-4,x;5,y$

(c) $5y+3{{y}^{2}}$

Ans: Terms: $5y,3{{y}^{2}}$ and factors: $5,y;3,y,y$

(d) $xy+2{{x}^{2}}{{y}^{2}}$

Ans: Terms: $xy,2{{x}^{2}}{{y}^{2}}$ and factors: $x,y;2,x,x,y,y$

(e) $pq+q$

Ans: Terms: $pq,q$ and factors: $p,q;q$

(f) $1.2ab-2.4b+3.6a$

Ans: Terms: $1,2ab,-2.4b,3.6a$ and factors: $1.2,a,b;-2.4,b;3.6,a$

(g) $\frac{3}{4}x+\frac{1}{4}$

Ans: Terms: $\frac{3}{4}x,\frac{1}{4}$ and factors: $\frac{3}{4},x;\frac{1}{4}$

(h) $0.1{{p}^{2}}+0.2{{q}^{2}}$

Ans: Terms: $0.1{{p}^{2}},0.2{{q}^{2}}$ and factors: $0.1,p,p;0.2,q,q$

3. Identify the numerical coefficients of terms (other than constants) in the following expressions:

(1) $5-3{{t}^{2}}$

Ans: Terms: $-3{{t}^{2}}$ , Numerical coefficients: $-3$

(2) $1+t+{{t}^{2}}+{{t}^{3}}$

Ans: Terms: $t,{{t}^{2}},{{t}^{3}}$ , Numerical coefficients: $1,1,1$

(3) $x+2xy+3y$

Ans: Terms: $x,2xy,3y$ , Numerical coefficients: $1,2,3$

(4) $100m+1000n$

Ans: Terms: $100m,1000n$ , Numerical coefficients: $100,1000$

(5) $-{{p}^{2}}{{q}^{2}}+7pq$

Ans: Terms: $-{{p}^{2}}{{q}^{2}},7pq$ , Numerical coefficients: $-1,7$

(6) $1.2a+0.8b$

Ans: Terms: $1.2a,0.8b$ , Numerical coefficients: $1.2,0.8$

(7) $3.14{{r}^{2}}$

Ans: Terms: $3.14{{r}^{2}}$ , Numerical coefficients: $3.14$

(8) $2\left( l+b \right)$

Ans: Terms: $2l,2b$ , Numerical coefficients: $2,2$

(9) $0.1y+0.01{{y}^{2}}$

Ans: Terms: $0.1y,0.01{{y}^{2}}$ , Numerical coefficients: $0.1,0.01$

4.

(a) Identify terms which contain $x$ and give the coefficient of $x$.

(1)  ${{y}^{2}}x+y$

Ans: Terms: ${{y}^{2}}x$ , coefficients: ${{y}^{2}}$

(2) $13{{y}^{2}}-8yx$

Ans: Terms: $-8yx$ , coefficients: $-8y$

(3) $x+y+2$

Ans: Terms: $x$ , coefficients: $1$

(4) $5+z+zx$

Ans: Terms: $zx$ , coefficients: $z$

(5) $1+x+xy$

Ans: Terms: $x,xy$ , coefficients: $1,y$

(6) $12x{{y}^{2}}+25$

Ans: Terms: $12x{{y}^{2}}$ , coefficients: $12{{y}^{2}}$

(7) $7x+x{{y}^{2}}$

Ans: Terms: $7x,x{{y}^{2}}$ , coefficients: $7,{{y}^{2}}$

(b) Identify terms which contain ${{y}^{2}}$ and give the  coefficient of ${{y}^{2}}$.

(1) $8-x{{y}^{2}}$

Ans: Terms: $-x{{y}^{2}}$ , coefficients: $-x$

(2) $5{{y}^{2}}+7x$

Ans: Terms: $5{{y}^{2}}$ , coefficients: $5$

(3) $2{{x}^{2}}y-15x{{y}^{2}}+7{{y}^{2}}$

Ans: Terms: $-15x{{y}^{2}},7{{y}^{2}}$ , coefficients: $-15x,7$

5. Classify into the monomial, binomial and trinomials:

1. $4y-7x$

Ans: Binomial 

2. ${{y}^{2}}$

Ans: Monomial

3. $x+y-yx$

Ans: Trinomial 

4. $100$

Ans: Monomial

5. $ab-a-b$

Ans: Trinomial

6. $5-3t$

Ans: Binomial

7. $4{{p}^{2}}q-4p{{q}^{2}}$

Ans: Binomial

8. $7mn$

Ans: Monomial

9. ${{z}^{2}}-3z+8$

Ans: Trinomial

10. ${{a}^{2}}+{{b}^{2}}$

Ans: Binomial

11. ${{z}^{2}}+z$

Ans: Binomial

12. $1+x+{{x}^{2}}$

Ans: Trinomial

6. State whether a given pair of terms is of like or unlike terms:

1. $1,100$

Ans: Like terms

2. $-7x,\frac{5}{2}x$

Ans: Like terms

3. $-29x,-29y$

Ans: Unlike terms

4. $14xy,42yx$

Ans: Like terms

5. $4{{m}^{2}}p,4m{{p}^{2}}$

Ans: Unlike terms

6. $12xz,12{{x}^{2}}{{z}^{2}}$

Ans: Unlike terms

7. Identify like terms in the following:

(1) $-x{{y}^{2}},-4y{{x}^{2}},8{{x}^{2}},2x{{y}^{2}},7y,-11{{x}^{2}},-100x,-11yx,20{{x}^{2}}y,-6{{x}^{2}},y,2xy,3x$

Ans: Like terms are:

$\left( -x{{y}^{2}},2x{{y}^{2}} \right),\left( -4y{{x}^{2}},20{{x}^{2}}y \right),\left( 8{{x}^{2}},-11{{x}^{2}},-6{{x}^{2}} \right),\left( 7y,y \right),\left( -110x,3x \right),\left( -11yx,2xy \right)$

(2)  $10pq,7p,8q,-{{p}^{2}}{{q}^{2}},-7qp,-100q,-23,12{{q}^{2}}{{p}^{2}},-5{{p}^{2}},41,2405p,78qp,13{{p}^{2}}q,q{{p}^{2}},701{{p}^{2}}$

Ans: Like terms are:

\[\left( 10pq,-7pq,78pq \right),\left( 7p,2405p \right),\left( 8q,-100q \right),\left( -{{p}^{2}}{{q}^{2}},12{{p}^{2}}{{q}^{2}} \right),\left( -12,41 \right),\left( -5{{p}^{2}},701{{p}^{2}} \right),\left( 13{{p}^{2}}q,q{{p}^{2}} \right)\]

Exercise 12.3

1. If $m=2$, find the value of :

(a) $m-2$

Ans: $\Rightarrow m-2$

$\Rightarrow 2-2$

$\Rightarrow 0$

(b) $3m-5$

Ans: $\Rightarrow 3m-5$

$\Rightarrow 6-5$

$\Rightarrow 1$

(c) $9-5m$

Ans: $\Rightarrow 9-5m$

$\Rightarrow 9-10$

$\Rightarrow -1$

(d) $3{{m}^{2}}-2m-7$

Ans: $\Rightarrow 3{{m}^{2}}-2m-7$

$\Rightarrow 12-4-7$

$\Rightarrow 1$

(e) $\frac{5}{2}m-4$

Ans: $\Rightarrow \frac{5}{2}m-4$

$\Rightarrow 5-4$

$\Rightarrow 1$

2. If $p=-2$, find the value of:

(a) $4p+7$

Ans: $\Rightarrow 4p+7$

$\Rightarrow -8+7$

$\Rightarrow -1$

(b) $-3{{p}^{2}}+4p+7$

Ans: $\Rightarrow -3{{p}^{2}}+4p+7$

$\Rightarrow -3\times 4+4\left( -2 \right)+7$

$\Rightarrow -12-8+7$

$\Rightarrow -13$

(c) $-2{{p}^{3}}-3{{p}^{2}}+4p+7$

Ans: $\Rightarrow -2{{p}^{3}}-3{{p}^{2}}+4p+7$

$\Rightarrow -2\left( -8 \right)-3\times 4-8+7$

$\Rightarrow 16-12-8+7$

$\Rightarrow 3$

 3. Find the value of the following expressions, when $x=-1$:

(a) $2x-7$

Ans:  $\Rightarrow 2x-7$

$\Rightarrow 2\left( -1 \right)-7$

$\Rightarrow -9$

(b) $-x+2$

Ans: $\Rightarrow -x+2$

$\Rightarrow -\left( -1 \right)+2$

$\Rightarrow 3$

(c) ${{x}^{2}}+2x+1$

Ans: $\Rightarrow {{x}^{2}}+2x+1$

$\Rightarrow {{\left( -1 \right)}^{2}}+2\left( -1 \right)+1$

$\Rightarrow 0$

(d) $2{{x}^{2}}-x-2$

Ans: $\Rightarrow 2{{x}^{2}}-x-2$

$\Rightarrow 2{{\left( -1 \right)}^{2}}-\left( -1 \right)-2$

$\Rightarrow 1$

4. If $a=2,b=-2$, find the value of:

(a) ${{a}^{2}}+{{b}^{2}}$

Ans: $\Rightarrow {{\left( -2 \right)}^{2}}+{{\left( -2 \right)}^{2}}$

$\Rightarrow 4+4$

$\Rightarrow 8$

(b) ${{a}^{2}}+ab+{{b}^{2}}$

Ans: \[\Rightarrow {{\left( -2 \right)}^{2}}+\left( -2 \right)\left( -2 \right)+{{\left( -2 \right)}^{2}}\]

$\Rightarrow 4-4+4$

$\Rightarrow 4$

(c) ${{a}^{2}}-{{b}^{2}}$

Ans: $\Rightarrow {{\left( -2 \right)}^{2}}-{{\left( -2 \right)}^{2}}$

$\Rightarrow 4-4$

$\Rightarrow 0$

5. If $a=0,b=-1$, find the value of given expression:

(a) $2a+2b$

Ans: $\Rightarrow 2\left( 0 \right)+2\left( -1 \right)$

$\Rightarrow 0-2$

$\Rightarrow -2$

(b) \[2{{a}^{2}}+{{b}^{2}}+1\]

Ans: $\Rightarrow 2{{\left( 0 \right)}^{2}}+{{\left( -1 \right)}^{2}}+1$

$\Rightarrow 0+1+1$

$\Rightarrow 2$

(c) \[2{{a}^{2}}b+2a{{b}^{2}}+ab\]

Ans: $\Rightarrow 2{{\left( 0 \right)}^{2}}\left( -1 \right)+2\left( 0 \right){{\left( -1 \right)}^{2}}+\left( 0 \right)\left( -1 \right)$

$\Rightarrow 0$

(d) \[{{a}^{2}}+ab+2\]

Ans: $\Rightarrow {{\left( 0 \right)}^{2}}+\left( 0 \right)\left( -1 \right)+2$

$\Rightarrow 0+0+2$

$\Rightarrow 2$

6. Simplify the expressions and find the value if $x$ is equal to $2$:

(a) $x+7+4\left( x-5 \right)$

Ans:

$\Rightarrow x+7+4x-20$

$\Rightarrow 5x-13$

$\Rightarrow 5\times 2-13$

$\Rightarrow 10-13$

$\Rightarrow -3$

(b) $3\left( x+2 \right)+5x-7$

Ans:

$\Rightarrow 3x+6+5x-7$

$\Rightarrow 8x-1$

$\Rightarrow 8\times 2-1$

$\Rightarrow 16-1$

$\Rightarrow 15$

(c) $6x+5\left( x-2 \right)$

Ans:

$\Rightarrow 6x+5x-10$

$\Rightarrow 11x-10$

$\Rightarrow 11\times 2-10$

$\Rightarrow 22-10$

$\Rightarrow 12$

(d) $4\left( 2x-1 \right)+3x+11$

Ans:

$\Rightarrow 8x-4+3x+11$

$\Rightarrow 11x+7$

$\Rightarrow 11\times 2+7$

$\Rightarrow 22+7$

$\Rightarrow 29$

7. Simplify these expressions and find their values if $x=3,a=-1,b=-2$:

(a) $3x-5-x+9$

Ans:

$\Rightarrow 2x+4$

$\Rightarrow 2\times 3+4$

$\Rightarrow 6+4$

$\Rightarrow 10$

(b) $2-8x+4x+4$

Ans:

$\Rightarrow 6-4x$

$\Rightarrow 6-4\times 3$

$\Rightarrow 6-12$

$\Rightarrow -6$

(c) $3a+5-8a+1$

Ans:

$\Rightarrow 6-5a$

$\Rightarrow 6-5\left( -1 \right)$

$\Rightarrow 6+5$

$\Rightarrow 11$

(d) $10-3b-4-5b$

Ans:

$\Rightarrow 6-8b$

$\Rightarrow 6-8\left( -2 \right)$

$\Rightarrow 6+16$

$\Rightarrow 22$

(e) $2a-2b-4-5+a$

Ans:

$\Rightarrow 3a-2b-9$

$\Rightarrow 3\left( -1 \right)-2\left( -2 \right)-9$

$\Rightarrow -3+4-9$

$\Rightarrow -8$

 8.

(a) If $z=10$, find the value of ${{z}^{3}}-3\left( Z-10 \right)$

Ans:

$\Rightarrow {{\left( 10 \right)}^{3}}-3\left( 10-10 \right)$

$\Rightarrow 1000-0$

$\Rightarrow 1000$

(b) If $p=-10$ , find the value of ${{p}^{2}}-2p-100$

Ans:

$\Rightarrow {{\left( -10 \right)}^{2}}-2\left( -10 \right)-100$

$\Rightarrow 100+20-100$

$\Rightarrow 20$

9. What should be the value of $a$ if the value of $2{{x}^{2}}+x-a$ equal to $5$, when $x=0$ ?

Ans:

Putting $x=0$ in $2{{x}^{2}}+x-a=5$, we get

$2{{\left( 0 \right)}^{2}}+0-a=5$

$0+0-a=5$

$a=-5$

Hence, the value of $a$ is $-5$ .

10. Simplify the expression and find its value when $a=5$ and $b=-3$: $2\left( {{a}^{2}}+ab \right)+3-ab$

Ans:

Simplifying the equation,

$\Rightarrow 2\left( {{a}^{2}}+ab \right)+3-ab$

$\Rightarrow 2{{a}^{2}}+2ab+3-ab$

$\Rightarrow 2{{a}^{2}}+ab+3$

Putting $a=5$ and $b=-3$ in the above equation

$\Rightarrow 2{{\left( 5 \right)}^{2}}+5\left( -3 \right)+3$

$\Rightarrow 2\times 25-15+3$

$\Rightarrow 50-15+3$

$\Rightarrow 38$

Value of the expression after simplifying and putting $a=5$ and $b=-3$ is $38$ .

Overview of Deleted Syllabus for CBSE Class 7 Maths Algebraic Expressions

Class 7 Maths Chapter 10: Exercises Breakdown

Conclusion

Chapter 10 of Class 7 Maths, Algebraic Expressions, is essential for developing a solid understanding of algebra. Key areas to focus on include identifying variables, constants, and coefficients, and mastering the operations of addition, subtraction, and simplification of expressions. Practice these concepts thoroughly to ensure a strong grasp. In the previous year's exams, there were about 4-5 questions from this chapter, emphasizing its importance. Consistent practice and a clear understanding of these fundamentals in class 7 maths chapter 10 pdf solutions will help students excel in this chapter and perform well in their exams.

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