CBSE Class 7 Mental Maths Algebraic Expression Worksheet - Free Printable

Let's solve each question from the given worksheet on Algebraic Expressions step by step, with explanations.

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1. Add the like terms:

$$
\frac{2}{3}x^2y, \quad -\frac{3}{7}x^2y, \quad \frac{2}{7}x^2y^3
$$

- Like terms have the same algebraic factors.
- Here, $\frac{2}{3}x^2y$ and $-\frac{3}{7}x^2y$ are like terms because both have $x^2y$.
- $\frac{2}{7}x^2y^3$ is not a like term (because it has $y^3$, not $y$).

So we add only:
$$
\frac{2}{3}x^2y + \left(-\frac{3}{7}x^2y\right) = \left(\frac{2}{3} - \frac{3}{7}\right)x^2y
$$

Find common denominator (LCM of 3 and 7 is 21):
$$
\frac{2}{3} = \frac{14}{21}, \quad \frac{3}{7} = \frac{9}{21}
\Rightarrow \frac{14}{21} - \frac{9}{21} = \frac{5}{21}
$$

✔ Answer: $\boxed{\frac{5}{21}x^2y}$

> Note: $\frac{2}{7}x^2y^3$ remains as it is (cannot be combined).

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2. Add the unlike terms:

$$
8x, \quad -\frac{4}{3}x, \quad \frac{2}{3}y, \quad 3p
$$

These are unlike terms — different variables or powers → cannot combine.

But we can group like terms:

- Terms with $x$: $8x - \frac{4}{3}x = \left(8 - \frac{4}{3}\right)x = \left(\frac{24}{3} - \frac{4}{3}\right)x = \frac{20}{3}x$
- Term with $y$: $\frac{2}{3}y$
- Term with $p$: $3p$

✔ Answer: $\boxed{\frac{20}{3}x + \frac{2}{3}y + 3p}$

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3. Add the unlike terms:

$$
1x^2, \quad 2y, \quad 3z, \quad 4x^2
$$

- Like terms: $1x^2$ and $4x^2$ → $1x^2 + 4x^2 = 5x^2$
- Others: $2y$, $3z$

✔ Answer: $\boxed{5x^2 + 2y + 3z}$

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4. Add the terms: $x^2$ and $-3y^2$

These are unlike terms (different variables), so they cannot be added.

✔ Answer: $\boxed{x^2 - 3y^2}$

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5. What is the numerical coefficient of algebraic expression $13 - y^2$?

We need to identify the numerical coefficient of $y^2$.

The term is $-y^2$, which means $-1 \cdot y^2$

✔ Answer: $\boxed{-1}$

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6. Add all the terms:

$$
12x, 12, -25x, -25y, 1, x, 12y, y, -25
$$

Group like terms:

- $x$-terms: $12x - 25x + x = (12 - 25 + 1)x = -12x$
- $y$-terms: $-25y + 12y + y = (-25 + 12 + 1)y = -12y$
- Constant terms: $12 + 1 - 25 = -12$

✔ Answer: $\boxed{-12x - 12y - 12}$

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7. Write the coefficient of $y^2$ in:

$$
2x^2y - 15xy^2 + 7y^2
$$

Look for terms with $y^2$:

- $-15xy^2$: contains $y^2$, but also $x$ → coefficient is $-15x$
- $7y^2$: pure $y^2$ → coefficient is $7$

But the question asks for the coefficient of $y^2$.

Since $y^2$ appears in two terms:
- $-15xy^2$: coefficient of $y^2$ is $-15x$
- $7y^2$: coefficient is $7$

But if we're asking for numerical coefficient of $y^2$, then only $7$ is purely numeric.

However, in algebra, coefficient includes variable parts unless specified otherwise.

But here, since the expression has multiple terms, and $y^2$ appears in two forms:

→ The total coefficient of $y^2$ is: $-15x + 7$

But the numerical coefficient of $y^2$ would be just the number multiplying $y^2$ when it’s alone.

But since $-15xy^2$ has $x$, its coefficient is $-15x$, not a number.

So the term $7y^2$ has numerical coefficient 7.

But the question says: *"Write the coefficient of $y^2$"*, so likely wants all coefficients of $y^2$ terms.

But typically, if no specification, we list the total coefficient.

So:

$$
\text{Coefficient of } y^2 = -15x + 7
$$

But if they mean numerical coefficient, then only $7$ counts.

But let's read carefully: "Write the coefficient of $y^2$"

In standard interpretation, coefficient refers to the number multiplied by the variable.

But in $-15xy^2$, the coefficient of $y^2$ is $-15x$, not a number.

So unless specified, we say:

- Coefficient of $y^2$ in $-15xy^2$ is $-15x$
- In $7y^2$ is $7$

So total expression: $(-15x + 7)y^2$

But the coefficient of $y^2$ is $\boxed{-15x + 7}$

✔ Answer: $\boxed{-15x + 7}$

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8. Add the algebraic expressions:

$$
(3x + 11) + (-2x + y)
$$

Remove parentheses:
$$
3x + 11 - 2x + y = (3x - 2x) + y + 11 = x + y + 11
$$

✔ Answer: $\boxed{x + y + 11}$

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9. Subtract $x + y$ from $\frac{3}{2}x - \frac{5}{2}y$

That is:
$$
\left(\frac{3}{2}x - \frac{5}{2}y\right) - (x + y)
$$

Distribute the minus sign:
$$
\frac{3}{2}x - \frac{5}{2}y - x - y
$$

Group like terms:

- $x$-terms: $\frac{3}{2}x - x = \frac{3}{2}x - \frac{2}{2}x = \frac{1}{2}x$
- $y$-terms: $-\frac{5}{2}y - y = -\frac{5}{2}y - \frac{2}{2}y = -\frac{7}{2}y$

✔ Answer: $\boxed{\frac{1}{2}x - \frac{7}{2}y}$

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10. Find the value of the expression for $x = 2$:

$$
15x - 5x^2
$$

Substitute $x = 2$:
$$
15(2) - 5(2)^2 = 30 - 5(4) = 30 - 20 = 10
$$

✔ Answer: $\boxed{10}$

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## ✔ Final Answers Summary:

1. $\frac{5}{21}x^2y$
2. $\frac{20}{3}x + \frac{2}{3}y + 3p$
3. $5x^2 + 2y + 3z$
4. $x^2 - 3y^2$
5. $-1$
6. $-12x - 12y - 12$
7. $-15x + 7$
8. $x + y + 11$
9. $\frac{1}{2}x - \frac{7}{2}y$
10. $10$

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