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 be combined.

So just write them together:
$$
8x - \frac{4}{3}x + \frac{2}{3}y + 3p
$$

Now combine only like terms: $8x$ and $-\frac{4}{3}x$

$$
8x = \frac{24}{3}x \Rightarrow \frac{24}{3}x - \frac{4}{3}x = \frac{20}{3}x
$$

So expression becomes:
$$
\frac{20}{3}x + \frac{2}{3}y + 3p
$$

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

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3. Add the unlike terms:

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

Here, $1x^2$ and $4x^2$ are like terms (both $x^2$)

So:
$$
1x^2 + 4x^2 = 5x^2
$$

Other terms remain unchanged.

✔ Answer: $\boxed{5x^2 + 2y + 3z}$

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

These are unlike terms ($x^2$ vs $y^2$), so they cannot be added.

✔ Answer: $\boxed{x^2 - 3y^2}$

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

- The expression is $13 - y^2$
- We are to find the numerical coefficient of the term involving $y^2$.
- The term is $-y^2$, which is $-1 \cdot y^2$

✔ Answer: $\boxed{-1}$

> Note: "Numerical coefficient" refers to the number in front of the variable.

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6. Add all the terms:

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

Group like terms:

#### Variables:
- $x$-terms: $12x - 25x + x = (12 - 25 + 1)x = -12x$
- $y$-terms: $-25y + 12y + y = (-25 + 12 + 1)y = -12y$
- Constants: $12 + 1 - 25 = -12$

So total:
$$
-12x - 12y - 12
$$

✔ Answer: $\boxed{-12x - 12y - 12}$

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

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

We need the coefficient of $y^2$, i.e., any term that has $y^2$.

Look at each term:
- $2x^2y$: has $y^1$, not $y^2$ → ignore
- $-15xy^2$: has $y^2$ → coefficient is $-15x$ (but this includes $x$)
- $7y^2$: pure $y^2$ → coefficient is $7$

But the question says: "coefficient of $y^2$" — does it mean numerical or algebraic?

Since it's an algebraic expression, and the term $-15xy^2$ has $y^2$, its coefficient is $-15x$. But if it asks for numerical coefficient, then only constant numbers.

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

So total coefficient of $y^2$ (as a whole) is $-15x + 7$

But if the question wants just the numerical coefficient of $y^2$, it might be ambiguous.

But standard interpretation: the coefficient of $y^2$ means the entire factor multiplying $y^2$.

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

But if the question expects only numerical coefficient (i.e., no variables), then only $7$ comes from $7y^2$, but $-15xy^2$ has $-15x$ as coefficient.

Wait — let’s clarify:

In $-15xy^2$, the coefficient of $y^2$ is $-15x$, because $-15x \cdot y^2$

In $7y^2$, the coefficient is $7$

So total coefficient of $y^2$ is $-15x + 7$

But unless specified otherwise, we consider the total coefficient of $y^2$ in the expression.

✔ Answer: $\boxed{-15x + 7}$

> However, sometimes questions ask for numerical coefficient, meaning only the number part.

But here, since $-15xy^2$ has a variable in the coefficient, the full coefficient is $-15x + 7$

So best answer: $\boxed{-15x + 7}$

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8. Add the algebraic expressions:

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

Remove parentheses:
$$
3x + 11 - 2x + y
$$

Combine like terms:
- $3x - 2x = x$
- $11$ stays
- $y$ stays

✔ Answer: $\boxed{x + y + 11}$

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

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

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

Now 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:

| Question | Answer |
|--------|--------|
| 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 | $10$ |

Let me know if you'd like these explained in simpler language or with more steps!