Test: Expressions using Letter-Numbers - Class 7 MCQ

To evaluate 3n + 5 when n = 4, follow these steps:

• Substitute 4 for n in the expression: 3(4) + 5.
• Calculate 3 × 4 which equals 12.
• Add 5 to 12: 12 + 5 = 17.

Therefore, the value of the expression is 17.

The perimeter of a square can be calculated using the formula:

• Each side of the square is represented by ‘q’.
• The perimeter is the total length around the square.
• Since a square has four equal sides, the formula is:
• Perimeter = 4 × q

Therefore, the perimeter of the square is 4q.

To simplify the expression, follow these steps:

• Combine like terms: 5m and -2m.
• Calculate: 5m - 2m = 3m.
• Add the constant: 3.

The simplified form of the expression is:

3m + 3

If the rule is to add both inputs, then the output is:

• m + n

The sequence increases by 4 each time. To find the nth term, we can express it using the formula:

• The first term (when n=1) is 4.
• The second term (when n=2) is 8.
• The pattern shows that each term can be represented as:

nth term = 4n

To find the result of the expression 2p - 7 when p = 10, follow these steps:

• Substitute 10 for p in the expression.
• The expression becomes: 2(10) - 7.
• Calculate 2(10), which equals 20.
• Now, subtract 7 from 20: 20 - 7 = 13.

The result of the expression is 13.

The expression can be simplified by combining like terms:

• Add the coefficients of c: 5c + 3c = 8c.
• The term 2d remains unchanged.

Therefore, the simplified expression is:

8c + 2d.

The expression “5 more than twice a number x” can be broken down as follows:

• Twice a number x is represented as 2x.
• To express “5 more than” this, you add 5 to it.
• Thus, the correct expression is 2x + 5.

Therefore, the correct answer is B.

The expression can be calculated as follows:

• Calculate 2a: 2 × 5 = 10
• Calculate 3b: 3 × 3 = 9
• Add the results: 10 + 9 = 19

Thus, the value of the expression is 19.

The expression that represents "3 less than a number y" is:

• y - 3

This means you subtract 3 from the value of y.

Meena's total cost for her purchase can be calculated using the following expression:

• The cost of notebooks: ₹25 each, so for n notebooks, the cost is 25n.
• The cost of pens: ₹10 each, so for p pens, the cost is 10p.
• Adding a fixed delivery fee of ₹50.

Therefore, the total cost expression is:

25n + 10p + 50

The correct answer is:

• 7p and 3p

Like terms are terms that contain the same variable raised to the same power. Here's a brief explanation of why the other options are not like terms:

• 4a and 4b are not like terms because they involve different variables.
• x² and x are not like terms as they have different powers of the variable.
• 5m and 5mn are also not like terms due to the different variable components.

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The cost of 5 notebooks can be calculated using the expression provided.

• First, substitute x with 5 in the expression: 40x.
• This gives: 40 × 5 = 200.
• Therefore, the cost of 5 notebooks is ₹200.

We are asked to find the area of a fence that runs inside a rectangular garden. The garden has length l metres and width w metres. The fence has a uniform width of 3 metres all around. That means the fence takes up a border of 3 metres on each side inside the garden.

Step 1: Dimensions of the inner garden
Because the fence takes away 3 metres from each side, the effective length of the inner garden is l - 6 and the effective width is w - 6.

Step 2: Area of the outer garden
The whole garden including the fence has area l × w.

Step 3: Area of the inner garden
The space left after removing the fence is (l - 6)(w - 6).

Step 4: Area of the fence
The fence covers the difference between the outer garden and the inner garden.
So, Fence area = lw - (l - 6)(w - 6).

Step 5: Simplify the expression
Expand (l - 6)(w - 6) = lw - 6l - 6w + 36.
Subtracting, Fence area = lw - (lw - 6l - 6w + 36).
This becomes Fence area = 6l + 6w - 36.

Step 6: Substitute values l = 10 and w = 8
Fence area = 6(10) + 6(8) - 36.
= 60 + 48 - 36.
= 72 square metres.

Final answer: The expression for the area of the fence is 6l + 6w - 36, and for l = 10 and w = 8, the area is 72 square metres.