GSEB Class 6 Maths Solutions Chapter 11 Algebra Exercise 11.3

Question 1. Makeup 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. Hint: Three possible expressions are 5 + (8 – 7), 5 – (8 – 7), (5 x 8) + 7; make the other expressions.
Answer: We need to use the given three numbers together. Each number should only be used once in any expression. We can use addition, subtraction, and multiplication.
So, we can create:
(i) \( 5 + (7 + 8) \)
(ii) \( 7 \times 5 + 8 \)
(iii) \( (8 - 5) \times 7 \)
(iv) \( (7 - 5) \times 8 \)
(v) \( (5 \times 7) - 8 \)
(vi) \( (8 \times 7) + 5 \)
(vii) \( 8 - 5 + 7 \)
(viii) \( (8 - 7) + 5 \), etc.
In simple words: Using the numbers 5, 7, and 8, and each number only once, we can make many different math statements using plus, minus, or multiply signs.

Exam Tip: When forming expressions, consider all possible combinations of numbers and operations. Parentheses are crucial to control the order of operations and create distinct expressions.

Question 2. Which out of the following are expressions with numbers only?
(a) \( y + 3 \)
(b) \( (7 \times 20) - 8z \)
(c) \( 5(21 - 7) + 7 \times 2 \)
(d) 5
(e) \( 3x \)
(f) \( 5 - 5n \)
(g) \( (7 \times 20) - (5 \times 10) - 45 + p \)
Answer: In expressions (c) and (d), no variables are present. Therefore, (c) and (d) are expressions made only of numbers.
In simple words: Expressions (c) and (d) are the ones that only have numbers and no letters (variables).

Exam Tip: Remember that an expression "with numbers only" means it contains no variables (letters). If a letter is present, it's not a number-only expression.

Question 3. Identify the operations (addition, subtraction, division, multiplication) informing the following expressions and tell how the expressions have been formed.
(a) \( z + 1, z - 1, y + 17, y - 17 \)
(b) \( 17y, \frac{y}{17}, 5z \)
(c) \( 2y + 17, 2y - 17 \)
(d) \( 7m, -7m + 3, -7m - 3 \)
Answer:

Exam Tip: Clearly state each operation and describe the sequence of steps involved in forming the expression. Be specific about whether a number is added, subtracted, multiplied, or divided by the variable.

Question 4. Give expressions for the following cases.
(a) 7 added to p
(b) 7 subtracted from p
(c) p multiplied by 7
(d) p divided by 7
(e) 7 subtracted from -m
(f) -p multiplied by 5
(g) -p divided by 5
(h) p multiplied by -5
Answer:
(a) \( p + 7 \)
(b) \( p - 7 \)
(c) \( 7p \)
(d) \( \frac{p}{7} \)
(e) \( -m - 7 \)
(f) \( -5p \)
(g) \( \frac{-p}{5} \)
(h) \( -5p \)
In simple words: We take each written instruction and turn it into a math expression using numbers and the letter 'p' or 'm', along with plus, minus, times, or divide signs.

Exam Tip: Pay close attention to the order of operations, especially in subtraction and division. "7 subtracted from p" is \( p - 7 \), not \( 7 - p \).

Question 5. Give expressions in the following cases.
(a) 11 added to 2m
(b) 11 subtracted from 2m
(c) 5 times y to which 3 is added
(d) 5 times y from which 3 is subtracted
(e) y is multiplied by -8
(f) y is multiplied by -8 and then 5 is added to the result
(g) y is multiplied by 5 and the result is subtracted from 16
(h) y is multiplied by -5 and the result is added to 16.
Answer:
(a) \( 2m + 11 \)
(b) \( 2m - 11 \)
(c) \( 5y + 3 \)
(d) \( 5y - 3 \)
(e) \( -8y \)
(f) \( -8y + 5 \)
(g) \( 16 - 5y \)
(h) \( 16 + (-5y) \)
In simple words: This lists several ways to combine numbers and a letter (like 'm' or 'y') using math operations. Each sentence describes how to make a math expression.

Exam Tip: Translate words like "added to," "subtracted from," and "times" into their corresponding mathematical symbols. For multi-step operations, write them in the correct sequence.

Question 6.
(a) Form expressions using t and 4. Use not more than one number operation. Every expression must have t in it.
(b) Form expressions using y, 2, and 7. Every expression must have in it. Use only two number operations. These should be different.
Answer:
(a) We can get these expressions:
\( t + 4, t - 4, 4t, \frac{t}{4}, 4 - t \)...
(b) \( 2y + 7, 2y - 7, 7y + 2, 7y - 2 \)...
In simple words: Part (a) asks you to make math statements with 't' and '4', using only one math sign. Part (b) asks you to use 'y', '2', and '7' with two different math signs to make expressions.

Exam Tip: For part (a), ensure each expression uses 't' and '4' with exactly one operation. For part (b), combine the three numbers using two different operations (e.g., multiplication and addition, or multiplication and subtraction).