Page 217 - Start Up Mathematics_6

Solution: The expressions with numbers only are (d) and (f).

Example 12: Identify the operations (addition, subtraction, division, multiplication) in forming
the following expressions and explain how these expressions are formed.
z
(a) x + 1 (b) 2y – 1 (c) + 4 (d) –2m – 3
3

Solution: S. No. Algebraic Operations used Formation
expression
(a) x + 1 Addition Adding 1 to x

(b) 2y – 1 Multiplication, subtraction Subtracting 1 from twice y
(c) z + 4 Division, addition Adding 4 to one-third of z
3
(d) –2m – 3 Multiplication, subtraction Subtracting 3 from the
product of –2 and m

Example 13: Give expressions for the following cases:
(a) 3 added to x (b) 7 subtracted from –m (c) –p divided by 4
– p
Solution: (a) x + 3 (b) –m – 7 (c)
4
Example 14: Give expressions in the following cases:

(a) 3 subtracted from 5m (b) 5 times y to which 3 is added
(c) 3 times y from which –7 is subtracted (d) x multiplied by –3

(e) y multiplied by 5 and the result subtracted from 12
Solution: (a) 5m – 3 (b) 5y + 3 (c) 3y – (–7) = 3y + 7

(d) –3x (e) 12 – 5y

Example 15: (a) Form expressions using m and 6. Use not more than one number operation.
Every expression must have m in it.
(b) Form expressions using x, 2 and 5. Every expression must have x in it. Use only
two number operations. These should be different.
m 6
Solution: (a) m + 6, m – 6, 6 – m, 6m, , (m ≠ 0)
6 m
x 2 x 5
(b) 2x + 5, 2x – 5, 5x + 2, 5x – 2, ,
5 2
Example 16: The length of a rectangular hall is 5 metres more than twice its breadth. What is its
length, if the breadth is a metres?
Solution: The breadth of the hall = a metres
Therefore, the length of the hall = 2 × a + 5 = (2a + 5) metres
Example 17: Meena, Beena and Leena are climbing the steps to the hilltop. Meena is at step s,
Beena is 8 steps ahead and Leena 7 steps behind. Where are Beena and Meena? What
is the difference between Beena and Leena in terms of the steps? The total number
of steps to the hilltop is 10 less than 4 times what Meena has reached. Express the
total number of steps using s. (NCERT)

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