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Learn Exercise 11.3 with Free Lessons & Tips

Make up 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 × 8) + 7;

make the other expressions.)

Many expressions can be formed by using the three numbers 5, 7, and 8.

Some of these are as follows.

5 × (8 − 7)

5 × (8 + 7)

(8 + 5) ×7

(8 − 5) ×7

(7 + 5) ×8

(7 − 5) ×8

Comments

Which out of the following are expressions with numbers only?

(a) y + 3 (b) (7 × 20) − 8z

(c) 5 (21 − 7) + 7 × 2 (d) 5

(e) 3x (f) 5 − 5n

(g) (7 × 20) − (5 × 10) − 45 + p

It can be observed that the expressions in alternatives (c) and (d) are formed by using numbers only.

Comments

Identify the operations (addition, subtraction, division, multiplication) in forming the following expressions and tell how the expressions have been formed.

(a) z + 1, z − 1, y + 17, y − 17 (b)

(c) 2y + 17, 2y − 17 (d) 7m, − 7m + 3, − 7m − 3

(a) Addition as 1 is added to z.

Subtraction as 1 is subtracted from z.

Addition as 17 is added to y.

Subtraction as 17 is subtracted from y.

(b) Multiplication as y is multiplied with 17.

Division as y is divided by 17.

Multiplication as z is multiplied with 5.

(c) Multiplication and addition

y is multiplied with 2, and 17 is added to the result.

Multiplication and subtraction

y is multiplied with 2, and 17 is subtracted from the result.

(d) Multiplication as m is multiplied with 7.

Multiplication and addition as m is multiplied with −7, and 3 is added

to the result.

Multiplication and subtractionas m is multiplied by −7, and 3 is

subtracted from the result.

Comments

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

(a) p + 7

(b) p − 7

(c) 7p

(d)

(e) − m − 7

(f) − 5p

(g)

(h) − 5p

Comments

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

(a) 2m + 11

(b) 2m − 11

(c) 5y + 3

(d) 5y − 3

(e) − 8y

(f) − 8y + 5

(g) 16 − 5y

(h) − 5y + 16

Comments

(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 y in it. Use only two number operations. These should be different.

(a) t + 4, t − 4, 4t, , , 4 − t, 4 + t

(b) 2y + 7, 2y − 7, 7y + 2,…

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