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Practice each question, then open the answer or worked solution.
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.
Some of the expressions formed by 5, 7 and 8 are as follows
5 × (8 – 7)
5 × (8 + 7)
(8 + 5) × 7
(8 – 5) × 7
(7 + 5) × 8
(7 – 5) × 8
Which out of the following are expressions with numbers only?
(e) 3x
(f) 5 – 5n
(g) (7 × 20) – (5 × 10) – 45 + p
(c) and (d) are the expressions with numbers only.
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) 17y, y / 17, 5z
(c) 2y + 17, 2y – 17
(d) 7m, -7m + 3, -7m – 3
(a) z + 1 = 1 is added to z = Addition
z – 1 = 1 is subtracted from z = Subtraction
y + 17 = 17 is added to y = Addition
y – 17 = 17 is subtracted from y = Subtraction
(b) 17y = y is multiplied by 17 = Multiplication
y / 17 = y is divided by 17 = Division
5z = z is multiplied by 5 = Multiplication
(c) 2y + 17 = y is multiplied by 2 and 17 is added to the result = Multiplication and addition
2y – 17 = y is multiplied by 2 and 17 is subtracted from the result = Multiplication and subtraction
(d) 7m = m is multiplied by 7 = multiplication
-7m + 3 = m is multiplied by -7 and 3 is added to the result = Multiplication and addition
-7m – 3 = m is multiplied by -7 and 3 is subtracted from the result = Multiplication and subtraction
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) 7 is added to p is (p + 7)
(b) 7 subtracted from p is (p – 7)
(c) p multiplied by 7 is (7p)
(d) p divided by 7 is (p / 7)
(e) 7 subtracted from –m is (-m – 7)
(f) –p multiplied by 5 is (-5p)
(g) –p divided by 5 is (–p / 5)
(h) p multiplied by -5 is (-5p)
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) 11 added to 2m is (2m + 11)
(b) 11 subtracted from 2m is (2m – 11)
(c) 5 times y to which 3 is added is (5y + 3)
(d) 5 times y from which 3 is subtracted is (5y – 3)
(e) y is multiplied by -8 is (-8y)
(f) y is multiplied by -8 and then 5 is added to the result is (-8y + 5)
(g) y is multiplied by 5 and the result is subtracted from 16 is (16 – 5y)
(h) y is multiplied by -5 and the result is added to 16 is (-5y + 16)
(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, (t / 4), (4 / t), (4 – t), (4 + t) are the expressions using t and 4
(b) 2y + 7, 2y – 7, 7y + 2,… are the expression using y, 2 and 7