Class 7 Properties of Integers — practice questions with answers
Integers · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Which property is shown by 7 + (-3) = (-3) + 7?
ACommutative property of addition
BAssociative property of addition
CDistributive property
DClosure property
Show answer
Answer: A) Commutative property of addition
Changing the order of the integers being added does not change the sum, so this is the commutative property of addition.
2. Find the value: (-15) + 15.
A-1
B0
C1
D2
Show answer
Answer: B) 0
15 is the additive inverse of -15, and a number plus its additive inverse is 0.
3. The product of any integer and its additive inverse is always:
AZero or negative
BAlways positive
CAlways zero
DAlways 1
Show answer
Answer: A) Zero or negative
For an integer a, a x (-a) = -(a²). If a = 0 the product is 0, otherwise -(a²) is negative. So the product is zero or negative.
4. An integer is multiplied by 1 and then 0 is added to the result. Which two properties have been used, and what happens to the original integer?
AMultiplicative identity and additive identity; it is unchanged
BDistributive and commutative; it doubles
CClosure and associative; it becomes 0
DCommutative and identity; it changes sign
Show answer
Answer: A) Multiplicative identity and additive identity; it is unchanged
(a x 1) + 0 = a + 0 = a. Multiplying by 1 (multiplicative identity) and adding 0 (additive identity) both leave the integer unchanged.
5. An accountant simplifies (-25) x (-13) + (-25) x 13. Using the distributive property in reverse, she factors out -25 first. What is the final value?
A-1
B0
C2
D1
Show answer
Answer: B) 0
(-25) x (-13) + (-25) x 13 = (-25) x (-13 + 13) = (-25) x 0 = 0. Factoring out -25 leaves a sum of additive inverses, which is 0.