Identity & Inverse of Integers | Integers | Assessment | English | Grade 7

Which of the following statement is correct?

• 0 is the additive inverse of 8.

• (-1) is the multiplicative identity of integers.

• 0 is the additive identity of integers.

• 1 is the additive identity of integers.

Answer explanation

Additive inverse of 8 is (-8) because the result of its sum is 0 8 + (-8) = 0. So option 1 is wrong answer. Multiplicative identity of integer is 1. So option 2 is wrong answer. When we add 0 with any integer, the answer is the integer itself. Therefore 0 is the additive identity of integers. Option 4 is also wrong. Hence, option 3 is the right answer.

Tags

CCSS.7.NS.A.1B

Fill in the blank a + ___ = 0

• 0

• (-a)

• 1

• -1

Answer explanation

The sum of two integers is zero only when both the integers are additive inverse of each other. We know that 0, 1 and (-1) are not additive inverse of a. Therefore Additive inverse of a is (-a)

Tags

CCSS.7.NS.A.1B

Which of the following is not the additive inverse of z?

• -z

• -(-z)

• z ÷ (-1)

• z × (-1)

Answer explanation

The additive inverse of number z is a number which when added to z gives 0. Therefore additive inverse of a number has the opposite sign. So additive inverse of z is (-z). we know that z × (-1) = (-z) and z ÷ (-1) = (-z). But -(-z) = +z which is not the additive inverse of z. Hence option 2 is the answer.

Tags

CCSS.7.NS.A.1B

Which one of the following options represents the multiplicative identity for 2?

• -2

• 0

• -1

• 1

Answer explanation

When an integer is multiplied by 1 then its product is the same integer. In option 1, -2 represents the additive inverse of 2. In option 2, 0 is multiplied by a number which gives 0, its product is not the same integer. Therefore option 2 is wrong answer. In option 3 an integer is multiplied by (-1) this results in the change of sign. So option 3 is also the wrong answer. In option 4, an integer is multiplied by 1 and its product remains the same. Hence option 4 is the right answer.

Tags

CCSS.7.NS.A.3

Observe the following picture in which all icons represents the integers. State that what will be the value of white coloured icon?

• 0

• 1

• -1

• All of the above

Answer explanation

In the given picture all icons (the sun and half moon) represent integers. There is the sign of addition between them. The sum of integers represented by sun and half moon is equal to the integer represented by sun. It means there is not any change in the value of integer represented by sun. If we add 1 or (-1) with any of the integer. Then the value of integer will change. But when we add 0 to the integer there is no change in its value. Hence 0 is the additive identity of integers. Therefore option 1 is the right answer.

Tags

CCSS.7.NS.A.1C

In a quiz competition (+1) marks are given for each right answer and (-1) marks are given for each wrong answer. Roshan has given 14 correct answers and a few incorrect answers. He got zero marks. So what is the number of incorrect answers given by Roshan?

• -14

• 14

• -15

• 15

Answer explanation

Roshan has given 14 correct answers. In the quiz competition (+1) marks are given for each correct answer and (-1) marks are given for each incorrect answer. Therefore the marks of 14 correct answers is 14 × (+1) = +14. Roshan has got 0 marks. So marks of right questions + marks of wrong questions = the total number of marks. That is +(14) + marks of wrong questions = 0 . We know about additive inverse that a + (-a) = 0. Additive inverse of 14 is (-14), i.e., 14 + (-14) = 0. So the number of incorrect answers given by Roshan is 14.

Tags

CCSS.7.NS.A.3

P and Q are integers. P when multiplied by Q gives P as the product. So what is the value Q?

• 0

• -1

• 1

• Can not be determined

Answer explanation

When we multiply 1 with any of the integer then its product is the integer itself. Therefore if we multiply P and 1 = P × 1 its product will be P. That means the value of Q is 1 and Q is multiplicative identity of P. If we multiply P with 0 then the product will be 0. If we multiply P with (-1) then result will be -P. Therefore option 3 is the right answer.

Tags

CCSS.6.NS.B.4