Adding Integers with Counters

Front

What is the result of adding two negative integers, for example, -3 + -2?

Back

The result is -5, which is more negative than either of the original integers.

Front

How do you add a positive integer to a negative integer, such as 5 + -3?

Back

You subtract the absolute value of the negative integer from the positive integer: 5 - 3 = 2.

Front

What is the sum of two positive integers, for example, 4 + 6?

Back

The sum is 10, which is a positive integer.

Front

What is the result of adding zero to any integer, such as 7 + 0?

Back

The result is the same integer, so 7 + 0 = 7.

Front

How do you determine the sum of integers with different signs, like -4 + 2?

Back

You subtract the smaller absolute value from the larger absolute value and take the sign of the integer with the larger absolute value: -4 + 2 = -2.

Front

What is the result of adding two integers with the same sign, for example, -5 + -3?

Back

The result is -8, which is also a negative integer.

Front

What is the principle of integer addition regarding the commutative property?

Back

The commutative property states that the order of addition does not affect the sum: a + b = b + a.

Front

What is the principle of integer addition regarding the associative property?

Back

The associative property states that the way in which numbers are grouped does not affect the sum: (a + b) + c = a + (b + c).

Front

What is the result of adding two integers where one is positive and the other is negative, such as -7 + 4?

Back

The result is -3, since you subtract 4 from 7 and keep the negative sign.

Front

How do counters help visualize the addition of integers?

Back

Counters can represent positive integers as one color and negative integers as another, helping to visualize the net result.