Learn on PengiBig Ideas Math, Course 2Chapter 1: Integers

Lesson 4: Multiplying Integers

In this Grade 7 lesson from Big Ideas Math Course 2, Chapter 1, students learn the rules for multiplying integers, discovering that the product of two integers with the same sign is positive and the product of two integers with different signs is negative. Using repeated addition, number lines, and pattern tables, students practice multiplying positive and negative integers and apply those rules to expressions involving exponents such as evaluating (-2)² and (-4)³.

Section 1

Rules for Multiplying Integers

Property

For multiplication of two signed numbers:

If the signs are the same, the product is positive.
If the signs are different, the product is negative.

Same Signs (Product is Positive)

Two positives: $7 \cdot 4 = 28$
Two negatives: $-8(-6) = 48$

Different Signs (Product is Negative)

Positive $\cdot$ negative: $7(-9) = -63$
Negative $\cdot$ positive: $-5 \cdot 10 = -50$

Section 2

Powers of Negative Numbers

Property

To show that a negative number is raised to a power, we enclose the negative number in parentheses. For example, to indicate the square of $-5$ , we write

(-5)^2 = (-5)(-5) = 25

If the negative number is not enclosed in parentheses, the exponent applies only to the positive number.

-5^2 = -(5 \cdot 5) = -25

Examples

To calculate $(-3)^4$ , we multiply four factors of $-3$ : $(-3)(-3)(-3)(-3) = 81$ .

The expression $-3^4$ means the negative of $3^4$ , so we calculate $3 \cdot 3 \cdot 3 \cdot 3 = 81$ and then apply the negative sign to get $-81$ .

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Rules for Multiplying Integers

Property

For multiplication of two signed numbers:

If the signs are the same, the product is positive.
If the signs are different, the product is negative.

Same Signs (Product is Positive)

Two positives: $7 \cdot 4 = 28$
Two negatives: $-8(-6) = 48$

Different Signs (Product is Negative)

Positive $\cdot$ negative: $7(-9) = -63$
Negative $\cdot$ positive: $-5 \cdot 10 = -50$

Section 2

Powers of Negative Numbers

Property

To show that a negative number is raised to a power, we enclose the negative number in parentheses. For example, to indicate the square of $-5$ , we write

(-5)^2 = (-5)(-5) = 25

If the negative number is not enclosed in parentheses, the exponent applies only to the positive number.

-5^2 = -(5 \cdot 5) = -25

Examples

To calculate $(-3)^4$ , we multiply four factors of $-3$ : $(-3)(-3)(-3)(-3) = 81$ .

The expression $-3^4$ means the negative of $3^4$ , so we calculate $3 \cdot 3 \cdot 3 \cdot 3 = 81$ and then apply the negative sign to get $-81$ .

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Rules for Multiplying Integers

Property

For multiplication of two signed numbers:

If the signs are the same, the product is positive.
If the signs are different, the product is negative.

Same Signs (Product is Positive)

Two positives: $7 \cdot 4 = 28$
Two negatives: $-8(-6) = 48$

Different Signs (Product is Negative)

Positive $\cdot$ negative: $7(-9) = -63$
Negative $\cdot$ positive: $-5 \cdot 10 = -50$

Section 2

Powers of Negative Numbers

Property

To show that a negative number is raised to a power, we enclose the negative number in parentheses. For example, to indicate the square of $-5$ , we write

(-5)^2 = (-5)(-5) = 25

If the negative number is not enclosed in parentheses, the exponent applies only to the positive number.

-5^2 = -(5 \cdot 5) = -25

Examples

To calculate $(-3)^4$ , we multiply four factors of $-3$ : $(-3)(-3)(-3)(-3) = 81$ .

The expression $-3^4$ means the negative of $3^4$ , so we calculate $3 \cdot 3 \cdot 3 \cdot 3 = 81$ and then apply the negative sign to get $-81$ .