## Math 6 Chapter 2 Lesson 11: Multiplying two integers with the same sign

## 1. Summary of theory

### 1.1. Multiply two positive integers

We already know how to multiply two positive integers (two non-zero natural numbers).

**Example 1:** twelfth . 3 = 36

### 1.2. Multiply two negative integers

**Rule:** To multiply two negative integers, we multiply their absolute values.

**Example 2:** (-4) . (-25) = 4 . 25 = 100

**Comment:** The product of two negative integers is a positive integer.

### 1.3. Conclusion

- a . 0 = 0 . a = 0
- If a and b have the same sign, then a . b = |a| . |b|

## 2. Illustrated exercise

**Question 1:** Do the following calculations:

a) (-15).(-4)

b) (-20).(-6)

c) 20.7

**Solution guide**

a) (-15).(-4) = 15. 4 = 60

b) (-20).(-6) = 20. 6 = 120

c) 20.7 = 140

**Verse 2:** Compare

a) (-14).(-10) and 7.20

b) (-81).(-8) and 10.24

**Solution guide**

a) (-14).(-10) = 14. 10 = 140

7.20 = 140

So (-14).(-10) = 7.20

b) (-81).(-8) = 81.8 = 648

10.24 = 240

Since 648 > 240, so (-81).(-8) > 10.24

## 3. Practice

### 3.1. Essay exercises

**Question 1: **Compare

a. (-9) . (-8) with 0

b. (-twelfth) . 4 with (-2) . (-3)

c. (+20) . (+8) with (-19) . (-9)

**Verse 2:** Calculate the value of the expression, with x = -4, y = -3

a. (-15)x + (-7)y

b. (315 – 427)x + (46 – 89)y

**Question 3:** Compare

a. (-14) (-10) with 7.20

b. (-81) (-8) with 10.24

### 3.2. Multiple choice exercises

**Question 1: **Calculating (-42).(-5) results in:

A. -210

B. 210

C. -47

D. 37

**Verse 2: **Select the correct answers

A. (-20).(-5) = -100

B. (-50).(-12) = 600

C. (-18).25 = -400

D. 11.(-11) = -1111

**Question 3:** Choose the wrong sentence:

A. (-19).(-7) > 0

B. 3.(-121) < 0

C. 45.(-11) < -500

D. 46.(-11) < -500

**Question 4: **When x = 12, the value of the expression (x – 8).(x + 7) is which of the following four numbers:

A. -100

B. 100

C. -96

D. -196

**Question 5: **Which of the following statements is true:

A. If ab > 0, then a and b are two positive integers

B. If ab > 0, then a and b are two negative integers

C. If ab = 0 then a = 0 and b = 0

D. If ab < 0, then a and b are two integers with different signs

## 4. Conclusion

Through this lesson, you should know the following:

- Know how to multiply two positive integers.
- Know how to multiply two negative integers.

.

=============