## Math 6 Chapter 2 Lesson 10: Multiplying two integers with different signs

## 1. Summary of theory Tóm

To multiply two integers with different signs, multiply their absolute values and put a “-” sign in front of the result.

**Attention: **The product of an integer a and zero is 0.

**For example:**

5. (-3) = -(5.3) = -15

6.(-4) = -(6.4) = -24

(-2.3 = -(2.3) = -6

## 2. Illustrated exercise

**Question 1:** Workers of a company receive wages according to the product: Making a product according to specifications is 20 000 dong, making a wrong product is fined 10 000 dong. Last month, worker A made 40 standard products and 10 wrong products. How much was worker A’s salary last month?

__Solution guide__

When an incorrect product is deducted 10 000 VND, that means an additional – 10 000 VND. So, last month’s salary of worker A is:

40 . 20 000 + 10 . (-10 000) = 700 000 (VND)

**Verse 2:** Calculate 225.8. Then deduce the result of:

a. (225) . 8

b. (-8) . 225

c. 8 . (-225)

__Solution guide__

225.8 = 1800, so:

a. (225) . 8 = -1800

b. (-8) . 225= -1800

c. 8 . (-225) = -1800

**Question 3: **Do not make love, or compare:

a. (-34) . 4 with 0

b. 25 . (-7) with 25

c. (-9) . 5 with – 9

__Solution guide__

a. (-34) . 4 with 0

(-34) . 4 < 0

b. 25 . (-7) with 25

25 . (-7) < 25

c. (-9) . 5 with – 9

(-9) . 5 < -9

## 3. Practice

### 3.1. Essay exercises

**Question 1: ** Calculate the value of the expression, with x = -7; y = -5

a. 4x – 3y

b. x(y + 9) + 5x

**Verse 2: **Total

a. S = 1 – 2 + 3 – 4 + … + 2009 – 2010

b. P = 0 – 2 + 4 – 6 + … + 2010 – 2012.

**Question 3:** Find five values of \(x \in \mathbb{Z}\) such that:

a. 4 (x – 8) < 0

b. -3 (x – 2) < 0

### 3.2. Multiple choice exercises Bài

**Question 1: **The result of the calculation (-125).8 is:

A. 1000

B. -1000

C. -100

D. -10000

**Verse 2: **Choose the wrong sentence:

A. (-5).25 = -125

B. 6.(-15) = -90

C. 125.(-20) = -250

D. 225.(-18) = -4050

**Question 3:** Choose the correct answer:

A. -365.366 < 1

B. -365.366 = 1

C. -365.366 = -1

D. -365.366 > 1

**Question 4: **Fast calculation (-5).125.(-8).20.(-2) we get the result:

A. -200000

B. -2000000

C. 200000

D. -100000

**Question 5: **Calculate the value of the expression x – 2 + x – 2 + x – 2 + x – 2 + x – 2 at x = -7

A. – 30

B. 30

C. – 45

D. 45

## 4. Conclusion

Through this lesson, you should be able to understand the following:

- Can multiply two integers with different signs.
- Apply to solve related problems.

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