** **In algebra, a fundamental arithmetic number of fact (addition, subtraction, multiplication, and division) is general used in day-to-day life. Addition (+) defined as adding the two numbers. Subtraction (-) defined as the inverse of addition. Multiplication (x) defined as the product of numbers. Division (÷) is a result of dividing two rational numbers when a divisor is not a zero.

Math facts consist of indeterminate expressions. In math, there is a particular facts in which we are not capable to modify those facts. Example for division** “Positive ÷ Negative = Negative”**. It is a procedure of interactive teaching about the practice math facts.In these articles, we are going to see about number fact families.

A fact family is a group of four statements each of which represent the same meaning. All the four statements have the same meanings. Fact families contain 3 numbers and 2 types of operations. There are 2 types of fact families: addition and subtraction fact families; multiplication and division fact families.

To see the fact families we need to understand the meaning of following words:

Here you could see addition fact families and subtraction fact families that discussed below.

Below are the **addition and subtraction rules** and examples for **number fact families**-

**Addition rules**

- Positive + Positive =
**Positive**

10 + 8 = 18

- Negative + Negative =
**Negative**

(- 10) + (- 5) = - 15

- Addition of a
**negative**and a**positive integer**: Use the sign of the larger number and subtract, examples,

(- 12) + 6 = -6

10 + (-8) = 2

** **1. (-10) + 7 = ?

**Answer:** (-3)

2. 14 + (-10) = ?

**Answer:** 4

**Negative rules**

- Negative - Positive =
**Negative**

(- 16) - 13 = -16 + (-13) = (-29)

- Positive - Negative = Positive + Positive =
**Positive**

16 - (-14) = 16 + 14 = 30

- Negative - Negative = Negative + Positive =
**Use the sign of the larger number and subtract**(Change double negatives to a non negative)

(-17) - (-12) = (-17) + 12 = -5

(-12) - (-15) = (-12) + 15 = -3

1. (-18) – 20 = ?

**Answer:** (-38)

2. 15 - (-13) = ?

**Answer**: 28

Here you could see multiplication fact families and division fact families that discussed below.

Below are the**Rule1**: Multiplication of two integers by the linked signs resolve be positive sign

a) Positive x positive = **positive**

b) Negative x negative = **positive**

**Rule2:** Multiplication of two integers by the different signs will be negative

a) Positive x negative = **negative**

b) Negative x positive = **negative**

**Example problems:**

1. Positive x positive = **positive**

**Example:** 13 × 12 = 156

2. Negative x negative = **positive**

**Example:** (-15) × (-11) = (165)

3. Positive x negative = **negative**

**Example:** 11 × (-12) = (-132)

4. Negative x positive =** negative **

**Example:** (-4) × 16 = (-64)

**Practice problems:**

1. (-16) × 10 = ?

**Answer: **(-160)

2. (-5) × (-60) = ?

**Answer:** 300

**Rule 1**: Division of two integers by the linked signs resolve be positive sign

a) Positive ÷ positive = positive

b) Negative ÷ negative = positive

**Rule 2: ** Division of two integers by the different signs will be negative

a) Positive ÷ negative = negative

b) Negative ÷ positive = negative

**Example problems:**

1. Positive ÷ positive = positive

**Example:** 100 ÷ 50 = 2

2. Negative ÷ negative = positive

**Example:** (-80) ÷ (-10) = 8

3. Positive ÷ negative = negative

**Example:** 120 ÷ (-10) = (-12)

4. Negative ÷ positive = negative

**Example:** (-90) ÷ (10) = (-9)

**Practice problems:**

1. (-15) ÷ 15 = ?

**Answer:** (-1)

2. 65 ÷ (-5) = ?

**Answer:** (-13)

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