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# Fact Families

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.

## What are 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:

Addends: The numbers being added in an addiotion operation. Like 2 and 3 in 2 + 3 = 5

Multiplicands: The numbers being multiplied in a multiplication operation. Like 4 and 5 in 4 x 5 = 20

Inverse operation: Reverse of an operation like inverse operation of addition is subtraction and inverse of multiplication is division.

## Addition and Subtraction Fact Families

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-

• 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

### Practice problems:

1. (-10) + 7 = ?

2. 14 + (-10) = ?

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

### Practice problems:

1. (-18) – 20 = ?

2. 15 - (-13) = ?

## Multiplication and Division Fact Families

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

Below are the multiplication and division rules and examples for number fact families

### Multiplication rules

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 = ?

2. (-5) × (-60) = ?

### Division rules

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 = ?