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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

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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

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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

Practice problems:

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

Practice problems:

1. (-18) – 20 = ?

Answer: (-38)

2. 15 - (-13) = ?

Answer: 28

Multiplication and Division Fact Families

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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 = ?

Answer: (-160)

2. (-5) × (-60) = ?

Answer: 300

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 = ?

Answer: (-1)

2. 65 ÷ (-5) = ?

Answer: (-13)

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