Introduction to Solving Multiplying Integers:
Integers are the set of numbers that include all natural numbers (0, 1, 2, 3, 4, and so on) and their negatives. Integers include positive numbers, negative numbers and zero (zero is neither positive nor negative). Below they are just give few integers - they go on forever in both directions e.g.....-11,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11... Solving multiplying integers is made by using of properties.
Types of Integer:
There are two types of integer. We can do solving multiplying in both type of integers.
1. Positive Integer - 1, 2, 3, 4, 5,...
2. Negative Integers - -1, -2, -3, -4, -5, …
Properties on Solving Multiplying Integers:
The properties of solving multiplying integers are,
Closure under multiplication - a × b is an integer, for all integers a and b.
Commutativity of multiplication - a × b = b × a.
Multiplication by zero - a × 0 = 0 × a = 0.
Multiplicative Identity - a × 1 = 1 × a = a.
Associativity multiplication - (a × b) × c = a × (b × c).
Distributive property - a × (b + c) = a × b + a × c.
Examples on Solving Multiplying Integers:
Closure under multiplication:
1. Solve the multiplication of -20 and -5.
Solution:
(–20) × (–5) = 100.
Commutativity of multiplication:
1)Solve: 3 × (– 4) = –12
(– 4) × 3 = –12
So, 3 × (-4) = (-4) × 3
2.Solve: (-7) × 4 = -28
4 × (-7) = -28
So, (-7) × 4 = 4 × (-7)
Multiplication by zero:
1. (–3) × 0 = 0
2. 4 × 0 = 0
3. (-9) × 0 = 0
Multiplicative Identity:
1. (–3) × 1 = –3
2. (7) × 1 = 7
3. (-8) × 1 = -8
Associativty multiplication:
1. [(–3) × (–2)] × 5 = (–3) × [(–2) × 5]
2. [7× (-3)] × 2 = 7 × [(-3) × 2]
Distributive property:
1. (–2) × (3 + 5) = –2 × 8 = –16
and
[(–2) × 3] + [(–2) × 5] = (– 6) + (–10) = –16
2. (5) × ( 6 + 2 ) = 5 × 8 = 40
and
(5 × 6) + (5 × 2) = 30 + 10 = 40
These are the examples for solving multiplying integers.
Integers are the set of numbers that include all natural numbers (0, 1, 2, 3, 4, and so on) and their negatives. Integers include positive numbers, negative numbers and zero (zero is neither positive nor negative). Below they are just give few integers - they go on forever in both directions e.g.....-11,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11... Solving multiplying integers is made by using of properties.
Types of Integer:
There are two types of integer. We can do solving multiplying in both type of integers.
1. Positive Integer - 1, 2, 3, 4, 5,...
2. Negative Integers - -1, -2, -3, -4, -5, …
Properties on Solving Multiplying Integers:
The properties of solving multiplying integers are,
Closure under multiplication - a × b is an integer, for all integers a and b.
Commutativity of multiplication - a × b = b × a.
Multiplication by zero - a × 0 = 0 × a = 0.
Multiplicative Identity - a × 1 = 1 × a = a.
Associativity multiplication - (a × b) × c = a × (b × c).
Distributive property - a × (b + c) = a × b + a × c.
Examples on Solving Multiplying Integers:
Closure under multiplication:
1. Solve the multiplication of -20 and -5.
Solution:
(–20) × (–5) = 100.
Commutativity of multiplication:
1)Solve: 3 × (– 4) = –12
(– 4) × 3 = –12
So, 3 × (-4) = (-4) × 3
2.Solve: (-7) × 4 = -28
4 × (-7) = -28
So, (-7) × 4 = 4 × (-7)
Multiplication by zero:
1. (–3) × 0 = 0
2. 4 × 0 = 0
3. (-9) × 0 = 0
Multiplicative Identity:
1. (–3) × 1 = –3
2. (7) × 1 = 7
3. (-8) × 1 = -8
Associativty multiplication:
1. [(–3) × (–2)] × 5 = (–3) × [(–2) × 5]
2. [7× (-3)] × 2 = 7 × [(-3) × 2]
Distributive property:
1. (–2) × (3 + 5) = –2 × 8 = –16
and
[(–2) × 3] + [(–2) × 5] = (– 6) + (–10) = –16
2. (5) × ( 6 + 2 ) = 5 × 8 = 40
and
(5 × 6) + (5 × 2) = 30 + 10 = 40
These are the examples for solving multiplying integers.
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