Уроки математики и физики (RU + UA)

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среда, 1 июня 2016 г.

Lesson 5. Multiplying whole numbers

MULTIPLICATION Is multiplying whole numbers more difficult than adding or subtracting them?
Not really, if you remember to line up the numbers by place value. Then multiply the numbers by place value. Then multiply the entire top number by the ones place of the bottom number, and then by the tens place, and then by the hundreds place, and so on for larger numbers. Think of it as doing a few simple problems, one after the other. After you’ve finished multiplying, add the lines to find the product. The product is the answer to the entire multiplication problem.
The multiplication of two numbers  a  and  b  is denoted by
ab = c,
where  c  is the result of the multiplication of the numbers  a  and  b. Both numbers, a  and  b, are called factors (or multipliers), and  c  is the product of  a  and  b.

Remember…                          

Always multiply the entire top number by one bottom digit at a time. Use a different line for the product of each bottom digit.

There are certain rules or properties of math that are always true.
The Commutative Properties of addition and multiplication state that the order in which numbers are added or multiplied does not change the result.
a × b = b × a

EXAMPLE:

5 × 2 = 10
2 × 5 = 10

The Associative Properties of addition and multiplication state that the way in which addends or factors are grouped does not change the result.

(a × b) × c  = a × (b  × c)
(2 × 4) × 5 = 2 × (4 × 5)
8 × 5 = 2 × 20
40 = 40

The Identity Property of Multiplication states that the product of a factor and 1 is that factor.

4 × 1 = 4

The Properties of Zero state that the product of a factor and 0 is 0.

5 × 0 = 0

The Distributive Property combines the operations of addition and multiplication.

a × (b + c)  = (a × b) + (a × c)
3 × (2 + 5) = (3 × 2) + (3 × 5)
3 × 7 = 6 + 15
21 + 21

The Distributive Property states:

a × (b + c)  = (a × b) + (a × c)

This can help solve complex multiplication problems:
The same property also means that:

a × (b – c)  = (a × b) – (a × c)

This can help solve complex multiplication problems:
Tasks to the lesson 5
Other lessons:
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