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"Law of Multiplication" The relationship between multiplication and division and the law of multiplication PPT courseware 2
Observe the two equations in each group below. What is the relationship between them?
18×7○ 7×18
124×35○35×124
What do each set of equations above have in common?
What rules can be found from the above calculations?
①There are two factors in each set of calculations, and the two factors are the same, but their positions have been exchanged.
②In every equation, the products of the factors on the left and right sides are equal.
Which of the following calculations use the distributive law of multiplication?
117×3+117×7=117×(3+7)
24×(5+12)=24×17
4 × a +5 × a=(4+5) × a
When two factors switch places, the product remains unchanged. This is called the commutative law of multiplication.
If the letters a and b are used to represent two factors, they can be written as:
a×b＝b×a
Multiply the first two numbers first, or multiply the last two numbers first, and the product remains unchanged. This is called the associative law of multiplication.
If the letters a and b are used to represent two addends, it can be written as:
(a×b) ×c＝a× (b×c)
If the sum of two numbers is multiplied by a number, you can first multiply them by the number and then add them together. This is called the distributive law of multiplication.
If the letters a and b are used to represent two addends, it can be written as:
(a+b) ×c＝a×c+b×c
a×(b+c) =a×b+a×c
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