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.
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:
a
× (b
– c) = (a ×
b) – (a × c)
This can help
solve complex multiplication problems:
Other lessons:
- Lesson 1. Writing numbers
- Lesson 2. Adding whole numbers
- Lesson 3. Substracting whole numbers
- Lesson 4. Multiplication table
- Lesson 6. Division whole nambers
- Lesson 7. Exponentiation
- Lesson 8. Sizes and their measuring
- Lesson 9. Dividing whole numbers with remainder
- Lesson 10. Factors and prime numbers
- Lesson 11. Highest common factor
- Lesson 12. Lowest common multiple
- Lesson 13. Equivalent fractions
- Lesson 14. Transformation of fraction
- Lesson 15. Adding fractions
- Lesson 16. Subtract fractions
- Lesson 17. Multiplying fractions
- Lesson 18. Dividing fractions
- Lesson 21. Eventual decimal fractions
- Lesson 22. Adding decimals
- Lesson 23. Subtracting decimals
- Lesson 24. Multiplying decimals
- Lesson 25. Dividing decimals
- Lesson 26. Rounding numbers
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