Estimate
Round some or all of the factors so that it will be easy to multiply mentally.
There are no hard and fast rules as to how exactly you should round. The idea is round some of the numbers so that your new rounded numbers are easy to multiply in your head.
Estimate 8 × 189.189 can be rounded to 200.
The estimated product is 8 × 200 = 1,600. / Estimate 42 × 78.
42 ≈ 40 and 78 ≈ 80.
The estimated product is 40 × 80 = 3,200. / Estimate 21 × $4.56.
Round the numbers to 20 and $4.50. Multiply in parts:
20 × $4 = $80 and 20 × 50¢ = 1000¢ = $10. Then add: $80 + $10 = $90.
Rounding
Rounding involves either increasing or decreasing a number to the next digit.
A store needs at least $15,000 in sales per month. If the store averages $525 per day, will the store make a profit?
525 rounds to 500
31 rounds to 30 (days in a month)
30 x 500 = 15,000
Underestimate
An estimate that is less than the actual answer.
Overestimate
An estimate that is over the actual answer.
Inverse Operations
Operations that undo each other: Adding 6 and subtracting 6 are inverse operations.
Reasonableness
Is your answer reasonable? Is your answer close to the exact/estimated answer?
Use many other techniques for estimating sums and discovering if your answer is reasonable.
Associative Property
The associative property states that you can add regardless of how the numbers are grouped.
By 'grouped' we mean 'how you use parenthesis'. If you are adding it does not matter where you put the parenthesis.
Variable
A symbol for a number we don't know yet.
Factors
Factors are numbers you can multiply together to get another number
A number can have MANY factors!
What are the factors of 12?
3 and 4 are factors of 12, because 3 × 4 = 12.
Also 2 × 6 = 12 so 2 and 6 are also factors of 12.
And 1 × 12 = 12 so 1 and 12 are factors of 12 as well.
So 1, 2, 3, 4, 6 and 12 are all factors of 12
Multiple
A multiple of a number is the product of that number and any other whole number.
Example 2: / Find the multiples of the whole number 5.Multiplication: / 5 x 1 / 5 x 2 / 5 x 3 / 5 x 4 / 5 x 5 / 5 x 6 / 5 x 7 / 5 x 8
Multiples of 5: / 5 / 10 / 15 / 20 / 25 / 30 / 35 / 40
Solution: / The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40,.
Product
The answer when two or more numbers are multiplied together.
Area Model
A Base 10, grid demonstration of how multiplication is related to an area; as in 16 by 27.
Partial Products
The Partial Products Method helps simplify long multiplication. It is a very accessible method because it breaks down complex numbers into simpler, more easily-multiplied, ones.
To use the Partial Products method, you need to decompose - that means "break apart" each number into its smaller forms. For example, the number 77 is actually seven tens plus seven ones.