PROPERTIES
What is the commutative property of multiplication?
Changing the order of the factors does not change the product. (e.g., 3 × 4 = 4 × 3)
What is 100 × 6?
600
Why do we estimate in real life?
To get a quick, close answer when an exact answer isn’t needed or to make calculations easier.
What is a partial product?
The result of multiplying one part of a number by another number before adding all the parts together.
What is 219 x 300 =
65,700
Give an example of the associative property using the numbers 2, 3, and 4.
(2 × 3) × 4 = 2 × (3 × 4) = 24
What happens to a number when you multiply it by 1,000?
The number gets three zeros added to the end (it becomes 1,000 times bigger).
Round 88 × 51 to the nearest ten and estimate the product.
90 × 50 = 4,500
Solve using partial products: 62 × 28
62 × 8 = 496; 62 × 20 = 1,240; 496 + 1,240 = 1,736
Multiply 354 × 120.
42,480
What does the identity property of multiplication state?
Any number multiplied by 1 is itself. (e.g., 8 × 1 = 8)
Fill in the blank: 4,000 × 8 = ____
32,000
Estimate: 31 × 43 ≈ ___ × ___ = ____
30 × 40 = 1,200
Show the steps for 54 × 26 using partial products.
54 × 6 = 324; 54 × 20 = 1,080; 324 + 1,080 = 1,404
Explain why it’s important to keep your work organized when multiplying by three-digit numbers.
To avoid mistakes, keep track of each partial product, and make sure all place values are correct when adding the results.
Which property is shown: 10 × (4 + 3) = (10 × 4) + (10 × 3)?
Distributive property
If you multiply 50 × 7, how many zeros are in the answer?
One zero (50 × 7 = 350)
If you have $4.89 × 29, what is a good estimate?
5 X 30 = 150
Why do we add the partial products at the end?
To get the total product by combining the results of each multiplication step.
Multiply 305 × 360.
109,800
Name all five multiplication properties you learned in this unit.
Commutative, Associative, Identity, Zero, Distributive
Create your own multiplication problem using a power of ten and solve it.
(Example) 200 × 5 = 1,000
Explain the steps to estimate a product.
Round each factor to its greatest place value, then multiply the rounded numbers.
Multiply 43 × 44 using partial products.
43 × 4 = 172; 43 × 40 = 1,720; 172 + 1,720 = 1,892
Show the steps for 417 × 131 using partial products.
417 × 1 = 417
417 × 30 = 12,510
417 × 100 = 41,700
417 + 12,510 + 41,700 = 54,627