Find the product of the following whole numbers using suitable properties.
a. 459 x 236 + 459 x 123
b. 218 x 136 - 208 x 136
c. 438 x 1003
d. 8 x 392 x 25
Answer (2)
By applying the distributive property and rearranging factors, we can simplify the calculations for the products. The results are 164,784 for part a, 1,360 for part b, 439,314 for part c, and 78,400 for part d. These techniques help in efficiently computing large products by breaking them down into smaller, manageable calculations.
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To find the product using suitable properties, you can make use of the distributive property, which simplifies calculations when dealing with multiplication and addition or subtraction. Let's solve each part step-by-step.
a. 459 × 236 + 459 × 123
Here, you can apply the distributive property: a × ( b + c ) = a × b + a × c
In this case, a = 459 , b = 236 , and c = 123 .
So, it simplifies to:
459 × ( 236 + 123 )
Calculate inside the parentheses first:
236 + 123 = 359
Now, multiply:
459 × 359
This would require more straightforward multiplication, which isn't the main focus here. But, using the distributive property helps us recognize this setup.
b. 218 × 136 − 208 × 136
Here, again use the distributive property: a × ( b − c ) = a × b − a × c .
In this instance, a = 136 , b = 218 , c = 208 .
Simplified, it becomes:
136 × ( 218 − 208 )
Calculate inside the parentheses first:
218 − 208 = 10
Then multiply:
136 × 10 = 1360
c. 438 × 1003
You can express 1003 as 1000 + 3 :
Use the distributive property:
438 × ( 1000 + 3 ) = 438 × 1000 + 438 × 3
Calculate:
438 × 1000 = 438000
438 × 3 = 1314
Add the products together:
438000 + 1314 = 439314
d. 8 × 392 × 25
To simplify, notice that 8 and 25 can be multiplied to make 200, making it easier:
Reorganize as:
( 8 × 25 ) × 392 = 200 × 392
Multiply:
200 × 392
This equals 78400 .
This approach shows how recognizing patterns or using properties like the distributive and associative properties can make calculations easier.
