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Mathematics

Grade5

Easy

Question

284 × 81 ______.

24,268
23,004
25,168
23,168

hint Hint:

In this question we have to multiply as three-digit number with a two-digit number. We can use the distributive law to do this question. Distributive law relates multiplication and addition as follows: $a left parenthesis b plus c plus d right parenthesis equals left parenthesis a cross times b right parenthesis plus left parenthesis a cross times c right parenthesis plus left parenthesis a cross times space d right parenthesis$ This law shows that first adding some numbers and the multiplying the sum by some numbers gives same result as first multiplying each number by separately with the number and then adding them

The correct answer is: 23,004

Step1: We have to use the standard algorithm to find the multiplication so we will first break the one number into small numbers that can be easily multiplied to get the result. So, we will divide $284$ and $81$ as follows:
$284 equals 200 plus 80 plus 4$
$81 equals 80 plus 1$
Step2: Now we will use the distributive property to multiply this:
$left parenthesis 80 plus 1 right parenthesis cross times left parenthesis 400 plus 80 plus 4 right parenthesis equals left parenthesis 80 cross times 400 right parenthesis plus left parenthesis 80 cross times 80 right parenthesis plus left parenthesis 80 cross times 4 right parenthesis plus left parenthesis 1 cross times 400 right parenthesis plus left parenthesis 1 cross times 80 right parenthesis plus left parenthesis 1 cross times 4 right parenthesis$
Step3: Now we will do simple multiplication of which are as follows:
$80 cross times 400 equals 32 comma 000$
$80 cross times 80 equals 6 comma 400$
$80 cross times 4 equals 320$
$1 cross times 400 equals 400$
$1 cross times 80 equals 80$
$1 cross times 4 equals 4$
Step4: Now we have to add these numbers.
$left parenthesis 80 cross times 400 right parenthesis plus left parenthesis 80 cross times 80 right parenthesis plus left parenthesis 80 cross times 4 right parenthesis plus left parenthesis 1 cross times 400 right parenthesis plus left parenthesis 1 cross times 80 right parenthesis plus left parenthesis 1 cross times 4 right parenthesis equals 32 comma 000 plus 6 comma 400 plus 320 plus 400 plus 80 plus 4$
=> $23 comma 004$
So, the answer of the multiplication of $81 cross times 484$ is $23 comma 004$ .

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