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Mathematics

Grade5

Easy

Question

345 × 12=______.

4057
4157
4977
4140

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: 4140

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 $345$ and $12$ as follows:
$345 equals 300 plus 40 plus 5$
$12 equals 10 plus 2$
Step2: Now we will use the distributive property to multiply this:
$left parenthesis 10 plus 2 right parenthesis cross times left parenthesis 700 plus 40 plus 5 right parenthesis equals left parenthesis 10 cross times 700 right parenthesis plus left parenthesis 10 cross times 40 right parenthesis plus left parenthesis 10 cross times 5 right parenthesis plus left parenthesis 2 cross times 700 right parenthesis plus left parenthesis 2 cross times 40 right parenthesis plus left parenthesis 2 cross times 5 right parenthesis$
Step3: Now we will do simple multiplication of which are as follows:
$10 cross times 700 equals 7000$
$10 cross times 40 equals 400$
$10 cross times 5 equals 50$
$2 cross times 700 equals 1400$
$2 cross times 40 equals 80$
$2 cross times 5 equals 10$
Step4: Now we have to add these numbers.
$left parenthesis 10 cross times 700 right parenthesis plus left parenthesis 10 cross times 40 right parenthesis plus left parenthesis 10 cross times 5 right parenthesis plus left parenthesis 2 cross times 700 right parenthesis plus left parenthesis 2 cross times 40 right parenthesis plus left parenthesis 2 cross times 5 right parenthesis equals 7000 plus 400 plus 50 plus 1400 plus 80 plus 10$
=>4140
So, the answer of the multiplication of $745 cross times 12$ is $4140$ .

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