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Mathematics

Grade5

Easy

Question

394 × 71=_______.

28,740
95,800
27,974
12,354

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: 27,974

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 $394$ and $71$ as follows:
$394 equals 300 plus 90 plus 4$
$71 equals 70 plus 1$
Step2: Now we will use the distributive property to multiply this:
$left parenthesis 70 plus 1 right parenthesis cross times left parenthesis 300 plus 90 plus 4 right parenthesis equals left parenthesis 70 cross times 300 right parenthesis plus left parenthesis 70 cross times 90 right parenthesis plus left parenthesis 70 cross times 4 right parenthesis plus left parenthesis 1 cross times 300 right parenthesis plus left parenthesis 1 cross times 90 right parenthesis plus left parenthesis 1 cross times 4 right parenthesis$
Step3: Now we will do simple multiplication of which are as follows:
$70 cross times 300 equals 21 comma 000 70 cross times 90 equals 6 comma 300 70 cross times 4 equals 280 1 cross times 300 equals 300 1 cross times 90 equals 90 1 cross times 4 equals 4$
Step4: Now we have to add these numbers.
$left parenthesis 70 cross times 300 right parenthesis plus left parenthesis 70 cross times 90 right parenthesis plus left parenthesis 70 cross times 4 right parenthesis plus left parenthesis 1 cross times 300 right parenthesis plus left parenthesis 1 cross times 90 right parenthesis plus left parenthesis 1 cross times 4 right parenthesis equals 21 comma 000 plus 6 comma 300 plus 280 plus 300 plus 90 plus 4$
=> $27 comma 974$
So, the answer of the multiplication of $71 cross times 394$ is $27 comma 974$ .

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