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Mathematics

Grade5

Easy

Question

A librarian is ordering books for the brand new library in town. The library has 372 shelves that can each hold 43 books. Find the total books can the librarian order.

15,996
15,600
13,000
13,590

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: 15,996

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 $372$ and $43$ as follows:
$473 equals 400 plus 70 plus 3$
$43 equals 40 plus 3$
Step2: Now we will use the distributive property to multiply this:
$left parenthesis 40 plus 3 right parenthesis cross times left parenthesis 300 plus 70 plus 2 right parenthesis equals left parenthesis 40 cross times 300 right parenthesis plus left parenthesis 40 cross times 70 right parenthesis plus left parenthesis 40 cross times 2 right parenthesis plus left parenthesis 3 cross times 300 right parenthesis plus left parenthesis 3 cross times 70 right parenthesis plus left parenthesis 3 cross times 2 right parenthesis$
Step3: Now we will do simple multiplication of which are as follows:
$40 cross times 300 equals 12 comma 000 40 cross times 70 equals 2 comma 800 40 cross times 2 equals 80 3 cross times 300 equals 900 3 cross times 70 equals 210 3 cross times 2 equals 6$
Step4: Now we have to add these numbers.
$left parenthesis 40 cross times 300 right parenthesis plus left parenthesis 40 cross times 70 right parenthesis plus left parenthesis 40 cross times 2 right parenthesis plus left parenthesis 3 cross times 300 right parenthesis plus left parenthesis 3 cross times 70 right parenthesis plus left parenthesis 3 cross times 2 right parenthesis equals 12 comma 000 plus 2 comma 800 plus 80 plus 900 plus 210 plus 6$
=> $15 comma 996$
So, Librarian ordered $15 comma 996$ books.

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