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Mathematics

Grade5

Easy

Question

There are 287 bags filled with coins. There are 91 coins in each bag. Find the total coins are there in all.

22,676
27,789
26,117
27,700

hint Hint:

The total number of coin will be equal to the product of the bags and the number of coins in each bag. 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: 26,117

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 $287$ and $91$ as follows:
$287 equals 200 plus 80 plus 7$
$91 equals 90 plus 1$
Step2: Now we will use the distributive property to multiply this:
$left parenthesis 90 plus 1 right parenthesis cross times left parenthesis 200 plus 80 plus 7 right parenthesis equals left parenthesis 90 cross times 200 right parenthesis plus left parenthesis 90 cross times 80 right parenthesis plus left parenthesis 90 cross times 1 right parenthesis plus left parenthesis 1 cross times 200 right parenthesis plus left parenthesis 1 cross times 80 right parenthesis plus left parenthesis 1 cross times 7 right parenthesis$
Step3: Now we will do simple multiplication of which are as follows:
$90 cross times 200 equals 18 comma 000 90 cross times 80 equals 7 comma 200 90 cross times 1 equals 90 1 cross times 200 equals 200 1 cross times 80 equals 80 1 cross times 7 equals 7$
Step4: Now we have to add these numbers.
$left parenthesis 90 cross times 200 right parenthesis plus left parenthesis 90 cross times 80 right parenthesis plus left parenthesis 90 cross times 1 right parenthesis plus left parenthesis 1 cross times 200 right parenthesis plus left parenthesis 1 cross times 80 right parenthesis plus left parenthesis 1 cross times 7 right parenthesis equals 18 comma 000 plus 7 comma 200 plus 90 plus 200 plus 80 plus 7$
=> $26 comma 117$
So, the total number of coins are $26 comma 117$ .

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