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Mathematics

Grade5

Easy

Question

A store received a shipment of 78 televisions. Each television is worth $592. Find the shipment worth.

$42,750
$41,275
$46,176
$91,020

hint Hint:

The total shipment worth will be equal to the product of the total number of television shipped and the price of each television. 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: $46,176

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 $592$ and $78$ as follows:
$592 equals 500 plus 90 plus 2$
$78 equals 70 plus 8$
Step2: Now we will use the distributive property to multiply this:
$left parenthesis 70 plus 8 right parenthesis cross times left parenthesis 500 plus 90 plus 2 right parenthesis equals left parenthesis 70 cross times 500 right parenthesis plus left parenthesis 70 cross times 90 right parenthesis plus left parenthesis 70 cross times 2 right parenthesis plus left parenthesis 8 cross times 500 right parenthesis plus left parenthesis 8 cross times 90 right parenthesis plus left parenthesis 8 cross times 2 right parenthesis$
Step3: Now we will do simple multiplication of which are as follows:
$70 cross times 500 equals 35 comma 000 70 cross times 90 equals 6 comma 300 70 cross times 2 equals 140 8 cross times 500 equals 4 comma 000 8 cross times 90 equals 720 8 cross times 2 equals 16$
Step4: Now we have to add these numbers.
$left parenthesis 70 cross times 500 right parenthesis plus left parenthesis 70 cross times 90 right parenthesis plus left parenthesis 70 cross times 2 right parenthesis plus left parenthesis 8 cross times 500 right parenthesis plus left parenthesis 8 cross times 90 right parenthesis plus left parenthesis 8 cross times 2 right parenthesis equals 35 comma 000 plus 6 comma 300 plus 140 plus 4 comma 000 plus 720 plus 16$
=> $46 comma 176$
So, the total shipment worth is $46 comma 176$ .

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