A factory manufactures 67698 bulbs every year. How many bulbs will be manufactured in seven years?
The first piece of information that we’re told in this problem is the number of bulbs that a factory makes or manufactures every year, and that number is 67698. The question then asks us to find how many bulbs will be manufactured in seven years. So, how are we going to calculate the total? We need to find a value of seven lots of 67698. Now of course, we could add this number seven times. But, there is a quicker method we could use. We could find the answer to 67698 multiplied by seven. Now, we can use short multiplication to find the answer. We’re going to multiply every single digit in 67698 by seven. We’re going to do so one digit at a time.
To start with, we’ll multiply the ones. What are eight ones multiplied by seven? We know that 10 sevens are 70. And so, eight sevens are two lots of seven less than 70. One lot of seven less than 70 is actually nine sevens. We’ll work this out because we’re going to need this in a second. 70 take away seven equals 63. So, we know nine sevens are 63, eight sevens are seven less than 63. 63 take away seven gives us 56. So, eight ones multiplied by seven equals 56 ones. We can’t write 56 ones in the ones place, so we’re going to have to exchange 50 of our ones for five tens.
Next, we’ll multiply the tens digit. What is nine tens multiplied by seven? This is where our nine times seven fact comes in useful. Nine times seven equals 63. So, nine tens multiplied by seven equals 63 tens. We’ve already got five tens underneath that we’ve just exchanged, so 63 plus five equals 68. And, 68 tens is the same as six hundreds and eight tens.
Now, we can multiply the hundreds digit. What are six hundreds multiplied by seven? Well, if we know that 10 times seven equals 70, then we know that half of this is equal to five times seven. Half of 70 is 35. So, five times seven equals 35. We want to find the answer to six times seven, so we need to add one more seven to 35. 35 plus seven equals 42. So, six hundreds multiplied by seven equals 42 hundreds. We’ve also got six hundreds underneath that we need to include. So, that takes us to 48 hundreds. We could exchange 40 of those hundreds for four thousands.
Onto the thousands column. What are seven thousands multiplied by seven? Well, if we know six sevens are 42, then seven sevens must be another seven on top of 42. 42 plus seven equals 49. So, seven hundreds multiplied by seven equals 49 hundreds. And, we also have four hundreds underneath, which takes us to 53 hundreds. And, we need to write the five digit to represent 50 thousands.
Finally, we could multiply our tens of thousands digit, which is six. What are six tens of thousands multiplied by seven? Well, we know six times seven equals 42. So, six tens of thousands multiplied by seven equals 42 tens of thousands. We’ve got five tens of thousands underneath, so the answer is 47 tens of thousands, which is the same was 470000.
Although when we looked at the calculation, we might have thought to ourselves, “how can we multiply such a large number by seven? Are we gonna have to know some really large number facts?” The only number fact we’ve had to know are the seven times table up to 10 times seven. We multiplied each digit, one at a time, by seven, and we used short multiplication to set out our calculation. If a factory manufactures 67698 bulbs every year, the number of bulbs that will be manufactured in seven years can be found by multiplying 67698 by seven. And, the answer is 473886.