Attention Getting Question:
Have you ever tried to divide a four-digit number?
When we divide numbers, we determine how many equally sized groups are contained in the number being split. We represent division using either a division bar or a division sign. The number being divided is called the dividend, and the number we are dividing by, or the number of groups we want to have, is the divisor.
Imagine your best friend just moved far away. Your parents tell you they will take you to visit your friend if you determine how fast the plane has to go in order to make the trip in 8 hours or less. You know your friend moved 2,608 miles away. One way of findinga solution would be to count how many times we have to add 8 together in order to get to 2,608. However, division helps solve this problem much faster.
We use what is called the standard algorithm for division. Since we want to divide 2,608 by 8, we will first write a division bar on our page with the dividend on the inside and the divisor on the outside. Starting with the digit furthest to the left, in this case the thousands, we determine how many times the divisor will go into that number evenly. Since 8 will not go into 2 evenly, we look at the next digit as well. Eight will go into 26 three times. We write a three above the 6 on top of the division bar where the quotient goes. Three times 8 is 24, so we will write a 24 below the 26 and subtract these two numbers. We are left with 208 after we bring down the rest of the digits. Next, we look at what we have left. Eight will go into 20 two times. Again, write a two above the division bar next to the three that is already written. Eight times 2 is 16, so this time we will subtract 16 from 20. This leaves us with 48 after we bring down the 8. Eight will go into 48 six times evenly. We will write an 8 next to the 2 already written. Eight times six is 48, so when we subtract the two numbers, we will have a 0 left. The number that is left at the endis called the remainder because it is what is remaining after division is complete. In this case, we have a 0 remainder. We do not have to show that there is any remainder at all. This tells us that your plane has to go three hundred and twenty-six miles per hour to get to see your friend in 8 hours. Better start looking for fast planes!
In summary, division is determining how many equally sized groups will fit into a number. In order to perform division easily, we use the standard algorithm for division. We will write the dividend on the inside of the division bar, the divisor on the outside of the division bar to the left of the dividend, and the quotient, or our answer, will be on top of the division bar at the end. Now that you see division is easy, you can do it, too!