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Division: Help & Review9 chapters | 48 lessons

Instructor:
*Laura Pennington*

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

In this lesson, we will learn how to divide 13 by 2. We will go through each step in this process, and relate it to a real life situation to make it more understandable. We will then discuss how to check our work when solving this problem.

Before we get to the problem, let's have a quick review of some vocabulary involved in a division problem. Suppose we are dividing *x* by *y*. In this case, we call *y* the **divisor** and *x* the **dividend**. The number of times *y* fits into *x* is called the **quotient**, and anything that is left over is called the **remainder**.

Now that we've reviewed the vocabulary, suppose that you and I are out for a walk, and we find 13 one dollar bills on the sidewalk. We decide to split the money evenly between us. In other words, we want to divide $13.00 between two people. This scenario represents a division problem where we want to divide 13 by 2.

In this problem, the divisor is 2, and the dividend is 13. To perform the division, we need to find out how many times 2 fits into 13, which will give us the quotient. To do this, let's consider multiples of 2.

2*1 = 2

2*2 = 4

2*3 = 6

2*4 = 8

2*5 = 10

2*6 = 12

2*7 = 14

Notice that 2*6 = 12, so we can fit 2 into 13 six times. However, 2*7 = 14, so we can't fit 7 copies of 2 into 13 because it would go over. Therefore, we find that when we divide 13 by 2, the quotient is 6, so you and I would each get $6 from the $13 we found. But wait! 2*6 = 12, and we have $13! After we each get $6, there is $1 left over. The $1 represents the remainder in the division problem 13 / 2. In conclusion, when we divide 13 by 2, we get 6 with a remainder of 1. This can be carried out using long division with a remainder, which is illustrated in the image below.

Well, that's all fine and dandy, but what are we going to do with the extra dollar? We could donate it to charity, or we could use long division to divide 13 by 2 to a decimal point. After we find the remainder, we can bring up the decimal point and continue with the division to see exactly how much we should each get. Look at the image below to see how to divide 13 by 2 using long division and continuing past the decimal.

When we divide 13 by 2, we get 6 with a remainder of 1. We can also use long division to a decimal point to solve 13 divided by 2 in decimal form, which shows that 13 divided by 2 is 6.5. This tells us that we each get $6 with $1 left over, or we can get change for that $1, and we each get $6.50.

To check your work in this problem, just undo the division. In general, when we divide *x* by *y*, and we get a quotient *q*, and a remainder *r*, then if we multiply *y* by *q* and add *r* to that, we will get *x*. That is, in a division problem, if we multiply the divisor by the quotient and add the remainder, it will equal the dividend.

When we did our division problem the first way, we found that 13 is the dividend, 2 is the divisor, 6 is the quotient, and 1 is the remainder. Therefore, if we multiply 2 by 6 and add 1, we should get 13.

(2*6) + 1 = 12 + 1 = 13

Sure enough, it checks out! But what about when we did it the second way? In that case, the dividend is 13, the divisor is 2, the quotient is 6.5, and the remainder is 0. Therefore, if we multiply 2 by 6.5 and add 0, we should get 13.

2*6.5 + 0 = 13 + 0 = 13

Once again, it checks out!

As we've seen in this lesson, division shows up fairly often in our daily lives, so it is important to be comfortable dividing numbers. The processes outlined in this lesson provide a solid base on understanding how to perform division.

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Division: Help & Review9 chapters | 48 lessons

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