Finding the Quotient in a Division Problem: Explanation and Examples

How to Find the Quotient in Division

When you solve a division problem, your goal is to find the quotient, which is the solution to the problem. Division problems also have a dividend, which is the number that's being divided into parts, and a divisor, which is the number you're dividing by. The divisor tells you how many units should be in each of the parts that you split the dividend into. For example, in the equation 8 ÷ 2 = 4, which is the same as 8/2 = 4, eight is the dividend, two is the divisor and four is the quotient.

Finding the Quotient in a Word Problem

Say you have one dollar, and your teacher asks you how many nickels you'd need to make change for that dollar. To answer the question, you'll need to figure out how many five cent 'parts' the dollar can be divided into. The dividend is 100 cents, because that's what's being split up. The divisor is five cents, because five is the number of units in each part you're splitting the dividend into. The quotient is the number of five cent parts that you can make out of 100 cents. To find that, divide 100 by five to get a quotient of 20 (100 ÷ 5 = 20). This means you'd need 20 nickels to make change for a dollar.

Finding Quotients with Remainders

Sometimes the quotient of your division problem will have a remainder. This is the part that's left over when the divisor doesn't fit into the dividend evenly. For instance, imagine that instead of asking you to divide a dollar into five cent parts, your teacher asked you to divide it into seven cent parts. If you divided 100 pennies into groups of seven cents, you could make 14 whole groups, but you'll still have two pennies left over. These two are your remainder. You'd write it like this:

100 ÷ 7 = 14, remainder 2

Writing Quotients with Fractions

When your quotient has a remainder, you might be asked to write it with a fraction. Instead of just writing how many parts are left over, like we did with '14, remainder 2,' we have to figure out what fraction of a whole group is left over. For example, there were two pennies out of a possible group of seven left over, so we'd write that there were 2/7 of a group left over. Since seven went into 100 14 whole times, and there were 2/7 left over, the quotient would be 14 2/7 if you wrote it with a fraction.

Writing Quotients as Decimals

Quotients that have fractions, like 14 2/7, can also be written as decimals. In a decimal, the number to the left of the point is the number of times the divisor goes completely into the dividend. For example, seven went into 100 14 times, so there would be a 14 to the left of the point.

The remainder, which is the fraction, goes to the right of the point. To turn the fraction into a decimal, work out the division in the fraction. In this example, two divided by seven equals approximately 0.286 (2 ÷ 7 = 0.286). Seven goes into 100 14 2/7 times or, written as a decimal, 14.286 times. Remember that when you're dividing fractions, you always divide the top number by the bottom number.