Math Background

Division by One-Digit Divisors: Overview

Concepts and Terms
Division is the inverse operation of multiplication, just as subtraction is the inverse operation of addition. The result of dividing one number (the dividend) by another (the divisor) is the quotient.

division problem

The concept of dividing can be explained by using base-ten blocks. 37 ÷ 2 can be modeled as shown below.

base-ten blocks

One ten is placed in each group. The remaining ten is regrouped as 10 ones. There are now 17 ones that must be divided into two equal groups. Eight ones are placed in each group; 1 one is left over.

The division is complete. There are two equal groups. Each group contains 1 ten and 8 ones; there is 1 one left over.

division problem

The number in all is the dividend. In this example the number of groups is the divisor. The number in each group is the quotient. The remainder is the number that is left over after dividing.

Interpreting the remainder is a necessary skill in solving division word problems. Sometimes the answer is the remainder, sometimes the remainder is dropped, and sometimes the quotient is increased. For example:

Thirty-five oranges are placed in crates. A crate can hold 8 oranges. Every crate is filled except for one.

division problem

How many full crates are there? (4)
How many oranges are in the unfilled crate? (3)
How many crates are needed for all 35 oranges? (5)

The Division Algorithm
When beginning the division algorithm, deciding where to place the first digit in the quotient is the initial step.

In a problem such as division problem, look at the first digit in the dividend. Since 1 < 5, there are not enough hundreds to divide. No number will be placed above the 1. Look at the first two digits of the dividend. Sixteen tens can be divided into five equal groups. Place the first digit above the 6.

Follow the steps below to complete the division algorithm.

Step 1 Divide.
16 tens ÷ 5 = 3 tens
Step 2 Multiply.
5 x 3 tens = 15 tens
Step 3 Subtract.
16 tens − 15 tens = 1 ten
Step 4 Bring down the next digit.
Step 5 Repeat the process.
13 ÷ 5 = 2
5 x 2 = 10
13 − 10 = 3
division problem

Dividing money by a whole number is the same as dividing whole numbers. The dollar sign and the decimal point in the quotient are placed directly above the corresponding symbols in the dividend.

division problem Divide. Multiply. Subtract.
Bring down the next digit.
1 < 3, so there are not enough tenths to divide, place 0 above the 1.
Multiply. Then Subtract.
Bring down the next digit.
Repeat the process: divide, multiply, and subtract.

Houghton Mifflin Math Grade 4