Lesson 5: Divide Whole Numbers

New Concept

Mastering division means understanding it as splitting into equal groups. You'll learn different notations, see how it's the inverse of multiplication, and practice the long division method to find quotients and remainders.

What’s next

You're about to put this into practice with interactive examples and challenge problems that build your long division skills from the ground up.

Property

Division is a way to represent repeated subtraction. We call the number being divided the dividend and the number dividing it the divisor. The result is the quotient.

Examples

• The expression $81 \div 9$ is read as eighty-one divided by nine, and the result is the quotient of eighty-one and nine.
• The expression $\frac{48}{6}$ is read as forty-eight divided by six, and the result is the quotient of forty-eight and six.
• The expression $5)\overline{45}$ is read as forty-five divided by five, and the result is the quotient of forty-five and five.

Explanation

Think of division as sharing! The dividend is what you have, the divisor is how many groups you're making, and the quotient is how many go in each group. We can write it in a few different ways, but they all mean the same thing.

Property

Division is the inverse operation of multiplication. We check our answer to division by multiplying the quotient by the divisor to determine if it equals the dividend.

Examples

• To solve $56 \div 7$, we can think 'what number times 7 equals 56?'. The answer is 8. Check: $8 \cdot 7 = 56$.
• To solve $\frac{48}{8}$, we can think 'what number times 8 equals 48?'. The answer is 6. Check: $6 \cdot 8 = 48$.
• To solve $54 \div 9$, we can think 'what number times 9 equals 54?'. The answer is 6. Check: $6 \cdot 9 = 54$.

Explanation

Division and multiplication are opposites that undo each other. You can use your multiplication facts to solve division problems and to check if your answer is correct. It's a great way to be sure you have the right quotient!

Property

Dividing any number(except 0) by itself produces a quotient of 1. Also, any number divided by 1 produces a quotient of the number. These two ideas are stated in the Division Properties of One.

Examples

• Any number divided by itself is 1, so $23 \div 23 = 1$.
• Any number divided by one is itself, so $\frac{35}{1} = 35$.
• Using both properties, we know $14 \div 1 = 14$ and $14 \div 14 = 1$.

Explanation

These are awesome shortcuts! If you divide a number by itself, the answer is always 1. If you divide any number by 1, the number stays the same. These rules make some division problems super fast to solve.

Property

Zero divided by any number is 0.

Dividing a number by zero is undefined.

Property

When the divisor or the dividend has more than one digit, it is usually easier to use the $b)\overline{a}$ notation. This process is called long division.

How to divide whole numbers:

1. Divide the first digit(s) of the dividend by the divisor.
2. Write the quotient above the dividend.
3. Multiply the quotient by the divisor and write the product under the dividend.
4. Subtract that product from the dividend.
5. Bring down the next digit of the dividend.
6. Repeat from Step 1 until there are no more digits to bring down.
7. Check by multiplying the quotient by the divisor.

Examples

• To divide 96 by 4: 4 goes into 9 two times. $2 \cdot 4 = 8$. $9-8=1$. Bring down the 6 to make 16. 4 goes into 16 four times. So, $96 \div 4 = 24$.
• To divide 345 by 5: 5 goes into 34 six times. $6 \cdot 5 = 30$. $34-30=4$. Bring down the 5 to make 45. 5 goes into 45 nine times. So, $345 \div 5 = 69$.
• To divide 852 by 6: 6 goes into 8 one time. $1 \cdot 6 = 6$. $8-6=2$. Bring down the 5 to make 25. 6 goes into 25 four times. $4 \cdot 6 = 24$. $25-24=1$. Bring down the 2 to make 12. 6 goes into 12 two times. So, $852 \div 6 = 142$.