Method 1: Converting to Fractions

One way to tackle decimal division is by turning the decimal into a fraction. Let’s look at our first example:

Example 1: $6.4 \div 2 = ?$

1. Rewrite the division as multiplication by a fraction: Instead of dividing by 2, we can multiply by $\frac{1}{2}$.
   $$\frac{6.4}{2} = 6.4 \times \frac{1}{2}$$
2. Convert the decimal to a fraction: $6.4$ is the same as sixty-four tenths, or $\frac{64}{10}$.
   $$\frac{64}{10} \times \frac{1}{2}$$
3. Multiply the fractions: Multiply the numerators ($64 \times 1 = 64$) and the denominators ($10 \times 2 = 20$). Or, simplify first: half of $64$ is $32$.
   $$\frac{32}{10}$$
4. Convert back to a decimal: Thirty-two tenths is written as 3.2.
   $$\frac{32}{10} = 3.2$$

Method 2: Long Division (The Traditional Way)

If you prefer the classic long division method, it works perfectly for decimals too! The key is to keep your decimal point lined up.

Example 1 (Revisited): $6.4 \div 2 = ?$

• Set it up like a normal long division problem: $2 \overline{) 6.4}$

• Divide 6 by 2. It goes in 3 times. Write the 3 above the 6.

• Bring the decimal point straight up into your answer.

• Divide 4 by 2. It goes in 2 times. Write the 2 above the 4.

• The final answer is 3.2.

Method 3: Direct Simplification (The Fast Way)

Once you get comfortable, you can often simplify directly, treating the decimal like a whole number and then placing the decimal point at the end.

Example 2: $12.96 \div 4 = ?$

1. Think of it as $1296 \div 4$.

2. $12 \div 4 = 3$

3. $9 \div 4 = 2$ (with a remainder of 1)

4. The remainder 1 makes the next number 16. $16 \div 4 = 4$.

5. Now, place your decimal point back in the same position it was in the original number (two places from the right).

6. The result is 3.24.

Summary Table