Solve Decimal Division: 0.15 ÷ 0.05 Step-by-Step Solution

Q: Why do I need to convert decimals to fractions?

Converting to fractions makes division much clearer! You can see exactly what you're dividing and use the multiply by reciprocal rule instead of confusing decimal division.

Q: How do I know which decimal places to use?

Count the decimal places in each number. 0.15 has 2 places (so it's 15/100), and 0.05 has 2 places (so it's 5/100). Always use the same denominator!

Q: What does 'multiply by the reciprocal' mean?

Instead of dividing by a fraction, you multiply by its flip. So $ \frac{15}{100} ÷ \frac{5}{100} $ becomes $ \frac{15}{100} × \frac{100}{5} $.

Q: Why does the 100 cancel out?

When you multiply $ \frac{15}{100} × \frac{100}{5} $, the 100 in the numerator and denominator cancel each other, leaving you with $ \frac{15}{5} = 3 $!

Q: Can I just move the decimal points instead?

Yes! You can move both decimal points the same number of places to make whole numbers. But the fraction method helps you understand why it works.

Q: How do I check if 3 is correct?

Multiply your answer by the divisor: 3 × 0.05 = 0.15. Since this equals the original dividend, your answer is correct!

Decimal Division with Fraction Conversion Method

$(+0.15):(+0.05)=$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Positive divided by positive is always positive

00:08 Convert from decimal numbers to fractions

00:31 Write division as multiplication by reciprocal

00:36 Switch between numerator and denominator

00:39 Reduce what is possible

00:44 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(+0.15):(+0.05)=$ ?

Step-by-step solution

Since we are dividing two positive numbers, the result must be a positive number:

$+:+=+$

First, we will convert each mixed fraction into an improper fraction as follows:

$0.15=\frac{15}{100}$

$0.05=\frac{5}{100}$

This leaves us with:

$\frac{15}{100}:\frac{5}{100}=$

Next, we will convert the division into a multiplication, remembering to switch the numerator and denominator:

$\frac{15}{100}\times\frac{100}{5}=$

Finally, we will simplify the 100 to get:

$\frac{15}{5}=3$

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive divided by positive always equals positive
Technique: Convert 0.15 to 15/100 and 0.05 to 5/100 first
Check: Multiply answer by divisor: 3 × 0.05 = 0.15 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to apply division rules for fractions
Don't just divide decimals directly without converting = confusing calculations! This leads to computational errors and wrong answers. Always convert decimals to fractions first, then multiply by the reciprocal.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why do I need to convert decimals to fractions?

Converting to fractions makes division much clearer! You can see exactly what you're dividing and use the multiply by reciprocal rule instead of confusing decimal division.

How do I know which decimal places to use?

Count the decimal places in each number. 0.15 has 2 places (so it's 15/100), and 0.05 has 2 places (so it's 5/100). Always use the same denominator!

What does 'multiply by the reciprocal' mean?

Instead of dividing by a fraction, you multiply by its flip. So $\frac{15}{100} ÷ \frac{5}{100}$ becomes $\frac{15}{100} × \frac{100}{5}$ .

Why does the 100 cancel out?

When you multiply $\frac{15}{100} × \frac{100}{5}$ , the 100 in the numerator and denominator cancel each other, leaving you with $\frac{15}{5} = 3$ !

Can I just move the decimal points instead?

Yes! You can move both decimal points the same number of places to make whole numbers. But the fraction method helps you understand why it works.

How do I check if 3 is correct?

Multiply your answer by the divisor: 3 × 0.05 = 0.15. Since this equals the original dividend, your answer is correct!

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