Solve the Division Problem: 10/9 ÷ 5 Step-by-Step

Q: Why do I multiply by the reciprocal instead of just dividing?

Multiplying by the reciprocal is the definition of division with fractions! When you divide by 5, you're really multiplying by $ \frac{1}{5} $. This method makes the calculation much clearer and prevents errors.

Q: How do I find the reciprocal of a whole number like 5?

A whole number like 5 can be written as $ \frac{5}{1} $. To find its reciprocal, just flip the fraction: $ \frac{1}{5} $. The reciprocal of any number n is $ \frac{1}{n} $.

Q: Do I always need to simplify my final answer?

Yes, always simplify! Find the GCD of numerator and denominator. In this problem, $ \frac{10}{45} $ simplifies to $ \frac{2}{9} $ because both 10 and 45 are divisible by 5.

Q: What if I get confused about which number to flip?

Remember: you flip the number you're dividing by (the second number). In $ \frac{10}{9} ÷ 5 $, you flip the 5 to get $ \frac{1}{5} $, not the $ \frac{10}{9} $!

Q: How can I check if my answer is correct?

Multiply your answer by the original divisor: $ \frac{2}{9} × 5 = \frac{10}{9} $ ✓. If you get back to the original dividend, your division is correct!

Fraction Division with Reciprocal Multiplication

Solve the following exercise:

$\frac{10}{9}:5=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Let's write the number as a fraction

00:09 Any number divided by 1 is always equal to itself

00:13 Make sure to divide numerator by numerator and denominator by denominator

00:18 Let's calculate the quotients

00:22 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

Solve the following exercise:

$\frac{10}{9}:5=\text{?}$

Step-by-step solution

To solve the problem $\frac{10}{9} : 5$ , we will convert the division into a multiplication with a reciprocal.

Step 1: Recognize that dividing by $5$ is the same as multiplying by $\frac{1}{5}$ .
Step 2: Rewrite the problem as: $\frac{10}{9} \times \frac{1}{5}$ .
Step 3: Multiply the fractions: $\frac{10 \times 1}{9 \times 5} = \frac{10}{45}$ .
Step 4: Simplify the fraction $\frac{10}{45}$ by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 5.
Step 5: $\frac{10 \div 5}{45 \div 5} = \frac{2}{9}$ .

Therefore, the solution to the problem is $\frac{2}{9}$ .

Final Answer

$\frac{2}{9}$

Key Points to Remember

Essential concepts to master this topic

Rule: Division by a number equals multiplication by its reciprocal
Technique: Convert $\frac{10}{9} ÷ 5$ to $\frac{10}{9} × \frac{1}{5} = \frac{10}{45}$
Check: Simplify final answer by finding GCD: $\frac{10}{45} = \frac{2}{9}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing fractions incorrectly by cross-multiplying
Don't try to cross-multiply $\frac{10}{9} ÷ 5$ = $\frac{50}{9}$ ! This gives completely wrong results because you're treating division like it's a proportion. Always convert division to multiplication by the reciprocal first.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

$\frac{1}{2}:\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

Why do I multiply by the reciprocal instead of just dividing?

Multiplying by the reciprocal is the definition of division with fractions! When you divide by 5, you're really multiplying by $\frac{1}{5}$ . This method makes the calculation much clearer and prevents errors.

How do I find the reciprocal of a whole number like 5?

A whole number like 5 can be written as $\frac{5}{1}$ . To find its reciprocal, just flip the fraction: $\frac{1}{5}$ . The reciprocal of any number n is $\frac{1}{n}$ .

Do I always need to simplify my final answer?

Yes, always simplify! Find the GCD of numerator and denominator. In this problem, $\frac{10}{45}$ simplifies to $\frac{2}{9}$ because both 10 and 45 are divisible by 5.

What if I get confused about which number to flip?

Remember: you flip the number you're dividing by (the second number). In $\frac{10}{9} ÷ 5$ , you flip the 5 to get $\frac{1}{5}$ , not the $\frac{10}{9}$ !

How can I check if my answer is correct?

Multiply your answer by the original divisor: $\frac{2}{9} × 5 = \frac{10}{9}$ ✓. If you get back to the original dividend, your division is correct!

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