Solve the Fraction Division: 4/11 ÷ 4 Step-by-Step

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

Division and multiplication by the reciprocal are equivalent operations! Multiplying by $ \frac{1}{4} $ is exactly the same as dividing by 4, but it's easier to work with fractions this way.

Q: How do I find the reciprocal of a whole number like 4?

Write the whole number as a fraction first: $ 4 = \frac{4}{1} $. Then flip it to get $ \frac{1}{4} $. The reciprocal of any number n is always $ \frac{1}{n} $.

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

Yes, always simplify! Look for common factors in the numerator and denominator. In this problem, both 4 and 44 are divisible by 4, so $ \frac{4}{44} = \frac{1}{11} $.

Q: What if the original fraction has a larger denominator than numerator?

The same process works! For example, $ \frac{3}{8} \div 2 = \frac{3}{8} \times \frac{1}{2} = \frac{3}{16} $. Just multiply by the reciprocal and simplify if possible.

Q: Can I check my answer by working backwards?

Absolutely! Multiply your answer by the divisor: $ \frac{1}{11} \times 4 = \frac{4}{11} $. If you get the original dividend, your answer is correct!

Fraction Division with Reciprocal Method

Solve the following exercise:

$\frac{4}{11}:4=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve the problem, step by step.

00:10 First, write the number as a fraction.

00:15 Remember, dividing by 1 keeps the number the same.

00:19 Make sure to divide numerators together, and denominators together.

00:25 Now, let's calculate these quotients.

00:29 Great job! That's the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{4}{11}:4=\text{?}$

Step-by-step solution

To solve the equation $\frac{4}{11} \div 4$ , let's follow these steps:

Step 1: Identify the reciprocal of the divisor $4$ . The reciprocal of $4$ is $\frac{1}{4}$ .
Step 2: Multiply the original fraction by the reciprocal. Thus, $\frac{4}{11} \times \frac{1}{4}$ .
Step 3: Perform the multiplication. Multiplying two fractions involves multiplying their numerators and their denominators:

$\frac{4}{11} \times \frac{1}{4} = \frac{4 \times 1}{11 \times 4} = \frac{4}{44}$ .

Step 4: Simplify the resulting fraction. Notice that $\frac{4}{44}$ can be simplified because 4 and 44 share a common factor of 4:

$\frac{4}{44} = \frac{1}{11}$ .

Therefore, the solution to the division problem $\frac{4}{11} \div 4$ is $\frac{1}{11}$ .

Final Answer

$\frac{1}{11}$

Key Points to Remember

Essential concepts to master this topic

Rule: Dividing by a number equals multiplying by its reciprocal
Technique: $\frac{4}{11} \div 4 = \frac{4}{11} \times \frac{1}{4} = \frac{4}{44}$
Check: Simplify $\frac{4}{44} = \frac{1}{11}$ by dividing both by 4 ✓

Common Mistakes

Avoid these frequent errors

Dividing the numerator and denominator separately
Don't divide 4÷4=1 and 11÷4=2.75 separately = wrong answer! This treats the fraction incorrectly as two separate numbers. 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?

Division and multiplication by the reciprocal are equivalent operations! Multiplying by $\frac{1}{4}$ is exactly the same as dividing by 4, but it's easier to work with fractions this way.

How do I find the reciprocal of a whole number like 4?

Write the whole number as a fraction first: $4 = \frac{4}{1}$ . Then flip it to get $\frac{1}{4}$ . The reciprocal of any number n is always $\frac{1}{n}$ .

Do I always need to simplify the final answer?

Yes, always simplify! Look for common factors in the numerator and denominator. In this problem, both 4 and 44 are divisible by 4, so $\frac{4}{44} = \frac{1}{11}$ .

What if the original fraction has a larger denominator than numerator?

The same process works! For example, $\frac{3}{8} \div 2 = \frac{3}{8} \times \frac{1}{2} = \frac{3}{16}$ . Just multiply by the reciprocal and simplify if possible.

Can I check my answer by working backwards?

Absolutely! Multiply your answer by the divisor: $\frac{1}{11} \times 4 = \frac{4}{11}$ . If you get the original dividend, your answer is correct!

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