Solve Fraction Division: 6/7 ÷ 2 Step-by-Step

Q: Why do I need to use reciprocals when dividing fractions?

Division by a number is the same as multiplication by its reciprocal. This rule works consistently for all division problems, making it easier to solve complex fraction operations.

Q: What's the reciprocal of a whole number like 2?

The reciprocal of any whole number is 1 over that number. So the reciprocal of 2 is $ \frac{1}{2} $, the reciprocal of 5 is $ \frac{1}{5} $, and so on.

Q: How do I know when to simplify my answer?

Always check if your fraction can be simplified! Find the greatest common divisor (GCD) of the numerator and denominator. If the GCD is greater than 1, divide both parts by it.

Fraction Division with Whole Numbers

$\frac{6}{7}:2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Any number divided by 1 is always equal to itself

00:16 Convert division to multiplication by reciprocal

00:25 Make sure to multiply numerator by numerator and denominator by denominator

00:30 Calculate the multiplications

00:40 Simplify what's 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

$\frac{6}{7}:2=$

Step-by-step solution

To solve the problem $\frac{6}{7} \div 2$ , we need to remember how to divide a fraction by a whole number:

Step 1: Convert the division problem into a multiplication problem by multiplying by the reciprocal of the whole number. The reciprocal of 2 is $\frac{1}{2}$ .

Step 2: Therefore, we rewrite the problem as $\frac{6}{7} \times \frac{1}{2}$ .

Step 3: Multiply the numerators together and the denominators together:

\frac{6 \times 1}{7 \times 2} = \frac{6}{14}

Step 4: Simplify the fraction $\frac{6}{14}$ by finding the greatest common divisor of 6 and 14, which is 2. Divide both the numerator and the denominator by 2:

\frac{6 \div 2}{14 \div 2} = \frac{3}{7}

Therefore, the solution to the problem is $\frac{3}{7}$ .

Final Answer

$\frac{3}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert division to multiplication using reciprocals
Technique: $\frac{6}{7} \div 2 = \frac{6}{7} \times \frac{1}{2} = \frac{6}{14}$
Check: Simplify by finding GCD: $\frac{6}{14} = \frac{3}{7}$ ✓

Common Mistakes

Avoid these frequent errors

Directly dividing the numerator by the whole number
Don't just divide 6 by 2 to get $\frac{3}{7}$ without proper steps! This skips the reciprocal method and can lead to confusion with more complex problems. Always convert division to multiplication by using the reciprocal of the whole number.

Practice Quiz

Test your knowledge with interactive questions

$\frac{1}{2}:3=$ $$ $$ $$

FAQ

Everything you need to know about this question

Why do I need to use reciprocals when dividing fractions?

Division by a number is the same as multiplication by its reciprocal. This rule works consistently for all division problems, making it easier to solve complex fraction operations.

What's the reciprocal of a whole number like 2?

The reciprocal of any whole number is 1 over that number. So the reciprocal of 2 is $\frac{1}{2}$ , the reciprocal of 5 is $\frac{1}{5}$ , and so on.

How do I know when to simplify my answer?

Always check if your fraction can be simplified! Find the greatest common divisor (GCD) of the numerator and denominator. If the GCD is greater than 1, divide both parts by it.

Can I just divide 6 by 2 to get 3 and keep the denominator as 7?

While this gives the correct answer for this problem, it's not the proper method. Always use the reciprocal method to build good habits for more complex fraction division problems.

What if I forget to simplify my fraction?

Your answer would still be mathematically correct, but not in simplest form. For example, $\frac{6}{14}$ equals $\frac{3}{7}$ , but $\frac{3}{7}$ is the preferred final answer.

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