Solve Fraction Division: 2/5 ÷ 6/7 Step-by-Step

Q: Why do I flip the second fraction instead of the first one?

Because division means "how many times does the divisor go into the dividend". We keep the first fraction as-is and flip only the fraction we're dividing by. Think of it as $ \frac{2}{5} $ ÷ $ \frac{6}{7} $ = $ \frac{2}{5} $ × $ \frac{7}{6} $.

Q: What's the easiest way to remember the reciprocal rule?

Remember "Keep, Change, Flip"! Keep the first fraction the same, change division to multiplication, and flip the second fraction. So ÷ becomes × and $ \frac{6}{7} $ becomes $ \frac{7}{6} $.

Q: Do I always need to simplify my answer?

Yes, always simplify! Look for the greatest common divisor (GCD) of the numerator and denominator. In this case, both 14 and 30 can be divided by 2, giving us the simplified answer $ \frac{7}{15} $.

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

Multiply your answer by the original divisor! If $ \frac{7}{15} × \frac{6}{7} = \frac{42}{105} = \frac{2}{5} $, then your division is correct. This works because multiplication and division are opposite operations.

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

Always flip the fraction that comes after the division sign (÷). In $ \frac{2}{5} ÷ \frac{6}{7} $, flip $ \frac{6}{7} $ to get $ \frac{7}{6} $. The first fraction stays exactly the same!

Fraction Division with Reciprocal Method

Complete the following exercise:

$\frac{2}{5}:\frac{6}{7}=\text{?}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Instead of division, we'll use multiplication by reciprocal

00:09 We'll flip between the numerator and denominator of the fraction

00:14 Make sure to multiply numerator by numerator and denominator by denominator

00:22 Calculate the multiplications

00:27 Reduce the fraction as much as possible

00:32 Make sure to divide both numerator and denominator

00:35 Calculate the quotients

00:39 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

Complete the following exercise:

$\frac{2}{5}:\frac{6}{7}=\text{?}$

Step-by-step solution

To solve the problem $\frac{2}{5} : \frac{6}{7}$ , we can follow these steps:

Step 1: Identify the operation and fractions involved. We are dividing $\frac{2}{5}$ by $\frac{6}{7}$ .
Step 2: Convert the division of fractions into multiplication by the reciprocal. We rewrite $\frac{2}{5} : \frac{6}{7}$ as $\frac{2}{5} \times \frac{7}{6}$ .
Step 3: Perform the multiplication of fractions. Multiply the numerators together and the denominators together:

Numerator: $2 \times 7 = 14$
Denominator: $5 \times 6 = 30$

Step 4: Form the resulting fraction: $\frac{14}{30}$ .
Step 5: Simplify the fraction $\frac{14}{30}$ by finding the greatest common divisor (GCD) of 14 and 30, which is 2:

Divide both 14 and 30 by their GCD:
Simplified numerator: $14 \div 2 = 7$
Simplified denominator: $30 \div 2 = 15$
Resulting simplified fraction: $\frac{7}{15}$

Therefore, the solution to the problem is $\mathbf{\frac{7}{15}}$ .

Final Answer

$\frac{7}{15}$

Key Points to Remember

Essential concepts to master this topic

Rule: Division by a fraction equals multiplication by its reciprocal
Technique: Change $\frac{2}{5} ÷ \frac{6}{7}$ to $\frac{2}{5} × \frac{7}{6}$
Check: Simplify $\frac{14}{30}$ by dividing by GCD of 2 to get $\frac{7}{15}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing numerators and denominators directly
Don't divide 2÷6 and 5÷7 separately = $\frac{1}{3} ÷ \frac{5}{7}$ ! This creates a complex fraction that's harder to solve. Always flip the second fraction first, then multiply straight across.

Practice Quiz

Test your knowledge with interactive questions

$\frac{1}{3}+\frac{1}{4}=$

FAQ

Everything you need to know about this question

Why do I flip the second fraction instead of the first one?

Because division means "how many times does the divisor go into the dividend". We keep the first fraction as-is and flip only the fraction we're dividing by. Think of it as $\frac{2}{5}$ ÷ $\frac{6}{7}$ = $\frac{2}{5}$ × $\frac{7}{6}$ .

What's the easiest way to remember the reciprocal rule?

Remember "Keep, Change, Flip"! Keep the first fraction the same, change division to multiplication, and flip the second fraction. So ÷ becomes × and $\frac{6}{7}$ becomes $\frac{7}{6}$ .

Do I always need to simplify my answer?

Yes, always simplify! Look for the greatest common divisor (GCD) of the numerator and denominator. In this case, both 14 and 30 can be divided by 2, giving us the simplified answer $\frac{7}{15}$ .

How can I check if my division is correct?

Multiply your answer by the original divisor! If $\frac{7}{15} × \frac{6}{7} = \frac{42}{105} = \frac{2}{5}$ , then your division is correct. This works because multiplication and division are opposite operations.

What if I get confused about which fraction to flip?

Always flip the fraction that comes after the division sign (÷). In $\frac{2}{5} ÷ \frac{6}{7}$ , flip $\frac{6}{7}$ to get $\frac{7}{6}$ . The first fraction stays exactly the same!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solve Fraction Division: 2/5 ÷ 6/7 Step-by-Step

Fraction Division with Reciprocal Method

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I flip the second fraction instead of the first one?

What's the easiest way to remember the reciprocal rule?

Do I always need to simplify my answer?

How can I check if my division is correct?

What if I get confused about which fraction to flip?

🌟 Unlock Your Math Potential

More Questions

All Operations in Fractions

Solve the Fraction Division: 2/4 ÷ 4/3 Step-by-Step

Solve Fraction Division: Calculate 3/4 ÷ 5/6 Step-by-Step

Solve Fraction Division: 1/2 ÷ 5/3 Step-by-Step

Solve Fraction Division: 2/3 ÷ 7/5 Step-by-Step

Division of Fractions

Solve Fraction Division: 2/3 ÷ 3/8 Step-by-Step

Solve Fraction Division: 1/3 ÷ 1/4 Step-by-Step

Solve Fraction Division: 2/5 ÷ 1/4 Step-by-Step

Solve Fraction Division: 1/2 ÷ 2/3 Step-by-Step