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

Fraction Division with Reciprocal Method

Complete the following exercise:

23:75=? \frac{2}{3}:\frac{7}{5}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem together.
00:08 Here's a helpful tip: instead of dividing, we can multiply by the reciprocal. This makes things easier!
00:15 To find the reciprocal, we simply flip the fraction upside down - switch the numerator and denominator.
00:22 Now, remember this important rule: when multiplying fractions, multiply the top numbers together, and do the same for the bottom numbers.
00:30 Let's work out these multiplications step by step.
00:34 And there we have it! That's our final answer. Great job following along!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the following exercise:

23:75=? \frac{2}{3}:\frac{7}{5}=\text{?}

2

Step-by-step solution

To solve this problem, we'll use the reciprocal method for dividing fractions.

Step 1: Identify the reciprocal of the divisor.
The reciprocal of 75 \frac{7}{5} is 57 \frac{5}{7} .

Step 2: Multiply the dividend by the reciprocal of the divisor.
Multiply 23 \frac{2}{3} by 57 \frac{5}{7} :

23×57=2×53×7=1021 \frac{2}{3} \times \frac{5}{7} = \frac{2 \times 5}{3 \times 7} = \frac{10}{21}

There is no common factor between 10 and 21 other than 1, meaning 1021 \frac{10}{21} is already in its simplest form.

Therefore, the solution to the problem is 1021 \frac{10}{21} .

3

Final Answer

1021 \frac{10}{21}

Key Points to Remember

Essential concepts to master this topic
  • Rule: To divide fractions, multiply by the reciprocal of the divisor
  • Technique: 23÷75=23×57=1021 \frac{2}{3} ÷ \frac{7}{5} = \frac{2}{3} × \frac{5}{7} = \frac{10}{21}
  • Check: Verify 1021×75=70105=23 \frac{10}{21} × \frac{7}{5} = \frac{70}{105} = \frac{2}{3}

Common Mistakes

Avoid these frequent errors
  • Adding or subtracting denominators instead of using reciprocal method
    Don't try to find common denominators like in addition = completely wrong approach! Division requires a different method entirely. Always flip the second fraction and multiply instead of dividing.

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 and multiply?

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Dividing by a fraction is the same as multiplying by its reciprocal. Think of it this way: dividing by 75 \frac{7}{5} means 'how many 75 \frac{7}{5} pieces fit into 23 \frac{2}{3} ?' This is equivalent to 23×57 \frac{2}{3} × \frac{5}{7} .

What's the reciprocal of a fraction?

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The reciprocal is when you flip the numerator and denominator. For example, the reciprocal of 75 \frac{7}{5} is 57 \frac{5}{7} . For whole numbers like 3, write it as 31 \frac{3}{1} first, then flip to get 13 \frac{1}{3} .

How do I know if my answer is in simplest form?

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Check if the numerator and denominator share any common factors. Since 10 and 21 don't share any factors except 1, 1021 \frac{10}{21} is already simplified!

Can I convert to decimals instead?

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You could, but it's usually better to keep fractions as fractions for exact answers. Converting 23÷75 \frac{2}{3} ÷ \frac{7}{5} to decimals would give you approximations, not the precise answer.

What if I get confused about which fraction to flip?

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Remember: always flip the second fraction (the divisor). In 23÷75 \frac{2}{3} ÷ \frac{7}{5} , you flip 75 \frac{7}{5} to get 57 \frac{5}{7} , then multiply: 23×57 \frac{2}{3} × \frac{5}{7} .

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