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

Fraction Division with Mixed Number Results

Complete the following exercise:

25:14=? \frac{2}{5}:\frac{1}{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 this problem together.
00:09 Instead of dividing, we'll multiply by the reciprocal. This means flipp ing the fraction.
00:15 So, swap the numerator and the denominator. Great job so far!
00:21 Now, multiply the numerators, then multiply the denominators. K eep going!
00:28 Let's do the multiplication calculations now. You're doing gre at!
00:35 Break down the number eight into five plus three. Excellent!
00:40 Turn the fraction into a whole number and a remainder. Almost there!
00:47 Remember, any number divided by itself equals one. That's a key t ip!
00:52 Convert your answer to a mixed fraction. Well done!
00:57 And that's how we solve this question. Excellent work!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the following exercise:

25:14=? \frac{2}{5}:\frac{1}{4}=\text{?}

2

Step-by-step solution

To solve the problem of dividing 25\frac{2}{5} by 14\frac{1}{4}, we need to follow these steps:

  • Step 1: Identify the reciprocal of 14\frac{1}{4}.
    This reciprocate is 41\frac{4}{1}.
  • Step 2: Convert the division of fractions to multiplication with the reciprocal:
    25÷14=25×41\frac{2}{5} \div \frac{1}{4} = \frac{2}{5} \times \frac{4}{1}.
  • Step 3: Perform the multiplication:
    2×45×1=85\frac{2 \times 4}{5 \times 1} = \frac{8}{5}.
  • Step 4: Simplify 85\frac{8}{5} into a mixed number:
    85\frac{8}{5} can be written as 1351\frac{3}{5} because 5 goes into 8 once with 3 remaining.

Therefore, the solution to the problem is 135 1\frac{3}{5} .

3

Final Answer

135 1\frac{3}{5}

Key Points to Remember

Essential concepts to master this topic
  • Division Rule: To divide fractions, multiply by the reciprocal
  • Technique: 25÷14=25×41=85 \frac{2}{5} \div \frac{1}{4} = \frac{2}{5} \times \frac{4}{1} = \frac{8}{5}
  • Check: Convert 135 1\frac{3}{5} back to improper: 85 \frac{8}{5}

Common Mistakes

Avoid these frequent errors
  • Multiplying denominators and numerators straight across
    Don't multiply 25×14=220 \frac{2}{5} \times \frac{1}{4} = \frac{2}{20} directly! This treats division like multiplication and gives 110 \frac{1}{10} instead of 135 1\frac{3}{5} . Always flip the second fraction first, then multiply.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( \frac{1}{4}:\frac{1}{2}=\text{?} \)

FAQ

Everything you need to know about this question

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

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Division means "how many groups" of the second number fit into the first. When you flip the divisor (second fraction), you're asking "how many 14 \frac{1}{4} s fit into 25 \frac{2}{5} ?"

How do I convert 85 \frac{8}{5} to a mixed number?

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Divide 8 by 5: 8 ÷ 5 = 1 remainder 3. The whole number is 1, and the remainder 3 becomes the new numerator over the same denominator 5, giving 135 1\frac{3}{5} .

What does the reciprocal of 14 \frac{1}{4} mean?

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The reciprocal is what you get when you flip the fraction upside down. For 14 \frac{1}{4} , the reciprocal is 41 \frac{4}{1} or just 4.

Can I leave my answer as an improper fraction?

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Yes! 85 \frac{8}{5} and 135 1\frac{3}{5} are both correct. However, mixed numbers are often easier to understand because they show the whole number part clearly.

How can I check if 135 1\frac{3}{5} is correct?

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Multiply your answer by the original divisor: 135×14 1\frac{3}{5} \times \frac{1}{4} . Convert to improper fractions: 85×14=820=25 \frac{8}{5} \times \frac{1}{4} = \frac{8}{20} = \frac{2}{5}

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