Solve the Fraction Equation: 5/6 × ? = 1/3

Fraction Multiplication with Unknown Variables

56×?=13 \frac{5}{6}\times?=\frac{1}{3}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the unknown
00:03 Isolate the unknown
00:06 Write division as multiplication by reciprocal, and calculate the products
00:09 Reduce the fraction as much as possible
00:12 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

56×?=13 \frac{5}{6}\times?=\frac{1}{3}

2

Step-by-step solution

To solve the equation 56×?=13 \frac{5}{6} \times ? = \frac{1}{3} , we need to find the missing number represented by "?".

We can solve this problem by using the following steps:

  • Step 1: Identify the equation we are working with:
    We have the equation 56×?=13 \frac{5}{6} \times ? = \frac{1}{3} .
  • Step 2: Isolate the unknown variable, "?":
    To do this, divide both sides of the equation by 56 \frac{5}{6} .
  • Perform the division:
    ?=1356=13×65? = \frac{\frac{1}{3}}{\frac{5}{6}} = \frac{1}{3} \times \frac{6}{5}
  • Step 3: Simplify the expression:
    Now, multiply 13 \frac{1}{3} by the reciprocal of 56 \frac{5}{6} :
    ?=1×63×5=615? = \frac{1 \times 6}{3 \times 5} = \frac{6}{15}
  • Simplify the fraction 615\frac{6}{15}:
    The greatest common divisor of 6 and 15 is 3, so divide both the numerator and the denominator by 3:
    ?=6÷315÷3=25? = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}

Therefore, the solution to the problem is 25 \frac{2}{5} .

3

Final Answer

25 \frac{2}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Divide both sides by the known fraction to isolate unknown
  • Technique: Division by fraction equals multiplication by reciprocal: 13÷56=13×65 \frac{1}{3} \div \frac{5}{6} = \frac{1}{3} \times \frac{6}{5}
  • Check: Substitute back: 56×25=1030=13 \frac{5}{6} \times \frac{2}{5} = \frac{10}{30} = \frac{1}{3}

Common Mistakes

Avoid these frequent errors
  • Multiplying instead of dividing to isolate the unknown
    Don't multiply both sides by 56 \frac{5}{6} = wrong operation! This gives you 56 \frac{5}{6} instead of isolating the unknown. Always divide by the known fraction to get the unknown by itself.

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 divide by the fraction instead of multiplying?

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To isolate the unknown variable, you need to undo the multiplication. Since 56 \frac{5}{6} is multiplied by the unknown, you divide both sides by 56 \frac{5}{6} to cancel it out.

How do I divide by a fraction?

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Dividing by a fraction is the same as multiplying by its reciprocal. So 13÷56 \frac{1}{3} \div \frac{5}{6} becomes 13×65 \frac{1}{3} \times \frac{6}{5} .

What's the reciprocal of a fraction?

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The reciprocal means flip the fraction! For 56 \frac{5}{6} , the reciprocal is 65 \frac{6}{5} . The top and bottom numbers switch places.

Do I always need to simplify my answer?

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Yes! Always reduce fractions to their simplest form. Find the greatest common factor of the numerator and denominator, then divide both by it.

How can I check if my answer is correct?

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Substitute your answer back into the original equation. If 56×25=13 \frac{5}{6} \times \frac{2}{5} = \frac{1}{3} , then 25 \frac{2}{5} is correct!

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