Solve the Division Problem: 1/2 Divided by 4

Fraction Division with Reciprocal Method

12:4= \frac{1}{2}:4=

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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
00:11 We'll convert division to multiplication by reciprocal
00:15 We'll make sure to multiply numerator by numerator and denominator by denominator
00:24 Let's calculate the multiplications
00:28 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

12:4= \frac{1}{2}:4=

2

Step-by-step solution

To solve this problem, we need to compute 12÷4 \frac{1}{2} \div 4 . Here are the steps:

  • Step 1: Recognize that dividing by 4 is equivalent to multiplying by its reciprocal, 14 \frac{1}{4} .
  • Step 2: Rewrite the division as a multiplication: 12×14 \frac{1}{2} \times \frac{1}{4} .
  • Step 3: Perform the multiplication of fractions by multiplying their numerators and denominators. Thus, 1124=18 \frac{1 \cdot 1}{2 \cdot 4} = \frac{1}{8} .

Therefore, the solution to the problem is 18 \frac{1}{8} .

3

Final Answer

18 \frac{1}{8}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Division by whole number equals multiplication by reciprocal
  • Technique: Convert 12÷4 \frac{1}{2} \div 4 to 12×14=18 \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}
  • Check: Verify that 18×4=12 \frac{1}{8} \times 4 = \frac{1}{2} works ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying instead of dividing by the whole number
    Don't multiply 12×4=2 \frac{1}{2} \times 4 = 2 ! Division means you're splitting the fraction into smaller pieces, not making it bigger. Always convert division to multiplication by the reciprocal.

Practice Quiz

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

FAQ

Everything you need to know about this question

Why do I multiply by the reciprocal instead of just dividing?

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Multiplying by the reciprocal is the standard method for dividing fractions! It's easier to multiply 12×14 \frac{1}{2} \times \frac{1}{4} than to figure out complex division rules.

What exactly is a reciprocal?

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A reciprocal is when you flip a number upside down. The reciprocal of 4 is 14 \frac{1}{4} , and the reciprocal of 35 \frac{3}{5} is 53 \frac{5}{3} .

How do I multiply fractions?

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Multiply straight across: multiply the tops together and the bottoms together. So 12×14=1×12×4=18 \frac{1}{2} \times \frac{1}{4} = \frac{1 \times 1}{2 \times 4} = \frac{1}{8} .

Why is the answer smaller than what I started with?

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When you divide by a number greater than 1, you always get a smaller result! Think of it as splitting 12 \frac{1}{2} into 4 equal pieces.

Can I use this method for any division problem with fractions?

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Yes! The reciprocal method works for all fraction division: a÷b=a×1b a \div b = a \times \frac{1}{b} . Just remember to flip the second number and multiply.

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