Solve: Dividing Three-Fourths (3/4) by 4

Fraction Division with Whole Numbers

34:4= \frac{3}{4}:4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's solve this problem.
00:07 Remember, any number divided by one is always itself.
00:13 We can change division into multiplication by using the reciprocal.
00:27 Multiply the numerators together, and then multiply the denominators.
00:33 Now, let's calculate these multiplications.
00:37 And there you have it! That's the solution to the question.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

34:4= \frac{3}{4}:4=

2

Step-by-step solution

To solve this problem, follow these steps:

  • Step 1: Recognize that dividing by a number is equivalent to multiplying by its reciprocal.
  • Step 2: Apply this transformation to the problem, emphasizing the operation change.
  • Step 3: Perform the multiplication operation correctly.
  • Step 4: Simplify the resulting fraction to simplest terms.

Let's work through it:

Step 1: Start with the expression: 34÷4\frac{3}{4} \div 4.

Step 2: Convert the division by 4 into multiplication by its reciprocal, 14\frac{1}{4}. The expression becomes: 34×14\frac{3}{4} \times \frac{1}{4}.

Step 3: To multiply fractions, multiply the numerators together and the denominators together:
Numerator: 3×1=33 \times 1 = 3
Denominator: 4×4=164 \times 4 = 16

Therefore, the resulting fraction from the multiplication is 316\frac{3}{16}.

There is no need for additional simplification as 316\frac{3}{16} is already in simplest form.

Therefore, the solution to the problem is 316 \frac{3}{16} .

3

Final Answer

316 \frac{3}{16}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Dividing by a number equals multiplying by its reciprocal
  • Technique: Convert 34÷4 \frac{3}{4} \div 4 to 34×14 \frac{3}{4} \times \frac{1}{4}
  • Check: Multiply numerators (3×1=3) and denominators (4×4=16) to get 316 \frac{3}{16}

Common Mistakes

Avoid these frequent errors
  • Dividing numerator and denominator separately by the whole number
    Don't divide 3÷4 and 4÷4 separately to get 3/41 \frac{3/4}{1} = wrong answer! This ignores proper division rules for fractions. Always convert division to multiplication by the reciprocal first.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{1}{2}:3= \)\( \)\( \)\( \)

FAQ

Everything you need to know about this question

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

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Dividing by a whole number like 4 means "how many 4's fit into 34 \frac{3}{4} ?" Since 34 \frac{3}{4} is less than 1, only a fraction of 4 fits! Multiplying by 14 \frac{1}{4} gives us that exact fractional part.

How do I know what the reciprocal of 4 is?

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Any whole number can be written as a fraction: 4 = 41 \frac{4}{1} . The reciprocal flips the fraction, so the reciprocal of 41 \frac{4}{1} is 14 \frac{1}{4} !

Can I simplify 316 \frac{3}{16} further?

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No! Since 3 and 16 share no common factors other than 1, 316 \frac{3}{16} is already in simplest form. Always check if your final answer can be reduced.

What if I need to divide a fraction by another fraction?

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The same rule applies! Multiply by the reciprocal of the second fraction. For example: 12÷13=12×31=32 \frac{1}{2} \div \frac{1}{3} = \frac{1}{2} \times \frac{3}{1} = \frac{3}{2}

Why is my answer smaller than the original fraction?

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When you divide by a number greater than 1, the result is always smaller! Think of it as splitting 34 \frac{3}{4} into 4 equal parts - each part must be smaller than the whole.

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