Solve: Dividing Three-Fourths by 3 (¾ ÷ 3)

Fraction Division with Whole Number Divisors

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

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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 Make sure to divide numerator by numerator and denominator by denominator
00:14 Let's calculate the quotients
00:18 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

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

2

Step-by-step solution

To solve this problem, follow these steps:

  • Step 1: Identify the problem as dividing the fraction 34 \frac{3}{4} by the whole number 3.
  • Step 2: Understand that dividing by 3 is equivalent to multiplying by its reciprocal, which is 13 \frac{1}{3} .
  • Step 3: Multiply 34 \frac{3}{4} by 13 \frac{1}{3} .
  • Step 4: Simplify the result if possible.

Let's solve this step-by-step:
Step 1: The given expression is 34÷3 \frac{3}{4} \div 3 .
Step 2: Rewrite the division as a multiplication using the reciprocal: 34×13 \frac{3}{4} \times \frac{1}{3} .
Step 3: Perform the multiplication: 34×13=3×14×3=312 \frac{3}{4} \times \frac{1}{3} = \frac{3 \times 1}{4 \times 3} = \frac{3}{12} .
Step 4: Simplify 312 \frac{3}{12} by dividing the numerator and the denominator by their greatest common divisor, which is 3:
312=3÷312÷3=14\frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4}.

Therefore, the solution to the problem is 14 \frac{1}{4} .

3

Final Answer

14 \frac{1}{4}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Dividing by a whole number means multiplying by its reciprocal
  • Technique: Convert 34÷3 \frac{3}{4} \div 3 to 34×13=312 \frac{3}{4} \times \frac{1}{3} = \frac{3}{12}
  • Check: Simplify 312 \frac{3}{12} by dividing by GCD of 3 to get 14 \frac{1}{4}

Common Mistakes

Avoid these frequent errors
  • Multiplying the fraction by the whole number instead of its reciprocal
    Don't multiply 34×3=94 \frac{3}{4} \times 3 = \frac{9}{4} ! This gives a larger result when division should make numbers smaller. Always remember that dividing by 3 means multiplying by 13 \frac{1}{3} .

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 when dividing?

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Division and multiplication are opposite operations. When you divide by a number, it's the same as multiplying by its reciprocal (flip the fraction). So dividing by 3 equals multiplying by 13 \frac{1}{3} .

What's the reciprocal of a whole number like 3?

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The reciprocal of any whole number is 1 over that number. So the reciprocal of 3 is 13 \frac{1}{3} , the reciprocal of 5 is 15 \frac{1}{5} , and so on.

How do I know when to simplify my answer?

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Always check if you can simplify! Look for the greatest common divisor (GCD) of the numerator and denominator. In 312 \frac{3}{12} , both 3 and 12 can be divided by 3.

Can I use this method for any fraction divided by a whole number?

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Yes! This reciprocal method works for any fraction divided by any whole number. Just remember: division by a number = multiplication by its reciprocal.

What if my final answer is an improper fraction?

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That's fine! Some problems naturally give improper fractions as answers. You can leave it as an improper fraction or convert it to a mixed number, depending on what the problem asks for.

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