Solve: 3 × 8/12 Fraction Multiplication Problem

Fraction Multiplication with Whole Numbers

3×812= 3\times\frac{8}{12}=

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Step-by-step video solution

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00:00 Solve
00:03 Let's raise the product to the numerator
00:07 Let's calculate the product
00:13 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

3×812= 3\times\frac{8}{12}=

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Step-by-step solution

To solve this problem, we'll pursue a step-by-step method:

  • Step 1: Simplify the fraction 812\frac{8}{12}. The greatest common divisor of 8 and 12 is 4, so dividing both the numerator and denominator by 4 gives 23\frac{2}{3}.
  • Step 2: Multiply the integer 3 by the simplified fraction 23\frac{2}{3}.

Let's proceed with these steps:
Step 1: Simplify 812\frac{8}{12}:
812=8÷412÷4=23\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}.

Step 2: Multiply the integer by the fraction:
3×23=3×23=63=23 \times \frac{2}{3} = \frac{3 \times 2}{3} = \frac{6}{3} = 2.

Thus, the result of the multiplication is 2\boxed{2}.

3

Final Answer

2 2

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply whole number by numerator, keep denominator unchanged
  • Technique: Simplify first: 812=23 \frac{8}{12} = \frac{2}{3} then multiply 3×23 3 \times \frac{2}{3}
  • Check: Substitute back: 3×812=2412=2 3 \times \frac{8}{12} = \frac{24}{12} = 2

Common Mistakes

Avoid these frequent errors
  • Multiplying the denominator by the whole number
    Don't multiply 3 × 8 and 3 × 12 = 24/36! This creates a completely different fraction. Always multiply only the numerator by the whole number and keep the denominator the same.

Practice Quiz

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\( 5:\frac{2}{5}= \)

FAQ

Everything you need to know about this question

Should I simplify the fraction before or after multiplying?

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You can do either! Simplifying first like 812=23 \frac{8}{12} = \frac{2}{3} makes the numbers smaller and easier to work with. But you'll get the same answer if you multiply first then simplify.

Why don't I multiply the denominator by 3?

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When multiplying a whole number by a fraction, think of it as repeated addition. 3×812 3 \times \frac{8}{12} means "add 812 \frac{8}{12} three times" - the denominator stays the same!

How do I know if I need to simplify my answer?

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Always check if your final answer can be simplified! Look for common factors in the numerator and denominator. If the answer is an improper fraction, you might also convert it to a mixed number.

What if my answer comes out as a whole number?

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That's great! It means the fraction divided evenly. Like in this problem: 63=2 \frac{6}{3} = 2 . Just write it as a whole number - no fraction needed.

Can I convert the whole number to a fraction first?

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Yes! You can write 3 as 31 \frac{3}{1} , then multiply: 31×812=2412=2 \frac{3}{1} \times \frac{8}{12} = \frac{24}{12} = 2 . This method works well for more complex problems!

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