Multiply 3 × 1⅓: Mixed Number Arithmetic Solution

Fraction Multiplication with Mixed Numbers

3×113= 3\times1\frac{1}{3}=

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Step-by-step video solution

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00:00 Solve
00:03 First convert mixed fraction to fraction
00:15 Raise the product to numerator
00:20 Calculate the product
00:27 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

3×113= 3\times1\frac{1}{3}=

2

Step-by-step solution

To solve the problem 3×113 3 \times 1 \frac{1}{3} , follow these steps:

  • Convert the mixed number 113 1 \frac{1}{3} into an improper fraction.
  • Multiply the whole number by this improper fraction.

Let's execute these steps:
Step 1: Convert the mixed number 113 1 \frac{1}{3} to an improper fraction.
First, multiply the whole number part by the denominator: 1×3=31 \times 3 = 3.
Then, add the numerator: 3+1=43 + 1 = 4.
So, 1131 \frac{1}{3} converts to 43\frac{4}{3}.

Step 2: Multiply the whole number 33 by 43\frac{4}{3}.
The multiplication is performed as follows: 3×43=3×43=123=43 \times \frac{4}{3} = \frac{3 \times 4}{3} = \frac{12}{3} = 4.

Therefore, the solution to the problem is 4 4 .

3

Final Answer

4 4

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert mixed numbers to improper fractions first
  • Technique: 113=43 1\frac{1}{3} = \frac{4}{3} , then 3×43=123 3 \times \frac{4}{3} = \frac{12}{3}
  • Check: Simplify final fraction and verify: 123=4 \frac{12}{3} = 4

Common Mistakes

Avoid these frequent errors
  • Multiplying only the whole number part
    Don't multiply 3 × 1 = 3 and ignore the fraction! This gives 3 instead of 4. Always convert the mixed number to an improper fraction first, then multiply the entire fraction.

Practice Quiz

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

FAQ

Everything you need to know about this question

Why can't I just multiply 3 times 1 and 3 times 1/3 separately?

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That approach can work, but it's more complicated! You'd get 3×1=3 3 \times 1 = 3 and 3×13=1 3 \times \frac{1}{3} = 1 , then add: 3 + 1 = 4. Converting to improper fractions is more reliable.

How do I convert a mixed number to an improper fraction?

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Easy formula: Multiply the whole number by the denominator, then add the numerator. For 113 1\frac{1}{3} : (1 × 3) + 1 = 4, so it becomes 43 \frac{4}{3} .

When I multiply, do I need to find a common denominator?

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No! When multiplying fractions, you don't need common denominators. Just multiply straight across: 3×43=3×43=123 3 \times \frac{4}{3} = \frac{3 \times 4}{3} = \frac{12}{3} .

What if my answer comes out as an improper fraction?

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Always simplify your final answer! 123=4 \frac{12}{3} = 4 because 12 ÷ 3 = 4. If it doesn't divide evenly, convert back to a mixed number.

Is there a shortcut when multiplying by a whole number?

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Yes! Notice that 3×43 3 \times \frac{4}{3} has 3 in both numerator and denominator, so they cancel out, leaving just 4. Look for these cancellation opportunities!

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