Solve: (3/2) × 1 × (1/3) - Step-by-Step Fraction Multiplication

Fraction Multiplication with Mixed Terms

Solve the following exercise:

32×1×13= ? \frac{3}{2}\times1\times\frac{1}{3}=\text{ ?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this problem together.
00:10 Remember, any number multiplied by 1 stays the same. It's like magic!
00:16 Now, let's multiply the fractions step by step.
00:20 Great! Let's simplify these fractions as much as we can.
00:28 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

32×1×13= ? \frac{3}{2}\times1\times\frac{1}{3}=\text{ ?}

2

Step-by-step solution

According to the order of operations, we must solve the exercise from left to right since it contains only multiplication operations:

32×1=32 \frac{3}{2}\times1=\frac{3}{2}

32×13= \frac{3}{2}\times\frac{1}{3}=

Then, we will multiply the 3 by 3 to get:

12×1=12 \frac{1}{2}\times1=\frac{1}{2}

3

Final Answer

12 1\over2

Key Points to Remember

Essential concepts to master this topic
  • Order: Multiply fractions from left to right sequentially
  • Technique: 32×1=32 \frac{3}{2} \times 1 = \frac{3}{2} , then multiply by 13 \frac{1}{3}
  • Check: Cross-cancel 3 and 3 to get 12 \frac{1}{2}

Common Mistakes

Avoid these frequent errors
  • Adding fractions instead of multiplying
    Don't add 32+13=136 \frac{3}{2} + \frac{1}{3} = \frac{13}{6} ! This gives the wrong answer because the operation symbol is multiplication (×). Always multiply numerators together and denominators together when you see the × symbol.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why does multiplying by 1 not change the fraction?

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Multiplying any number by 1 gives you the same number! So 32×1=32 \frac{3}{2} \times 1 = \frac{3}{2} . Think of 1 as 11 \frac{1}{1} - when you multiply fractions, you get 3×12×1=32 \frac{3 \times 1}{2 \times 1} = \frac{3}{2} .

Can I cancel numbers before multiplying?

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Yes! You can cross-cancel matching numbers. Here, the 3 in 32 \frac{3}{2} cancels with the 3 in 13 \frac{1}{3} , leaving 12 \frac{1}{2} . This makes multiplication faster!

Do I need a common denominator like with addition?

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No! Unlike adding fractions, multiplication doesn't need common denominators. Just multiply straight across: numerator × numerator and denominator × denominator.

What if I get the answer 3/6 instead of 1/2?

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You're on the right track! 36 \frac{3}{6} equals 12 \frac{1}{2} when simplified. Always reduce fractions to their simplest form by dividing both top and bottom by their greatest common factor.

Why do we work from left to right?

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When you have only multiplication (no addition or subtraction), the order doesn't actually matter mathematically. But working left to right follows the standard order of operations and keeps your work organized!

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