Solve: Product of Mixed Numbers 4¼ × 3⅔ × 3 1/17

Q: Why can't I just multiply the whole numbers and fractions separately?

Mixed numbers are single values, not separate parts! For example, $ 4\frac{1}{4} $ means 4 + 1/4, which equals $ \frac{17}{4} $. Treating parts separately gives completely wrong results.

Q: How do I convert mixed numbers to improper fractions?

Use this formula: whole × denominator + numerator over the original denominator. For $ 4\frac{1}{4} $: (4×4+1)/4 = $ \frac{17}{4} $

Q: Can I simplify before multiplying everything?

Yes! Look for common factors you can cancel. In this problem, the 17 in $ \frac{17}{4} $ cancels with 17 in $ \frac{52}{17} $, making the calculation much easier!

Q: How do I know when to convert back to a mixed number?

If your final answer is an improper fraction (numerator ≥ denominator), convert it to a mixed number. Divide: 403 ÷ 9 = 44 remainder 7, so $ \frac{403}{9} = 44\frac{7}{9} $

Q: What if I make an error in my conversion?

Double-check each conversion! For $ 3\frac{4}{9} $: 3×9+4 = 27+4 = 31, so it's $ \frac{31}{9} $. One wrong conversion ruins the entire problem.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's solve the problem together.

00:16 First, change the whole number into a fraction.

00:20 Multiply the whole number by the denominator, then add the numerator.

00:25 Now, let's add the fractions.

00:29 Let's calculate: four times four.

00:34 Great! Now we have the fraction for the whole number.

00:40 Keep applying the same method with the next fractions.

00:44 Multiply the whole number by the denominator, add the numerator, and combine it with the fraction.

00:53 Again, we have the fraction for this whole number.

00:57 Let's move to the last number.

01:03 Again, multiply, add, and combine just like before.

01:10 And there we go, another fraction for the whole number.

01:16 Now, let's use these fractions for further calculations.

01:31 Let's reduce any fractions if possible.

01:35 Remember, multiply numerator with numerator and denominator with denominator.

01:48 Break down the fraction to find any whole numbers.

02:00 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$4\frac{1}{4}\cdot3\frac{4}{9}\cdot3\frac{1}{17}=\text{?}$

2

Step-by-step solution

Multiply each fraction as follows:

Multiply the whole number by the denominator of the fraction and add the number in the numerator of the fraction.

That is:

$4\frac{1}{4}=\frac{4\times4+1}{4}=\frac{16+1}{4}=\frac{17}{4}$

$3\frac{4}{9}=\frac{9\times3+4}{9}=\frac{27+4}{9}=\frac{31}{9}$

$3\frac{1}{17}=\frac{17\times3+1}{17}=\frac{51+1}{17}=\frac{52}{17}$

Now we get the exercise:

$\frac{17}{4}\times\frac{31}{9}\times\frac{52}{17}=$

We simplify the 17 and get:

$\frac{31\times52}{4\times9}=\frac{52}{4}\times\frac{31}{9}=13\times\frac{31}{9}=\frac{403}{9}=44\frac{7}{9}$

3

Final Answer

$44\frac{7}{9}$

Key Points to Remember

Essential concepts to master this topic

Conversion: Change mixed numbers to improper fractions first
Technique: Cancel common factors like $\frac{17}{4} \times \frac{52}{17} = \frac{52}{4}$
Check: Convert final answer back to mixed number form ✓

Common Mistakes

Avoid these frequent errors

Multiplying whole numbers and fractions separately
Don't multiply 4×3×3=36 and 1/4×4/9×1/17 separately = wrong answer! This ignores how mixed numbers work together. Always convert to improper fractions first, then multiply all numerators together and all denominators together.

Practice Quiz

Test your knowledge with interactive questions

$74+32+6+4+4=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just multiply the whole numbers and fractions separately?

+

Mixed numbers are single values, not separate parts! For example, $4\frac{1}{4}$ means 4 + 1/4, which equals $\frac{17}{4}$ . Treating parts separately gives completely wrong results.

How do I convert mixed numbers to improper fractions?

+

Use this formula: whole × denominator + numerator over the original denominator. For $4\frac{1}{4}$ : (4×4+1)/4 = $\frac{17}{4}$

Can I simplify before multiplying everything?

+

Yes! Look for common factors you can cancel. In this problem, the 17 in $\frac{17}{4}$ cancels with 17 in $\frac{52}{17}$ , making the calculation much easier!

How do I know when to convert back to a mixed number?

+

If your final answer is an improper fraction (numerator ≥ denominator), convert it to a mixed number. Divide: 403 ÷ 9 = 44 remainder 7, so $\frac{403}{9} = 44\frac{7}{9}$

What if I make an error in my conversion?

+

Double-check each conversion! For $3\frac{4}{9}$ : 3×9+4 = 27+4 = 31, so it's $\frac{31}{9}$ . One wrong conversion ruins the entire problem.

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Solve: Product of Mixed Numbers 4¼ × 3⅔ × 3 1/17

Mixed Number Multiplication with Simplification

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