Solve: 3⅚ × 5⅚ × ⅓x Mixed Number Multiplication

Mixed Number Multiplication with Algebraic Terms

Solve the following problem:

356×556×13x= 3\frac{5}{6}\times5\frac{5}{6}\times\frac{1}{3}x=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We want to convert from a mixed number to a fraction only
00:06 We'll do this by multiplying the whole number by the denominator
00:10 We'll use the same method for this fraction
00:19 Always solve multiplication and division before addition and subtraction
00:33 Make sure to multiply numerator by numerator and denominator by denominator
00:46 We'll use long multiplication to calculate
00:59 This is the numerator multiplication
01:06 Now we'll use long multiplication to calculate the denominator multiplication
01:20 This is the denominator multiplication
01:23 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

Solve the following problem:

356×556×13x= 3\frac{5}{6}\times5\frac{5}{6}\times\frac{1}{3}x=

2

Step-by-step solution

First, let's convert all mixed fractions to simple fractions:

3×6+56×5×6+56×13x= \frac{3\times6+5}{6}\times\frac{5\times6+5}{6}\times\frac{1}{3}x=

Let's solve the exercises with the eight fractions:

18+56×30+56×13x= \frac{18+5}{6}\times\frac{30+5}{6}\times\frac{1}{3}x=

236×356×13x= \frac{23}{6}\times\frac{35}{6}\times\frac{1}{3}x=

Since the exercise only involves multiplication, we'll combine all the numerators and denominators:

23×356×6×3x=805108x \frac{23\times35}{6\times6\times3}x=\frac{805}{108}x

3

Final Answer

805108x \frac{805}{108}x

Key Points to Remember

Essential concepts to master this topic
  • Conversion Rule: Change mixed numbers to improper fractions first
  • Technique: 356=236 3\frac{5}{6} = \frac{23}{6} by calculating 3×6+5
  • Check: Multiply numerators together and denominators together, then simplify ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of multiplying when converting mixed numbers
    Don't write 356=3+56=86 3\frac{5}{6} = \frac{3+5}{6} = \frac{8}{6} ! This gives completely wrong values that throw off your entire calculation. Always multiply the whole number by the denominator, then add the numerator: 356=3×6+56=236 3\frac{5}{6} = \frac{3×6+5}{6} = \frac{23}{6} .

Practice Quiz

Test your knowledge with interactive questions

\( 94+12+6= \)

FAQ

Everything you need to know about this question

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

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Multiplying whole numbers separately from fractions doesn't work because mixed numbers are single values, not separate parts. You must convert 356 3\frac{5}{6} to 236 \frac{23}{6} first to get the correct result.

How do I remember the conversion formula?

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Think of it as "multiply, then add": Take the whole number × denominator + numerator. For 356 3\frac{5}{6} , that's 3×6+5 = 23, so you get 236 \frac{23}{6} .

Do I need to simplify my final answer?

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Always check if your answer can be simplified! In this problem, 805108 \frac{805}{108} doesn't simplify further, but you should always look for common factors between numerator and denominator.

What if I get confused with all the fractions?

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Work step-by-step and write everything down. Convert one mixed number at a time, then multiply straight across: numerator × numerator on top, denominator × denominator on bottom.

Can I use decimals instead of fractions?

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While possible, fractions give exact answers while decimals might be rounded. Since this problem asks for a fractional result, stick with fractions throughout your calculation.

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