Solve: 3/4 × 2/3 × 2¼x - Fraction Multiplication with Mixed Numbers

Fraction Multiplication with Variable Terms

34×23×214x= \frac{3}{4}\times\frac{2}{3}\times2\frac{1}{4}x=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Make sure to multiply numerator by numerator and denominator by denominator
00:16 Let's solve the numerator and denominator products
00:23 Let's simplify the fraction
00:27 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

34×23×214x= \frac{3}{4}\times\frac{2}{3}\times2\frac{1}{4}x=

2

Step-by-step solution

Let's begin by combining the simple fractions into a single multiplication exercise:

3×24×3×214x= \frac{3\times2}{4\times3}\times2\frac{1}{4}x=

Let's now proceed to solve the exercise in the numerator and denominator:

612×214x= \frac{6}{12}\times2\frac{1}{4}x=

Finally we'll simplify the simple fraction in order to obtain the following:

12×214x=118x \frac{1}{2}\times2\frac{1}{4}x=1\frac{1}{8}x

3

Final Answer

118x 1\frac{1}{8}x

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert mixed numbers to improper fractions before multiplying
  • Technique: Multiply numerators together: 3×2×9 = 54, denominators: 4×3×4 = 48
  • Check: Simplify final fraction 9/8 equals 1⅛, then verify by converting back ✓

Common Mistakes

Avoid these frequent errors
  • Not converting mixed numbers to improper fractions first
    Don't multiply 2¼ directly as a mixed number = confusion and wrong setup! Mixed numbers can't be multiplied in that form. Always convert 2¼ to 9/4 first, then multiply all fractions together.

Practice Quiz

Test your knowledge with interactive questions

\( 94+12+6= \)

FAQ

Everything you need to know about this question

Why do I need to convert 2¼ to an improper fraction?

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You can't multiply mixed numbers directly! Convert 214 2\frac{1}{4} to 94 \frac{9}{4} first: multiply whole number by denominator (2×4=8), add numerator (8+1=9), keep same denominator.

Can I multiply the fractions in any order?

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Yes! Multiplication is commutative, so you can multiply in any order. Many students find it easier to multiply the simple fractions first: 34×23=12 \frac{3}{4} \times \frac{2}{3} = \frac{1}{2} .

Should I simplify fractions during multiplication or at the end?

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You can do either! Simplifying during multiplication (like canceling 3s) makes numbers smaller and easier to work with. But simplifying at the end works too.

How do I convert my improper fraction answer back to a mixed number?

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Divide numerator by denominator: 98=9÷8=1 \frac{9}{8} = 9 ÷ 8 = 1 remainder 1 1 , so the answer is 118 1\frac{1}{8} .

What if I forget to include the variable x in my answer?

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Don't forget the variable! Since you started with x in the problem, your final answer must include x too. The coefficient goes in front: 118x 1\frac{1}{8}x .

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