Math Problem Statement

Multiply. Write your answer as a fraction or as a whole or mixed number.

2 × 2 1 4

Solution

To multiply the fractions 2×942 \times \frac{9}{4}, let's first express the whole number 22 as a fraction. We can write 22 as 21\frac{2}{1}.

Now, we multiply:

21×94=2×91×4=184\frac{2}{1} \times \frac{9}{4} = \frac{2 \times 9}{1 \times 4} = \frac{18}{4}

Next, simplify the fraction 184\frac{18}{4}. Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:

184=18÷24÷2=92\frac{18}{4} = \frac{18 \div 2}{4 \div 2} = \frac{9}{2}

Now, 92\frac{9}{2} is an improper fraction, but we can also express it as a mixed number:

92=412\frac{9}{2} = 4 \frac{1}{2}

So, the answer is 4124 \frac{1}{2} or 92\frac{9}{2}.

Would you like more details or have any further questions?

Here are 5 related questions to explore:

  1. How do you convert an improper fraction to a mixed number?
  2. What is the process to simplify a fraction?
  3. Can you multiply a fraction by a whole number using the same method?
  4. How do you handle mixed numbers in multiplication?
  5. What is the greatest common divisor (GCD) of 18 and 4?

Tip: When simplifying fractions, always divide both the numerator and the denominator by their GCD to get the simplest form.

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Math Problem Analysis

Mathematical Concepts

Fraction Multiplication
Mixed Numbers
Simplification of Fractions

Formulas

a × b = (a/b) × (c/d) = (a × c) / (b × d)

Theorems

Simplification by GCD
Conversion of Improper Fractions to Mixed Numbers

Suitable Grade Level

Grades 4-6