Question
2. Use the diagram to show \( 3 \cdot \frac{3}{4} \). Then write the product in simplest form.
Ask by Powers Vaughn. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The product of \(3\) and \(\frac{3}{4}\) is \(\frac{9}{4}\) or \(2\frac{1}{4}\).
Solution
1. Write \( 3 \cdot \frac{3}{4} \) as a multiplication of a whole number by a fraction.
2. Multiply the whole number by the numerator:
\[
3 \cdot \frac{3}{4} = \frac{3 \cdot 3}{4} = \frac{9}{4}
\]
3. The fraction \(\frac{9}{4}\) is already in simplest form, and it can also be expressed as the mixed number:
\[
\frac{9}{4} = 2\frac{1}{4}
\]
Thus, the product is \(\frac{9}{4}\) or \(2\frac{1}{4}\).
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Simplify this solution Bonus Knowledge
To visualize \( 3 \cdot \frac{3}{4} \) using a diagram, you could represent it with three groups of fourths. Imagine three circles, each divided into four equal parts – that gives you 12 parts in total. Out of these, taking \( \frac{3}{4} \) from each circle means you would shade in 3 parts from each, resulting in 9 shaded parts. Now, let's simplify this: you have 9 out of 12 parts shaded, so you write that as \( \frac{9}{12} \). Dividing the numerator and denominator by their greatest common divisor (which is 3), you end up with \( \frac{3}{4} \) as the simplest form of the product. So, \( 3 \cdot \frac{3}{4} = \frac{9}{12} = \frac{3}{4} \).
