Questions: Nia found a fraction that is equivalent to 3/8. Is Nia's fraction work, shown below, correct? Explain. 3 × 4 / 8 × 3 = 12 / 24

$Nia found a fraction that is equivalent to 3/8. Is Nia's fraction work, shown below, correct? Explain. 3 × 4 / 8 × 3 = 12 / 24$

Transcript text: Nia found a fraction that is equivalent to $\frac{3}{8}$. Is Nia's fraction work, shown below, correct? Explain. \[ \frac{3 \times 4}{8 \times 3}=\frac{12}{24} \]

Solution

Solution Steps

Step 1: Define the Original Fraction

The original fraction given is $ \frac{3}{8} $.

Step 2: Define Nia's Fraction

Nia's fraction is calculated as $ \frac{12}{24} $.

Step 3: Simplify Nia's Fraction

To check for equivalence, we simplify $ \frac{12}{24} $: \[ \frac{12}{24} = \frac{12 \div 12}{24 \div 12} = \frac{1}{2} \]

Step 4: Compare the Two Fractions

Now we compare the simplified form of Nia's fraction $ \frac{1}{2} $ with the original fraction $ \frac{3}{8} $. Since $ \frac{1}{2} \neq \frac{3}{8} $, the two fractions are not equivalent.

Step 5: Conclusion

Nia's work is incorrect as $ \frac{12}{24} $ does not equal $ \frac{3}{8} $.