Question

bree and mai want to simplify \\(\frac{16}{24}\\) to find an equivalent fraction. their solutions are shown below. brees work \\(\frac{16 - 8}{24 - 8} = \frac{8}{16}\\) mais work \\(\frac{16 \div 8}{24 \div 8} = \frac{2}{3}\\) who is correct and why? bree is correct because she used a common factor to subtract the numerator and denominator. mai is correct because she used a common factor to divide the numerator and denominator. bree and mai are both incorrect.

Explanation:

To simplify a fraction, we use the property that dividing the numerator and denominator by their greatest common factor (or a common factor) gives an equivalent fraction. Subtracting a number from numerator and denominator does not preserve the fraction's value.

• Bree subtracted 8 from numerator and denominator: $\frac{16 - 8}{24 - 8}=\frac{8}{16}$, but this is incorrect because subtraction doesn't maintain equivalence (e.g., $\frac{16}{24}=\frac{2}{3}\approx0.666$, $\frac{8}{16}=\frac{1}{2} = 0.5$, not equal).
• Mai divided numerator and denominator by their common factor 8: $\frac{16\div8}{24\div8}=\frac{2}{3}$, which is correct because dividing by a common factor preserves the fraction's value ( $\frac{16}{24}=\frac{2}{3}$).

The first option is wrong (Bree used subtraction, not valid for simplifying). The second option correctly explains Mai's method. The third option is wrong as Mai is correct.

Answer:

Mai is correct because she used a common factor to divide the numerator and denominator.