Question

len and shawn simplify \\(\frac{18}{30}\\) to find an equivalent fraction. their solutions are shown below.
len’s work
\\(\frac{18 \div 6}{30 \div 6} = \frac{3}{5}\\)
shawn’s work
\\(\frac{18 \div 6}{30 \div 5} = \frac{3}{6}\\)
whose work is correct and why?
len is correct because he divided the numerator and denominator by the same number.
shawn is correct because he divided the numerator and denominator by different numbers.
len and shawn are both incorrect.

Explanation:

Step1: Recall fraction simplification rule

To simplify a fraction, we divide the numerator and the denominator by the same non - zero number (this is based on the property of equivalent fractions: $\frac{a}{b}=\frac{a\div c}{b\div c}$, where $b
eq0$ and $c
eq0$).

Step2: Analyze Len's work

Len divides the numerator $18$ and the denominator $30$ by $6$. So, $\frac{18\div6}{30\div6}=\frac{3}{5}$. Here, he divided the numerator and denominator by the same number ($6$), which follows the rule of equivalent fractions.

Step3: Analyze Shawn's work

Shawn divides the numerator $18$ by $6$ and the denominator $30$ by $5$. Since he divided the numerator and denominator by different numbers, his work does not follow the rule for finding equivalent fractions.

Step4: Evaluate the options

• The first option says "Len is correct because he divided the numerator and denominator by the same number." This matches our analysis of Len's work.
• The second option says "Shawn is correct because he divided the numerator and denominator by different numbers." But dividing by different numbers does not give an equivalent fraction, so this is wrong.
• The third option says "Len and Shawn are both incorrect." But Len's work is correct, so this is wrong.

Answer:

Len is correct because he divided the numerator and denominator by the same number.