Question

guided practice1. how do $\frac{5}{6}$ and $\frac{4}{6}$ compare? write >, <, or =.$\frac{5}{6} \bigcirc \frac{4}{6}$ look to see if the numerators or denominators are the same.since the denominators are the same, compare the numerators.solution: since 5 is greater than 4, $\frac{5}{6}$ is greater than $\frac{4}{6}$.$\frac{5}{6} > \frac{4}{6}$2. how do $\frac{3}{4}$ and $\frac{4}{8}$ compare? write >, <, or =.$\frac{3}{4} \bigcirc \frac{4}{8}$ begin by creating an equivalent fraction so that the numerator or denominator are the same.solution: to create a common numerator, multiply $\frac{3}{4} \times \frac{2}{2}$.then, compare $\frac{6}{8}$ and $\frac{4}{8}$.$\frac{6}{8}$ is greater than $\frac{4}{8}$, $\frac{6}{8} > \frac{4}{8}$independent practice3. which comparison is true?a. $\frac{1}{3} > \frac{3}{6}$b. $\frac{2}{3} < \frac{4}{6}$c. $\frac{1}{3} = \frac{5}{6}$d. $\frac{2}{3} < \frac{5}{6}$4. which statement shows how to correctly compare $\frac{1}{2}$ and $\frac{4}{6}$?a. $\frac{1}{2} < \frac{4}{5}$b. $\frac{3}{6} < \frac{4}{6}$c. $\frac{4}{8} > \frac{4}{6}$d. $\frac{1}{2} = \frac{4}{5}$5. members of a book club are reading the same book. the week before the club meets to discuss the book, tomas has read $\frac{1}{2}$ of the book. katie has read $\frac{1}{3}$ of the book. ethan has read $\frac{2}{5}$ of the book, and ashanti has read $\frac{4}{9}$ of the book. who has read the most?a. tomasb. katiec. ethand. ashanti

Explanation:

Step1: Simplify fractions for Q3

Option A: $\frac{1}{3} = \frac{2}{6}$, $\frac{2}{6} < \frac{3}{6}$ → False

Option B: $\frac{2}{3} = \frac{4}{6}$, $\frac{4}{6} = \frac{4}{6}$ → False

Option C: $\frac{1}{3} = \frac{2}{6}$, $\frac{2}{6}

eq \frac{5}{6}$ → False

Option D: $\frac{2}{3} = \frac{4}{6}$, $\frac{4}{6} < \frac{5}{6}$ → True

Step2: Match fractions for Q4

Convert $\frac{1}{2}$ to common denominator: $\frac{1}{2} = \frac{3}{6}$
Compare $\frac{3}{6}$ and $\frac{4}{6}$ → $\frac{3}{6} < \frac{4}{6}$ → Option B is correct.

Step3: Find common denominator for Q5

Common denominator of 2,3,5,9 is 90:

• Tomas: $\frac{1}{2} = \frac{45}{90}$
• Katie: $\frac{1}{3} = \frac{30}{90}$
• Ethan: $\frac{2}{5} = \frac{36}{90}$
• Ashanti: $\frac{4}{9} = \frac{40}{90}$

Compare numerators: $45 > 40 > 36 > 30$

Answer:

1. D. $\frac{2}{3}<\frac{5}{6}$
2. B. $\frac{3}{6}<\frac{4}{6}$
3. A. Tomas