Which numbers are between $6\frac{1}{3}$ and $7\frac{4}{9}$ ? $\newline$ Multi-select Choices: $\newline$ (A) $7\frac{2}{4}$ $\newline$ (B) $7\frac{4}{7}$ $\newline$ (C) $7\frac{1}{6}$ $\newline$ (D) $7\frac{6}{8}$

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Math Problems

Grade 6

Divisibility rules

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Q. Which numbers are between

6\frac{1}{3}

and

7\frac{4}{9}

\newline

Multi-select Choices:

\newline

(A)

7\frac{2}{4}

\newline

(B)

7\frac{4}{7}

\newline

(C)

7\frac{1}{6}

\newline

(D)

7\frac{6}{8}

Convert to Improper Fraction: Convert $6 \frac{1}{3}$ to an improper fraction. $6 \frac{1}{3} = (6 \times 3 + 1)/3 = \frac{19}{3}$ .
Comparison with $7\frac{2}{4}$ : Convert $7\frac{4}{9}$ to an improper fraction. $7\frac{4}{9} = (7 \times 9 + 4)/9 = \frac{67}{9}.$
Comparison with $7\frac{4}{7}$ : Convert $7\frac{2}{4}$ to an improper fraction for comparison. $7\frac{2}{4} = (7 \times 4 + 2)/4 = \frac{30}{4}$ , which simplifies to $\frac{15}{2}$ .
Comparison with $7\frac{1}{6}$ : Convert $7\frac{4}{7}$ to an improper fraction for comparison. $7\frac{4}{7} = (7 \times 7 + 4)/7 = \frac{53}{7}$ .
Comparison with $7\frac{6}{8}$ : Convert $7\frac{1}{6}$ to an improper fraction for comparison. $7\frac{1}{6} = (7 \times 6 + 1)/6 = \frac{43}{6}$ .
Check $\frac{15}{2}$ : Convert $7\frac{6}{8}$ to an improper fraction for comparison. $7\frac{6}{8} = (7 \times 8 + 6)/8 = \frac{62}{8}$ , which simplifies to $\frac{31}{4}$ .
Check $\frac{53}{7}$ : Check if $\frac{15}{2}$ is between $\frac{19}{3}$ and $\frac{67}{9}$ . $\frac{15}{2} = 7.5$ , $\frac{19}{3} \approx 6.33$ , $\frac{67}{9} \approx 7.44$ . $7.5$ is not between $6.33$ and $7.44$ .
Check $\frac{43}{6}$ : Check if $\frac{53}{7}$ is between $\frac{19}{3}$ and $\frac{67}{9}$ . $\frac{53}{7} \approx 7.57$ , $\frac{19}{3} \approx 6.33$ , $\frac{67}{9} \approx 7.44$ . $7.57$ is not between $6.33$ and $7.44$ .
Check $\frac{31}{4}$ : Check if $\frac{43}{6}$ is between $\frac{19}{3}$ and $\frac{67}{9}$ . $\frac{43}{6} \approx 7.17$ , $\frac{19}{3} \approx 6.33$ , $\frac{67}{9} \approx 7.44$ . $7.17$ is between $6.33$ and $7.44$ .
Check $\frac{31}{4}$ : Check if $\frac{43}{6}$ is between $\frac{19}{3}$ and $\frac{67}{9}$ . $\frac{43}{6} \approx 7.17$ , $\frac{19}{3} \approx 6.33$ , $\frac{67}{9} \approx 7.44$ . $7.17$ is between $6.33$ and $7.44$ . Check if $\frac{31}{4}$ is between $\frac{19}{3}$ and $\frac{67}{9}$ . $\frac{43}{6}$ $3$ , $\frac{19}{3} \approx 6.33$ , $\frac{67}{9} \approx 7.44$ . $\frac{43}{6}$ $6$ is not between $6.33$ and $7.44$ .