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Which number is between $1\frac{5}{7}$ and $6\frac{2}{7}$ ? $\newline$ Choices: $\newline$ (A) $1\frac{6}{7}$ $\newline$ (B) $1\frac{4}{12}$ $\newline$ (C) $1\frac{3}{7}$ $\newline$ (D) $1\frac{1}{7}$

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Interpret measures of center and variability

Full solution

Q. Which number is between

1\frac{5}{7}

and

6\frac{2}{7}

?

\newline

Choices:

\newline

(A)

1\frac{6}{7}

\newline

(B)

1\frac{4}{12}

\newline

(C)

1\frac{3}{7}

\newline

(D)

1\frac{1}{7}

Convert to Improper Fractions: Convert mixed numbers to improper fractions. $\newline$ $1 \frac{5}{7} = \frac{(7\cdot1 + 5)}{7} = \frac{12}{7}$ $\newline$ $6 \frac{2}{7} = \frac{(7\cdot6 + 2)}{7} = \frac{44}{7}$
Convert Choices: Convert choices to improper fractions for comparison. $\newline$ (A) $1 \frac{6}{7} = (7\cdot1 + 6)/7 = \frac{13}{7}$ $\newline$ (B) $1 \frac{4}{12}$ needs simplification: $\frac{4}{12} = \frac{1}{3}$ , so $1 \frac{4}{12} = (3\cdot1 + 1)/3 = \frac{4}{3}$ $\newline$ (C) $1 \frac{3}{7} = (7\cdot1 + 3)/7 = \frac{10}{7}$ $\newline$ (D) $1 \frac{1}{7} = (7\cdot1 + 1)/7 = \frac{8}{7}$
Check Fractions: Check which fractions are between $\frac{12}{7}$ and $\frac{44}{7}$ .
\frac{12}{7} < \frac{13}{7} < \frac{44}{7} (True)
\frac{12}{7} < \frac{4}{3} (False, $\frac{4}{3}$ is approximately $1.33$ , which is less than $\frac{12}{7}$ or about $1.71$ )
\frac{12}{7} < \frac{10}{7} (False, $\frac{10}{7}$ is about $\frac{44}{7}$ $0$ , which is less than $\frac{12}{7}$ )
$\frac{44}{7}$ $2$ (False, $\frac{44}{7}$ $3$ is about $\frac{44}{7}$ $4$ , which is less than $\frac{12}{7}$ )

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