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Estimate. Which sign makes the statement true? $\newline$ $5 \, ? \, \frac{1}{3} \times 6\frac{2}{3}$ $\newline$ Choices: $\newline$ (A) > $\newline$ (B) < $\newline$ (C) $=$

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Estimate products of fractions and whole numbers

Full solution

Q. Estimate. Which sign makes the statement true?

\newline

5 \, ? \, \frac{1}{3} \times 6\frac{2}{3}

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

Convert to Improper Fraction: Convert $6 \frac{2}{3}$ to an improper fraction: $\newline$ $6 \frac{2}{3} = (6 \times 3 + 2)/3 = \frac{20}{3}$
Calculate Product: Calculate the product of $\frac{1}{3}$ and $\frac{20}{3}$ : $\left(\frac{1}{3}\right) \times \left(\frac{20}{3}\right) = \frac{20}{9}$
Compare Fractions: Compare $5$ with $\frac{20}{9}$ :
$5 = \frac{45}{9}$ (since $5 = \frac{5}{1}$ and multiplying numerator and denominator by $9$ )
$\frac{45}{9} ? \frac{20}{9}$
Since $\frac{45}{9}$ is greater than $\frac{20}{9}$ , the correct sign is >

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