Estimate. Which sign makes the statement true? 1/3 × 6 4/5 ? 5 Choices: (A)> (B)< (C)=

Convert to Improper Fraction: Convert the mixed number 6 4/5 to an improper fraction: 6 4/5 = (6 × 5 + 4)/5 = (30 + 4)/5 = 34/5 Perform Multiplication: Perform the multiplication 1/3 × 34/5: (1/3) × (34/5) = 34/15 Compare with 5: Compare 34/15 with 5: Convert 5 to a fraction with a denominator of 15 for easy comparison: 5 = 5/1 = (5 × 15)/(1 × 15) = 75/15 Final Comparison: Now, compare 34/15 and 75/15: Since 34/15 is less than 75/15, the correct inequality sign is <.

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Estimate. Which sign makes the statement true? $\newline$ $\frac{1}{3} \times 6\frac{4}{5}$ ? $5$ $\newline$ Choices: $\newline$ (A) > $\newline$ (B) < $\newline$ (C) $=$

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Math Problems

Grade 6

Estimate products of fractions and whole numbers

Full solution

Q. Estimate. Which sign makes the statement true?

\newline

\frac{1}{3} \times 6\frac{4}{5}

5

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

Convert to Improper Fraction: Convert the mixed number $6 \frac{4}{5}$ to an improper fraction: $\newline$ $6 \frac{4}{5} = (6 \times 5 + 4)/5 = (30 + 4)/5 = \frac{34}{5}$
Perform Multiplication: Perform the multiplication $\frac{1}{3} \times \frac{34}{5}$ : $\newline$ $(\frac{1}{3}) \times (\frac{34}{5}) = \frac{34}{15}$
Compare with $5$ : Compare $\frac{34}{15}$ with $5$ : Convert $5$ to a fraction with a denominator of $15$ for easy comparison: $5 = \frac{5}{1} = \frac{(5 \times 15)}{(1 \times 15)} = \frac{75}{15}$
Final Comparison: Now, compare $\frac{34}{15}$ and $\frac{75}{15}$ : $\newline$ Since $\frac{34}{15}$ is less than $\frac{75}{15}$ , the correct inequality sign is <.