Estimate. Which sign makes the statement true? 361/6 ÷ 105/9 ? 8 Choices: (A)> (B)<

Calculate Division of Fractions: Calculate the division of the fractions 361/6 and 105/9. - Convert the division of fractions to multiplication by the reciprocal: (361/6) ÷ (105/9) = (361/6) * (9/105). - Simplify the multiplication: (361 * 9) / (6 * 105) = 3249 / 630.Simplify Result: Simplify the result of 3249/630. - Divide both numerator and denominator by their greatest common divisor, which is 9: 3249 ÷ 9 = 361, 630 ÷ 9 = 70. - So, 3249/630 simplifies to 361/70.Convert to Decimal: Convert 361/70 to a decimal to compare it with 8. - Perform the division: 361 ÷ 70 ≈ 5.157.Compare Decimal Result: Compare the decimal result to 8. - Since 5.157 is less than 8, the correct inequality sign is <.

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Estimate. Which sign makes the statement true? $\newline$ $\frac{361}{6} \div \frac{105}{9} \, ? \, 8$ $\newline$ Choices: $\newline$ (A) > $\newline$ (B) <

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Math Problems

Grade 6

Estimate quotients when dividing mixed numbers

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Q. Estimate. Which sign makes the statement true?

\newline

\frac{361}{6} \div \frac{105}{9} \, ? \, 8

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

Calculate Division of Fractions: Calculate the division of the fractions $\frac{361}{6}$ and $\frac{105}{9}$ . $\newline$ - Convert the division of fractions to multiplication by the reciprocal: $\left(\frac{361}{6}\right) \div \left(\frac{105}{9}\right) = \left(\frac{361}{6}\right) \times \left(\frac{9}{105}\right)$ . $\newline$ - Simplify the multiplication: $\left(\frac{361 \times 9}{6 \times 105}\right) = \frac{3249}{630}$ .
Simplify Result: Simplify the result of $3249/630$ .
- Divide both numerator and denominator by their greatest common divisor, which is $9$ : $3249 \div 9 = 361$ , $630 \div 9 = 70$ .
- So, $3249/630$ simplifies to $361/70$ .
Convert to Decimal: Convert $361/70$ to a decimal to compare it with $8$ . $\newline$ - Perform the division: $361 \div 70 \approx 5.157$ .
Compare Decimal Result: Compare the decimal result to $8$ . $\newline$ - Since $5.157$ is less than $8$ , the correct inequality sign is <.