Which sign makes the statement true? 3 4/12 ? 2 1/2 Choices: (A)> (B)< (C)=

Simplify Fractions: Simplify the fractions in each mixed number. 3 4/12 = 3 + 4/12 2 1/2 = 2 + 1/2Convert to Simplest Form: Convert 4/12 to its simplest form by dividing the numerator and the denominator by their greatest common divisor, which is 4. 4/12 = 1/3 So, 3 4/12 = 3 + 1/3 = 3 1/3Convert to Improper Fraction: Convert 2 1/2 to an improper fraction by multiplying the whole number by the denominator of the fraction and adding the numerator. 2 1/2 = 2*2 + 1 = 5/2Compare Mixed Numbers: Compare 3 1/3 and 5/2 by converting them to a common denominator. 3 1/3 = 10/3 (since 3 1/3 = 3*3 + 1 = 10/3) 5/2 = 5/2Find Common Denominator: Find a common denominator for 10/3 and 5/2, which is 6. 10/3 = 20/6 5/2 = 15/6Compare Fractions: Compare 20/6 and 15/6. Since 20/6 > 15/6, 3 1/3 > 2 1/2.

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Math Problems

Grade 6

Compare rational numbers

Full solution

Q. Which sign makes the statement true?

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3\frac{4}{12}\,?\,2\frac{1}{2}

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Choices:

\newline

(A)

>

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(B)

<

\newline

(C)

=

Simplify Fractions: Simplify the fractions in each mixed number. $\newline$ $3 \frac{4}{12} = 3 + \frac{4}{12}$ $\newline$ $2 \frac{1}{2} = 2 + \frac{1}{2}$
Convert to Simplest Form: Convert $\frac{4}{12}$ to its simplest form by dividing the numerator and the denominator by their greatest common divisor, which is $4$ . $\newline$ $\frac{4}{12} = \frac{1}{3}$ $\newline$ So, $3 \frac{4}{12} = 3 + \frac{1}{3} = 3\frac{1}{3}$
Convert to Improper Fraction: Convert $2\frac{1}{2}$ to an improper fraction by multiplying the whole number by the denominator of the fraction and adding the numerator. $\newline$ $2\frac{1}{2} = 2\times2 + 1 = \frac{5}{2}$
Compare Mixed Numbers: Compare $3 \frac{1}{3}$ and $\frac{5}{2}$ by converting them to a common denominator. $\newline$ $3 \frac{1}{3} = \frac{10}{3}$ (since $3 \frac{1}{3} = 3\times3 + 1 = \frac{10}{3}$ ) $\newline$ $\frac{5}{2} = \frac{5}{2}$
Find Common Denominator: Find a common denominator for $\frac{10}{3}$ and $\frac{5}{2}$ , which is $6$ . $\newline$ $\frac{10}{3} = \frac{20}{6}$ $\newline$ $\frac{5}{2} = \frac{15}{6}$
Compare Fractions: Compare $\frac{20}{6}$ and $\frac{15}{6}$ . $\newline$ Since \frac{20}{6} > \frac{15}{6}, 3 \frac{1}{3} > 2 \frac{1}{2}.