Which sign makes the statement true? 4/12 + 4/12 ? 6/12 Choices: (A)> (B)< (C)=

Add fractions: Step 1: Add the fractions on the left side of the equation. 4/12 + 4/12 = 8/12 Simplify 8/12 to its lowest terms by dividing the numerator and the denominator by their greatest common divisor, which is 4. 8/12 ÷ 4/4 = 2/3Compare fractions: Step 2: Compare the simplified sum with the fraction on the right side of the equation. 2/3 ? 6/12 First, simplify 6/12 by dividing both the numerator and the denominator by their greatest common divisor, which is 6. 6/12 ÷ 6/6 = 1/2Convert to common denominator: Step 3: Convert 2/3 and 1/2 to a common denominator to compare them. Common denominator for 3 and 2 is 6. 2/3 = 4/6 (Multiply both numerator and denominator by 2) 1/2 = 3/6 (Multiply both numerator and denominator by 3)Compare fractions: Step 4: Compare 4/6 and 3/6. Since 4/6 is greater than 3/6, The correct sign between 4/12 + 4/12 and 6/12 is '>'.

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Which sign makes the statement true? $\newline$ $\frac{4}{12} + \frac{4}{12}$ ? $\frac{6}{12}$ $\newline$ Choices: $\newline$ (A) > $\newline$ (B) < $\newline$ (C) $=$

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Math Problems

Grade 7

Inequalities with addition and subtraction of fractions and mixed numbers

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Q. Which sign makes the statement true?

\newline

\frac{4}{12} + \frac{4}{12}

\frac{6}{12}

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

Add fractions: Step $1$ : Add the fractions on the left side of the equation. $\newline$ $\frac{4}{12} + \frac{4}{12} = \frac{8}{12}$ $\newline$ Simplify $\frac{8}{12}$ to its lowest terms by dividing the numerator and the denominator by their greatest common divisor, which is $4$ . $\newline$ $\frac{8}{12} \div \frac{4}{4} = \frac{2}{3}$
Compare fractions: Step $2$ : Compare the simplified sum with the fraction on the right side of the equation. $\newline$ $\frac{2}{3}$ ? $\frac{6}{12}$ $\newline$ First, simplify $\frac{6}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $6$ . $\newline$ $\frac{6}{12} \div \frac{6}{6} = \frac{1}{2}$
Convert to common denominator: Step $3$ : Convert $\frac{2}{3}$ and $\frac{1}{2}$ to a common denominator to compare them. $\newline$ Common denominator for $3$ and $2$ is $6$ . $\newline$ $\frac{2}{3} = \frac{4}{6}$ (Multiply both numerator and denominator by $2$ ) $\newline$ $\frac{1}{2} = \frac{3}{6}$ (Multiply both numerator and denominator by $3$ )
Compare fractions: Step $4$ : Compare $\frac{4}{6}$ and $\frac{3}{6}$ . Since $\frac{4}{6}$ is greater than $\frac{3}{6}$ , The correct sign between $\frac{4}{12} + \frac{4}{12}$ and $\frac{6}{12}$ is '>'.