Which sign makes the statement true? 10/12 − 1/3 ? 2/3 Choices: (A)> (B)< (C)=

Simplify Fraction: Simplify 10/12 by reducing it to its lowest terms. 10 and 12 both divide by 2, so 10/12 = 5/6. Subtract Fractions: Next, subtract 1/3 from 5/6. To do this, find a common denominator, which is 6. Convert 1/3 to 2/6. Now, 5/6 - 2/6 = 3/6, which simplifies to 1/2. Compare Fractions: Compare 1/2 and 2/3. Since 1/2 (which is 0.5) is less than 2/3 (which is approximately 0.667), the correct sign is <.

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Math Problems

Grade 7

Inequalities with addition and subtraction of fractions and mixed numbers

Full solution

Q. Which sign makes the statement true?

\newline

\frac{10}{12} - \frac{1}{3}

?

\frac{2}{3}

\newline

Choices:

\newline

(A)

>

\newline

(B)

<

\newline

(C)

=

Simplify Fraction: Simplify $\frac{10}{12}$ by reducing it to its lowest terms. $10$ and $12$ both divide by $2$ , so $\frac{10}{12} = \frac{5}{6}$ .
Subtract Fractions: Next, subtract $\frac{1}{3}$ from $\frac{5}{6}$ . To do this, find a common denominator, which is $6$ . Convert $\frac{1}{3}$ to $\frac{2}{6}$ . Now, $\frac{5}{6} - \frac{2}{6} = \frac{3}{6}$ , which simplifies to $\frac{1}{2}$ .
Compare Fractions: Compare $\frac{1}{2}$ and $\frac{2}{3}$ . Since $\frac{1}{2}$ (which is $0.5$ ) is less than $\frac{2}{3}$ (which is approximately $0.667$ ), the correct sign is <.