Evaluate the expression. $\newline$ $\frac{1}{2} - \frac{1}{4} \div \frac{2}{3}$ $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ ______

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Grade 7

Evaluate numerical expressions involving fractions

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Q. Evaluate the expression.

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\frac{1}{2} - \frac{1}{4} \div \frac{2}{3}

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Write your answer as a fraction or as a whole or mixed number.

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______

Follow Order of Operations: First, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often abbreviated as PEMDAS. In this expression, we have division and subtraction. According to PEMDAS, we should perform the division before the subtraction.
Perform Division of Fractions: Now, let's perform the division $\frac{1}{4} \div \frac{2}{3}$ . To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$ . $\newline$ So, $\frac{1}{4} \div \frac{2}{3} = \frac{1}{4} \times \frac{3}{2}.$
Multiply Fractions: Next, we multiply the numerators and the denominators of the fractions: $(1 \times 3) / (4 \times 2) = \frac{3}{8}$ .
Find Common Denominator: Now we have the original expression simplified to $\frac{1}{2} - \frac{3}{8}$ . To subtract these fractions, they must have a common denominator. The least common denominator (LCD) for $2$ and $8$ is $8$ .
Convert $\frac{1}{2}$ to $\frac{4}{8}$ : We convert $\frac{1}{2}$ to a fraction with a denominator of $8$ . To do this, we multiply both the numerator and the denominator by $4$ , which gives us $\frac{4}{8}$ .
Subtract Fractions: Now we can subtract the two fractions: $\frac{4}{8} - \frac{3}{8} = \left(\frac{4 - 3}{8}\right) = \frac{1}{8}.$
Final Simplified Form: The final simplified form of the expression $\frac{1}{2} - \frac{1}{4} \div \frac{2}{3}$ is $\frac{1}{8}$ .