QuestionCalculate $-\frac{2}{7} \div \frac{1}{3} \cdot \frac{2}{3}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $-\frac{}{7} \div \frac{1}{3} \cdot \frac{}{3}$ . . We will follow the order of operations, which in mathematics is often remembered by the acronym PEMAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

STEP 2

First, we will perform the division operation. In order to divide by a fraction, we multiply by its reciprocal. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
$-\frac{2}{7} \div \frac{1}{} = -\frac{2}{7} \cdot \frac{}{1}$

STEP 3

Now, multiply the fractions $-\frac{2}{7}$ and $\frac{3}{1}$ .
$-\frac{2}{7} \cdot \frac{3}{1} = -\frac{2 \cdot3}{7 \cdot1}$

STEP 4

Calculate the multiplication in the numerator and the denominator.
$-\frac{2 \cdot3}{7 \cdot1} = -\frac{6}{7}$

STEP 5

Now, multiply the result $-\frac{}{7}$ with the fraction $\frac{2}{3}$ .
$-\frac{}{7} \cdot \frac{2}{3} = -\frac{ \cdot2}{7 \cdot3}$

STEP 6

Calculate the multiplication in the numerator and the denominator.
$-\frac{6 \cdot2}{ \cdot3} = -\frac{12}{21}$

STEP 7

The fraction $-\frac{12}{21}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is3.
$-\frac{12}{21} = -\frac{12 \div3}{21 \div3}$

STEP 8

Calculate the division in the numerator and the denominator.
$-\frac{12 \div3}{21 \div3} = -\frac{4}{7}$ So, $-\frac{2}{7} \div \frac{1}{3} \cdot \frac{2}{3} = -\frac{4}{7}$ .

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