Combine like terms to create an equivalent expression. Enter any coefficients as simplified proper or improper fractions or integers. 6((1)/(2)w-(3)/(4))

Distribute 6 to terms: Distribute the 6 to both terms inside the parentheses. We need to multiply 6 by each term inside the parentheses: (1/2)w and -(3/4). Calculation: 6 * (1/2)w - 6 * (3/4)Multiply 6 by (1/2)w: Multiply 6 by (1/2)w. To multiply a whole number by a fraction, we multiply the numerator by the whole number and keep the denominator the same. Calculation: 6 * (1/2)w = (6/1) * (1/2)w = (6*1/2)w = 3wMultiply 6 by -(3/4): Multiply 6 by -(3/4). Again, we multiply the whole number by the numerator of the fraction and keep the denominator the same. Calculation: 6 * -(3/4) = (6/1) * -(3/4) = (6*-3/4) = -18/4Simplify -18/4 fraction: Simplify the fraction -18/4. We can reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. Calculation: -18/4 = (-18/2) / (4/2) = -9/2Combine results from Step 2 and Step 4: Combine the results from Step 2 and Step 4. We now have the expression 3w - 9/2, which is the simplified form of the original expression after distributing and combining like terms.

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Algebra 1

Simplify variable expressions involving like terms and the distributive property

Full solution

Q. Combine like terms to create an equivalent expression.

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Enter any coefficients as simplified proper or improper fractions or integers.

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6\left(\frac{1}{2}w-\frac{3}{4}\right)

Distribute $6$ to terms: Distribute the $6$ to both terms inside the parentheses. $\newline$ We need to multiply $6$ by each term inside the parentheses: $(\frac{1}{2})w$ and $-(\frac{3}{4})$ . $\newline$ Calculation: $6 \times (\frac{1}{2})w - 6 \times (\frac{3}{4})$
Multiply $6$ by $(\frac{1}{2})w$ : Multiply $6$ by $(\frac{1}{2})w$ . $\newline$ To multiply a whole number by a fraction, we multiply the numerator by the whole number and keep the denominator the same. $\newline$ Calculation: $6 \times (\frac{1}{2})w = (\frac{6}{1}) \times (\frac{1}{2})w = (\frac{6 \times 1}{2})w = 3w$
Multiply $6$ by $-(\frac{3}{4})$ : Multiply $6$ by $-(\frac{3}{4})$ . $\newline$ Again, we multiply the whole number by the numerator of the fraction and keep the denominator the same. $\newline$ Calculation: $6 \times -(\frac{3}{4}) = (\frac{6}{1}) \times -(\frac{3}{4}) = (\frac{6\times-3}{4}) = -\frac{18}{4}$
Simplify $-\frac{18}{4}$ fraction: Simplify the fraction $-\frac{18}{4}$ . $\newline$ We can reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ Calculation: $-\frac{18}{4} = \left(-\frac{18}{2}\right) / \left(\frac{4}{2}\right) = -\frac{9}{2}$
Combine results from Step $2$ and Step $4$ : Combine the results from Step $2$ and Step $4$ . $\newline$ We now have the expression $3w - \frac{9}{2}$ , which is the simplified form of the original expression after distributing and combining like terms.