Which expression is equivalent to -9(2)/(3)+8(1)/(6) ? 8(1)/(6)+9(2)/(3) -9(2)/(3)-(-8(1)/(6)) -9(2)/(3)-8(1)/(6) 8(1)/(6)-(-9(2)/(3))

Convert to Improper Fractions: First, let's convert the mixed numbers to improper fractions. -9(2/3) becomes -9 + (-2/3) which is -27/3 - 2/3 = -29/3. 8(1/6) becomes 8 + (1/6) which is 48/6 + 1/6 = 49/6.Addition of Fractions: Now, let's look at the first option: 8(1/6) + 9(2/3). Convert to improper fractions: 49/6 + 29/3. To add these, we need a common denominator.Subtraction of Fractions: The common denominator for 6 and 3 is 6. So, convert 29/3 to 58/6. Now we have 49/6 + 58/6 = 107/6. This is not equivalent to our original expression.Common Denominator: Next, let's look at the second option: -9(2/3) - (-8(1/6)). Convert to improper fractions: -29/3 - (-49/6). We need a common denominator again.Final Comparison: The common denominator is 6. Convert -29/3 to -58/6. Now we have -58/6 - (-49/6) = -58/6 + 49/6 = -9/6. This simplifies to -3/2, which is not equivalent to our original expression.Now, let's look at the third option: -9(2/3) - 8(1/6). We already have the improper fractions: -29/3 and 49/6. We need a common denominator.The common denominator is 6. Convert -29/3 to -58/6. Now we have -58/6 - 49/6 = -107/6. This is equivalent to our original expression.Lastly, let's look at the fourth option: 8(1/6) - (-9(2/3)). Convert to improper fractions: 49/6 - (-29/3). We need a common denominator.The common denominator is 6. Convert -29/3 to -58/6. Now we have 49/6 - (-58/6) = 49/6 + 58/6 = 107/6. This is not equivalent to our original expression.

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Which expression is equivalent to
-9(2)/(3)+8(1)/(6) ?

8(1)/(6)+9(2)/(3)

-9(2)/(3)-(-8(1)/(6))

-9(2)/(3)-8(1)/(6)

8(1)/(6)-(-9(2)/(3))

Which expression is equivalent to $-9 \frac{2}{3}+8 \frac{1}{6}$ ? $\newline$ $8 \frac{1}{6}+9 \frac{2}{3}$ $\newline$ $-9 \frac{2}{3}-\left(-8 \frac{1}{6}\right)$ $\newline$ $-9 \frac{2}{3}-8 \frac{1}{6}$ $\newline$ $8 \frac{1}{6}-\left(-9 \frac{2}{3}\right)$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which expression is equivalent to

-9 \frac{2}{3}+8 \frac{1}{6}

\newline

8 \frac{1}{6}+9 \frac{2}{3}

\newline

-9 \frac{2}{3}-\left(-8 \frac{1}{6}\right)

\newline

-9 \frac{2}{3}-8 \frac{1}{6}

\newline

8 \frac{1}{6}-\left(-9 \frac{2}{3}\right)

Convert to Improper Fractions: First, let's convert the mixed numbers to improper fractions. $\newline$ $-9\left(\frac{2}{3}\right)$ becomes $-9 + \left(-\frac{2}{3}\right)$ which is $-\frac{27}{3} - \frac{2}{3} = -\frac{29}{3}$ . $\newline$ $8\left(\frac{1}{6}\right)$ becomes $8 + \left(\frac{1}{6}\right)$ which is $\frac{48}{6} + \frac{1}{6} = \frac{49}{6}$ .
Addition of Fractions: Now, let's look at the first option: $8\left(\frac{1}{6}\right) + 9\left(\frac{2}{3}\right)$ . Convert to improper fractions: $\frac{49}{6} + \frac{29}{3}$ . To add these, we need a common denominator.
Subtraction of Fractions: The common denominator for $6$ and $3$ is $6$ . So, convert $\frac{29}{3}$ to $\frac{58}{6}$ . Now we have $\frac{49}{6} + \frac{58}{6} = \frac{107}{6}$ . This is not equivalent to our original expression.
Common Denominator: Next, let's look at the second option: $-9\left(\frac{2}{3}\right) - \left(-8\left(\frac{1}{6}\right)\right)$ . Convert to improper fractions: $-\frac{29}{3} - \left(-\frac{49}{6}\right)$ . We need a common denominator again.
Final Comparison: The common denominator is $6$ . Convert $-\frac{29}{3}$ to $-\frac{58}{6}$ . Now we have $-\frac{58}{6} - (-\frac{49}{6}) = -\frac{58}{6} + \frac{49}{6} = -\frac{9}{6}$ . This simplifies to $-\frac{3}{2}$ , which is not equivalent to our original expression.
Final Comparison: The common denominator is $6$ . Convert $-29/3$ to $-58/6$ . Now we have $-58/6 - (-49/6) = -58/6 + 49/6 = -9/6$ . This simplifies to $-3/2$ , which is not equivalent to our original expression.Now, let's look at the third option: $-9(2/3) - 8(1/6)$ . We already have the improper fractions: $-29/3$ and $49/6$ . We need a common denominator.
Final Comparison: The common denominator is $6$ . Convert $-\frac{29}{3}$ to $-\frac{58}{6}$ . Now we have $-\frac{58}{6} - (-\frac{49}{6}) = -\frac{58}{6} + \frac{49}{6} = -\frac{9}{6}$ . This simplifies to $-\frac{3}{2}$ , which is not equivalent to our original expression. Now, let's look at the third option: $-9(\frac{2}{3}) - 8(\frac{1}{6})$ . We already have the improper fractions: $-\frac{29}{3}$ and $\frac{49}{6}$ . We need a common denominator. The common denominator is $6$ . Convert $-\frac{29}{3}$ to $-\frac{58}{6}$ . Now we have $-\frac{29}{3}$ $1$ . This is equivalent to our original expression.
Final Comparison: The common denominator is $6$ . Convert $-\frac{29}{3}$ to $-\frac{58}{6}$ . Now we have $-\frac{58}{6} - (-\frac{49}{6}) = -\frac{58}{6} + \frac{49}{6} = -\frac{9}{6}$ . This simplifies to $-\frac{3}{2}$ , which is not equivalent to our original expression. Now, let's look at the third option: $-9(\frac{2}{3}) - 8(\frac{1}{6})$ . We already have the improper fractions: $-\frac{29}{3}$ and $\frac{49}{6}$ . We need a common denominator. The common denominator is $6$ . Convert $-\frac{29}{3}$ to $-\frac{58}{6}$ . Now we have $-\frac{29}{3}$ $1$ . This is equivalent to our original expression. Lastly, let's look at the fourth option: $-\frac{29}{3}$ $2$ . Convert to improper fractions: $-\frac{29}{3}$ $3$ . We need a common denominator.
Final Comparison: The common denominator is $6$ . Convert $-\frac{29}{3}$ to $-\frac{58}{6}$ . Now we have $-\frac{58}{6} - (-\frac{49}{6}) = -\frac{58}{6} + \frac{49}{6} = -\frac{9}{6}$ . This simplifies to $-\frac{3}{2}$ , which is not equivalent to our original expression. Now, let's look at the third option: $-9(\frac{2}{3}) - 8(\frac{1}{6})$ . We already have the improper fractions: $-\frac{29}{3}$ and $\frac{49}{6}$ . We need a common denominator. The common denominator is $6$ . Convert $-\frac{29}{3}$ to $-\frac{58}{6}$ . Now we have $-\frac{29}{3}$ $1$ . This is equivalent to our original expression. Lastly, let's look at the fourth option: $-\frac{29}{3}$ $2$ . Convert to improper fractions: $-\frac{29}{3}$ $3$ . We need a common denominator. The common denominator is $6$ . Convert $-\frac{29}{3}$ to $-\frac{58}{6}$ . Now we have $-\frac{29}{3}$ $7$ . This is not equivalent to our original expression.