What is the sum of #3 1/6 + (-5.5)#, expressed as a mixed number in simplest form?

Question

Benjamin Altschul · Accepted Answer

#= color(green)( -2(1/3)#

#3(1/6) = ((6*3) + 1) / 6 = 19/6#

#5.5 = (5.5 * 10) / 10 = cancel(55)^color(brown)(11) / cancel(10 )^color(brown)(2)= 11 / 2#

L C M of denominator of the numbers 2,6 is 6.

#:. (19/6) - 11 / 2 = (19/6) - ((11 * 3) / (2 * 3))#

#=> (19/6) - (33 / 6) = (19 - 33 ) / 6 = -cancel(14)^color(brown)7 / cancel(6)^color(brown)(3)#

#=> -(7/3) = color(green)( -2(1/3)#

Benjamin Altschul · Answer

undefined To find the sum of $3 \frac{1}{6}$ and $-5.5$, expressed as a mixed number in simplest form:

Step 1: Convert $3 \frac{1}{6}$ to an improper fraction.
$$3 \frac{1}{6} = \frac{(3 \times 6) + 1}{6} = \frac{18 + 1}{6} = \frac{19}{6}$$

Step 2: Add the fractions.
$$\frac{19}{6} + (-5.5)$$

Step 3: Write $-5.5$ as an improper fraction.
$$-5.5 = -\frac{11}{2}$$

Step 4: Add the fractions.
$$\frac{19}{6} + \left(-\frac{11}{2}\right)$$

Step 5: Find a common denominator, which is 6.
$$\frac{19}{6} - \frac{33}{6}$$

Step 6: Subtract the fractions.
$$\frac{19 - 33}{6} = \frac{-14}{6}$$

Step 7: Simplify the fraction.
$$\frac{-14}{6} = -\frac{7}{3}$$

Therefore, the sum of $3 \frac{1}{6}$ and $-5.5$ expressed as a mixed number in simplest form is $-\frac{7}{3}$.