Solve: (-1/6) - (+4 2/4) Mixed Number Subtraction

Question

(16)(+424)= (-\frac{1}{6})-(+4\frac{2}{4})=

Video Solution

Solution Steps

00:00 Solve
00:03 Negative times positive is always negative
00:08 Let's reduce by 2
00:14 Let's multiply the fraction by 3 to get a common denominator
00:25 Let's reduce by 2
00:28 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert the mixed number to an improper fraction.
  • Step 2: Simplify the improper fraction, if possible.
  • Step 3: Find a common denominator for the fractions.
  • Step 4: Subtract the fractions by rewriting them with a common denominator.
  • Step 5: Simplify the result, if needed.

Now, let's work through each step:
Step 1: +424 +4\frac{2}{4} is first converted to an improper fraction:

424=4+24 4\frac{2}{4} = 4 + \frac{2}{4} . Since 24 \frac{2}{4} can be simplified to 12 \frac{1}{2} , it becomes 4+12=82+12=92 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} . Thus, +424=92 +4\frac{2}{4} = \frac{9}{2} .

Step 2: Simplification has already been done in the conversion.

Step 3: Determine a common denominator for 16-\frac{1}{6} and 92\frac{9}{2}. The least common denominator between 6 and 2 is 6.

Step 4: Rewrite each fraction with the common denominator:

  • 16-\frac{1}{6} remains as 16-\frac{1}{6}.
  • 92\frac{9}{2} needs to be converted to have a denominator of 6: 92=9×32×3=276\frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6}.

Now, perform the subtraction:

16276=1276=286 -\frac{1}{6} - \frac{27}{6} = \frac{-1 - 27}{6} = \frac{-28}{6} .

Step 5: Simplify the result: 286=143\frac{-28}{6} = \frac{-14}{3}. This can be expressed as a mixed number 423-4\frac{2}{3}.

Therefore, the solution to the problem is 423 -4\frac{2}{3} , which matches the correct choice: 423 -4\frac{2}{3} .

Answer

423 -4\frac{2}{3}