Solve Mixed Number Addition: 2¼ Plus Negative Fraction -12/24

Question

(+214)+(1224)= (+2\frac{1}{4})+(-\frac{12}{24})=

Video Solution

Solution Steps

00:00 Solve
00:05 Find the point on the axis
00:08 Positive times negative always equals negative, so subtract
00:12 To subtract, move left (negative) on the axis
00:30 Reduce the fraction to 12
00:38 Multiply the fraction by 2 to find a common denominator
00:49 Convert mixed fraction to improper fraction
00:54 Subtract between the fractions
00:58 Convert fraction to mixed fraction
01:01 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 negative fraction, if necessary.
  • Step 3: Find the least common denominator (LCD) to add both fractions.
  • Step 4: Perform the addition of the two fractions.
  • Step 5: Simplify the result or convert back to a mixed number.

Now, let's work through each step:

Step 1: The mixed number 2142\frac{1}{4} is converted to the improper fraction 94\frac{9}{4} because 2×4+1=92 \times 4 + 1 = 9.

Step 2: The fraction 1224-\frac{12}{24} simplifies to 12-\frac{1}{2} because 1224=12\frac{12}{24} = \frac{1}{2}.

Step 3: The least common denominator for 94\frac{9}{4} and 12-\frac{1}{2} is 4. We rewrite 12-\frac{1}{2} with this denominator: 1224-\frac{1}{2} \equiv -\frac{2}{4}.

Step 4: Add the fractions: 94+(24)=924=74\frac{9}{4} + \left(-\frac{2}{4}\right) = \frac{9 - 2}{4} = \frac{7}{4}.

Step 5: Convert 74\frac{7}{4} back to a mixed number: 1341\frac{3}{4}.

Therefore, the solution to the problem is 1341\frac{3}{4}.

Answer

134 1\frac{3}{4}