Solve: Adding (-1/5) and (+3⅓) with Mixed Numbers

Question

(15)+(+313)= (-\frac{1}{5})+(+3\frac{1}{3})=

Video Solution

Solution Steps

00:00 Solve
00:05 Find the point on the axis
00:10 To connect, we'll move in the right (positive) direction on the axis
00:28 Multiply each fraction by the second denominator to find a common denominator
00:34 Let's calculate
00:45 And this is the solution to the question

Step-by-Step Solution

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

  • Step 1: Convert 313 3\frac{1}{3} to an improper fraction.
  • Step 2: Find a common denominator for 15 -\frac{1}{5} and the improper fraction.
  • Step 3: Add the fractions.
  • Step 4: Simplify the result, converting it back to a mixed number if necessary.

Now, let's work through each step:

Step 1: Convert 313 3\frac{1}{3} to an improper fraction.
313=3×3+13=103 3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}

Step 2: Find a common denominator for 15 -\frac{1}{5} and 103 \frac{10}{3} .
The least common denominator of 5 and 3 is 15.

Step 3: Express each fraction with the common denominator:
15=315 -\frac{1}{5} = -\frac{3}{15} (multiply the numerator and denominator by 3)
103=5015 \frac{10}{3} = \frac{50}{15} (multiply the numerator and denominator by 5)

Step 4: Add the fractions:
315+5015=3+5015=4715 -\frac{3}{15} + \frac{50}{15} = \frac{-3 + 50}{15} = \frac{47}{15}

Step 5: Simplify 4715 \frac{47}{15} back to a mixed number if needed:
Performing the division, 47 divided by 15 is 3 with a remainder of 2.
Therefore, 4715=3215 \frac{47}{15} = 3\frac{2}{15} .

Therefore, the solution to the problem is 3215 3\frac{2}{15} .

Answer

3215 3\frac{2}{15}