Understanding the Problem
To solve the multiplication of 3 by the mixed fraction 5 1/5, we first need to convert the mixed fraction into an improper fraction.
Step 1: Convert the Mixed Fraction
- A mixed fraction consists of a whole number and a proper fraction. In this case, 5 1/5 can be converted as follows:
- Multiply the whole number (5) by the denominator (5): 5 x 5 = 25.
- Add the numerator (1) to this result: 25 + 1 = 26.
- So, 5 1/5 as an improper fraction is 26/5.
Step 2: Multiply the Whole Number by the Improper Fraction
- Now, we multiply 3 by the improper fraction 26/5:
- 3 can be expressed as 3/1 for ease of multiplication.
- Multiply the numerators: 3 x 26 = 78.
- Multiply the denominators: 1 x 5 = 5.
- This gives us the improper fraction 78/5.
Step 3: Convert Back to a Mixed Fraction
- To convert 78/5 back to a mixed fraction:
- Divide the numerator (78) by the denominator (5): 78 ÷ 5 = 15 remainder 3.
- The whole number is 15, and the remainder is 3, which becomes the numerator of the fractional part.
- The denominator remains 5.
Thus, 78/5 as a mixed fraction is 15 3/5.
Final Answer
The result of multiplying 3 by 5 1/5 is 15 3/5.