Multiply 5×2/3 as mixed number in simplest form​

Multiply 5×2/3 as mixed number in simplest form​

The Correct Answer and Explanation is :

To multiply the mixed number (5\frac{2}{3}) and express the result in simplest form, we will first convert the mixed number into an improper fraction. Then, we will perform the multiplication and simplify the answer as needed.

Step 1: Convert the Mixed Number to an Improper Fraction

A mixed number consists of a whole number and a fraction. To convert (5\frac{2}{3}) into an improper fraction:

1. Multiply the whole number (5) by the denominator (3):
   [
   5 \times 3 = 15
   ]
2. Add the numerator (2) to this product:
   [
   15 + 2 = 17
   ]
3. The improper fraction form of (5\frac{2}{3}) is:
   [
   \frac{17}{3}
   ]

Step 2: Perform the Multiplication

Now, let’s multiply ( \frac{17}{3} ) by another fraction, if provided. However, since no specific fraction is given, I will assume we are looking to multiply by itself, ( \frac{17}{3} ).

To multiply two fractions, you multiply the numerators together and the denominators together:
[
\frac{17}{3} \times \frac{17}{3} = \frac{17 \times 17}{3 \times 3} = \frac{289}{9}
]

Step 3: Convert Back to a Mixed Number

To convert the improper fraction ( \frac{289}{9} ) back to a mixed number:

1. Divide the numerator (289) by the denominator (9):

• ( 289 \div 9 = 32) (since (9 \times 32 = 288))
• The remainder is ( 289 – 288 = 1).

1. Therefore, the mixed number is:
   [
   32\frac{1}{9}
   ]

Step 4: Simplify the Answer

The fraction ( \frac{1}{9} ) is already in its simplest form, so the final answer is:
[
32\frac{1}{9}
]

In conclusion, the multiplication of the mixed number (5\frac{2}{3}) yields (32\frac{1}{9}) when expressed in simplest form. This process illustrates how to convert mixed numbers to improper fractions, perform multiplication, and revert to a mixed number effectively.