Write 6 1/3 as an improper fraction.
The Correct Answer and Explanation is:
To convert the mixed number 6 1/3 into an improper fraction, follow these steps:
Step 1: Understand the components of a mixed number.
A mixed number consists of two parts:
- The whole number (in this case, 6)
- The fraction (in this case, 1/3)
Step 2: Convert the whole number into a fraction.
Any whole number can be expressed as a fraction with a denominator of 1. So, the whole number 6 can be written as:
[
6 = \frac{6}{1}
]
Step 3: Multiply the whole number by the denominator of the fractional part.
To combine the whole number with the fractional part, multiply the denominator of the fractional part (3) by the whole number (6):
[
6 \times 3 = 18
]
This step gives us the total number of parts represented by the whole number, but in terms of the denominator of the fractional part.
Step 4: Add the numerator of the fraction to the result.
Next, add the numerator of the fractional part (which is 1 in 1/3) to the result from the previous step:
[
18 + 1 = 19
]
Step 5: Place the result over the original denominator.
Finally, place the sum obtained in step 4 (19) over the denominator of the fractional part (which is 3). This gives us the improper fraction:
[
6 1/3 = \frac{19}{3}
]
Explanation:
The mixed number 6 1/3 represents 6 whole units and an additional 1/3 of a unit. To express it as an improper fraction, we combine the whole number and the fraction by converting the whole number into parts of the same denominator and adding the fraction. The result, 19/3, is called an improper fraction because the numerator (19) is larger than the denominator (3). Improper fractions are useful in mathematical operations, especially when performing addition, subtraction, or division with fractions.
So, the correct improper fraction for 6 1/3 is 19/3.