Write 6 3 /7 as a simplified improper fraction.
The correct answer and explanation is:
To convert a mixed number like 6 3/7 into an improper fraction, follow these steps:
- Multiply the whole number by the denominator:
The whole number in this case is 6, and the denominator of the fractional part is 7. So, multiply 6 by 7:
6 × 7 = 42 - Add the numerator of the fraction to this result:
Now take the numerator of the fractional part, which is 3, and add it to the result from step 1.
42 + 3 = 45 - Write the result as the numerator over the original denominator:
The denominator stays the same, which is 7. So, the improper fraction is:
45/7
Thus, 6 3/7 as an improper fraction is 45/7.
Explanation:
- A mixed number consists of a whole number and a fraction. The whole number can be converted to an improper fraction by multiplying it by the denominator of the fraction and then adding the numerator of the fraction.
- This process turns the mixed number into a single fraction where the numerator is greater than the denominator, which is known as an improper fraction.
- The importance of converting a mixed number to an improper fraction arises when performing operations like addition, subtraction, multiplication, or division of fractions, where improper fractions are easier to handle.
For example, if you needed to add 6 3/7 and 2 1/7, you would first convert both mixed numbers to improper fractions and then proceed with the addition.