To convert the mixed number 6 7 into a fraction with a denominator of 42, we first need to understand how to represent this mixed number as an improper fraction.
The mixed number 6 7 consists of the whole number 6 and the fraction 7/1. To convert it into an improper fraction:
- Multiply the whole number (6) by the denominator of the fraction (1): 6 × 1 = 6.
- Now add the numerator (7) to the result: 6 + 7 = 13.
This gives us the improper fraction:
13/1
Next, we need to express this improper fraction with a denominator of 42. To do that, we can multiply the numerator and denominator by the same number:
- Since our current denominator is 1, we need to multiply by 42: 1 × 42 = 42.
- Now, multiply the numerator (13) by the same number (42): 13 × 42 = 546.
Thus, we have:
13/1 = 546/42
In conclusion, the mixed number 6 7 can be expressed as the fraction 546/42.