Introduction:
In this question, we are asked to express the rational number 42/98 as a fraction with denominator 7.

Reducing the fraction:
To express 42/98 as a fraction with denominator 7, we need to first reduce the given fraction to its simplest form. We can do this by finding the greatest common factor (GCF) of the numerator and denominator, and then dividing both by it.

Finding the GCF:
To find the GCF of 42 and 98, we can list their factors and find the largest one they have in common.

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 98: 1, 2, 7, 14, 49, 98

The largest factor they have in common is 14.

Dividing by the GCF:
To reduce the fraction 42/98 to its simplest form, we divide both the numerator and denominator by the GCF, which is 14.

42 ÷ 14 = 3
98 ÷ 14 = 7

So, 42/98 is equal to 3/7 in its simplest form.

Expressing as a fraction with denominator 7:
Since the denominator of 3/7 is already 7, we don't need to do anything further to express it as a fraction with denominator 7.

Final Answer:
Therefore, the rational number 42/98 expressed as a fraction with denominator 7 is 3/7.