Equivalent Rational Numbers of -2/7 with Denominator 98
Rational numbers are numbers that can be written as a ratio of two integers, where the denominator is not equal to zero. In this case, we are given the rational number -2/7 and asked to find an equivalent rational number with a denominator of 98. To solve this problem, we need to follow these steps:
Step 1: Find the equivalent fraction with a denominator of 98
To find an equivalent fraction with a denominator of 98, we need to multiply both the numerator and denominator of -2/7 by a factor that will make the denominator equal to 98. In this case, we can multiply both the numerator and denominator by 14, since 7 x 14 = 98:
-2/7 x 14/14 = -28/98
Step 2: Simplify the fraction
Now that we have an equivalent fraction with a denominator of 98, we need to simplify it to its lowest terms. To do this, we need to find the greatest common factor (GCF) of the numerator and denominator, which is 14 in this case:
-28/98 = (-28 ÷ 14)/(98 ÷ 14) = -2/7
Step 3: Check for accuracy
To check that our answer is correct, we can multiply the numerator and denominator of -2/7 by 14 and simplify:
-2/7 x 14/14 = -28/98
This confirms that -2/7 and -28/98 are equivalent rational numbers.
Conclusion
We can find an equivalent rational number of -2/7 with a denominator of 98 by multiplying both the numerator and denominator by a factor that will make the denominator equal to 98. We then simplify the resulting fraction to its lowest terms by finding the greatest common factor of the numerator and denominator. Finally, we can check our answer for accuracy by multiplying the numerator and denominator of the equivalent fraction and simplifying.