Use common denominators to compare the pairs of rational numbers. In each of the following identify which one is greater and explain how you know. 5/7, 5/8
What is the common denominator? What are the equivalent fractions?
1 over2
To compare the rational numbers 5/7 and 5/8 using common denominators, we need to find a common multiple of the denominators 7 and 8.
First, let's list the multiples of 7: 7, 14, 21, 28, 35, 42, and so on.
Next, let's list the multiples of 8: 8, 16, 24, 32, 40, 48, and so on.
Looking at the lists, we see that the least common multiple (LCM) of 7 and 8 is 56. Therefore, we need to express both fractions with a denominator of 56.
To do this, we can multiply the numerator and denominator of 5/7 by 8, and the numerator and denominator of 5/8 by 7.
For 5/7: (5/7) * (8/8) = 40/56
For 5/8: (5/8) * (7/7) = 35/56
Now that both fractions have a common denominator of 56, we can compare them.
Comparing the numerators, we see that 40/56 is greater than 35/56. Therefore, we can conclude that 5/7 is greater than 5/8.
In summary, to compare the rational numbers 5/7 and 5/8 using common denominators, we found the least common multiple (LCM) of the denominators 7 and 8, which was 56. We then converted both fractions to equivalent fractions with a denominator of 56 and determined that 5/7 is greater than 5/8 by comparing their numerators.