Finding the Largest Fractions in a Set

Let's practice identifying the greatest fraction in a set. Here we have 2/8, 4/8, 3/8, and 5/8.

Since there are all in terms of eighs, we can compare the numerators to see that 5/8 is the greatest fraction.

Now, what if the number of shaded parts is the same, but the total number of parts is different? We have 4 9ths, 410ths, 48s, and 416.

Since a larger denominator means that each part is smaller, the fraction with the smallest denominator has the largest parts. So 4/8 is the largest fraction.

Let's look at a different set where both the numerators and denominators are different.

We have 1/3, 26ths, 4 9ths, and 6 18.

To compare these, we can simplify them.

26ths equals 1/3 and 6 18 also equals 1/3. Now we compare 1/3 and 4 9th. Using 9 as a common denominator, 1/3 equals 3 9th. Comparing 3 9ths and 4 9ths, we see that 4 9ths is greater.

Let's try another set. The fractions are 1/2, 35ths, 7/10, and 12 20ths. Using 20 as a common denominator, 1/2 becomes 10 20ths. 3 fths becomes 12 20ths.

7/10ths becomes 14 20ths. and the last fraction is already 12 20ths. The largest numerator is 14. So 14 20ths or 7/10 is the greatest fraction.

For our last problem, let's compare these four fractions.

2/3 35ths 8 15 and 9 15. Using 15 as a common denominator, 2/3 equals 10 15 and 35ths equals 9 15. So we're comparing 10 15 8 15 and 9 15. The fraction with the largest numerator is 10 15 which means 2/3 is the greatest.

These examples show the key strategies for comparing fractions. Compare numerators when denominators are the same. Compare denominators when numerators are the same or find a common denominator to see which fraction is largest.