ordering fractions least to greatest
3/7 1/9 2/3
Change these fractions to equivalent fractions with a common denominator.
3/7 = 27/63
1/9 = 7/63
2/3 = 42/63
Put each set of fractions in order least to greatest.
4/5,4/12,7/10,5/6
To order fractions from least to greatest, you need to compare their values. One way to do this is by finding a common denominator for all the fractions and then comparing the numerators.
Let's order the fractions 3/7, 1/9, and 2/3:
Step 1: Find a common denominator.
The denominators of the given fractions are 7, 9, and 3, respectively. To find a common denominator, you can take the least common multiple (LCM) of these numbers, which is 63.
Step 2: Convert fractions to the common denominator.
To convert 3/7, 1/9, and 2/3 into fractions with a denominator of 63, you can multiply both the numerator and denominator of each fraction by the same number.
3/7 * (9/9) = 27/63
1/9 * (7/7) = 7/63
2/3 * (21/21) = 42/63
Now, the equivalent fractions with a common denominator are 27/63, 7/63, and 42/63.
Step 3: Compare the numerators.
Now that all the fractions have the same denominator, you can compare the numerators to determine the order.
7/63 < 27/63 < 42/63
Therefore, the fractions, from least to greatest, are 7/63, 27/63, 42/63.
However, it's worth noting that you can simplify these fractions by dividing the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD is 7.
7/63 ÷ (7/7) = 1/9
27/63 ÷ (7/7) = 3/9 (simplified to 1/3)
42/63 ÷ (7/7) = 6/9 (simplified to 2/3)
So the simplified fractions, from least to greatest, are 1/9, 1/3, 2/3.
1/9
3/7
2/3