Find equivalent fraction with a common denominator and order from least to greatest
To find equivalent fractions with a common denominator, follow these steps:
1. Identify the fractions for which you want to find equivalent fractions.
2. Determine the common denominator for all the fractions. The common denominator is the least common multiple (LCM) of the denominators of the given fractions.
3. Rewrite each fraction using the common denominator.
4. Compare and order the fractions from least to greatest.
Let's look at an example:
Example: Find equivalent fractions with a common denominator and order them from least to greatest for fractions 1/3, 2/5, and 3/8.
Step 1: Identify the fractions.
Given fractions: 1/3, 2/5, 3/8
Step 2: Determine the common denominator.
The denominators of the fractions are 3, 5, and 8. To find the LCM of 3, 5, and 8, you can use different methods. One way is to prime factorize each number and then find the LCM.
3 = 3
5 = 5
8 = 2^3
Now, multiply each prime number the greatest number of times it occurs in any of the factorizations. The LCM is the product of these prime factors.
LCM = 2^3 × 3 × 5 = 120
The common denominator for the fractions 1/3, 2/5, and 3/8 is 120.
Step 3: Rewrite each fraction using the common denominator.
To rewrite each fraction with the common denominator of 120, you need to multiply the numerator and denominator by the appropriate factor to make the denominator 120.
1/3 = (1 × 40) / (3 × 40) = 40/120
2/5 = (2 × 24) / (5 × 24) = 48/120
3/8 = (3 × 15) / (8 × 15) = 45/120
Step 4: Compare and order the fractions from least to greatest.
Now that the fractions have a common denominator, you can compare them and order them from least to greatest.
40/120, 48/120, 45/120
Divide both the numerator and denominator of each fraction by their greatest common divisor (GCD) to simplify the fractions if possible.
GCD(40, 120) = 40
40/40 = 1
120/40 = 3
GCD(48, 120) = 24
48/24 = 2
120/24 = 5
GCD(45, 120) = 15
45/15 = 3
120/15 = 8
So, the simplified fractions are:
1/3, 2/5, 3/8
Therefore, the equivalent fractions with a common denominator, ordered from least to greatest, are 1/3, 2/5, and 3/8.