arrange in ascending order 7/22, 2/5, 10/24
what is the prime factorization of 87750 in exponent form
Change the fractions to decimals, and your order should be clear.
10/24 2/5 7/22
To arrange the fractions in ascending order, you need to compare them and determine their relative sizes.
The given fractions are: 7/22, 2/5, 10/24.
To do this, you can find the least common denominator (LCD) of the fractions, which is the smallest number that each denominator can divide into evenly.
To find the LCD, you need to find the least common multiple (LCM) of the denominators. For the given fractions, the denominators are 22, 5, and 24.
To find the LCM, you can list the multiples of each denominator until you find the smallest number that is a multiple of each denominator.
22: 22, 44, 66, 88, ...
5: 5, 10, 15, 20, 25, ...
24: 24, 48, 72, 96, ...
The smallest number that is divisible by 22, 5, and 24 is 120.
Now, you can convert each fraction to have a denominator of 120:
7/22 = (7 * 5) / (22 * 5) = 35/110
2/5 = (2 * 24) / (5 * 24) = 48/120
10/24 = (10 * 5) / (24 * 5) = 50/120
Now that all the fractions have the same denominator, you can compare the numerators:
35/110 < 48/120 < 50/120
Therefore, arranging the fractions in ascending order:
35/110, 48/120, 50/120
Now, let's move on to finding the prime factorization of 87750 in exponent form.
To find the prime factorization, you need to determine the prime numbers that can divide into 87750. You can start by dividing 87750 by the smallest prime number, which is 2:
87750 ÷ 2 = 43875
The result, 43875, is not divisible by 2. Now, you move on to the next prime number, which is 3:
43875 ÷ 3 = 14625
Again, the result is not divisible by 3. Moving on to the next prime number, which is 5:
14625 ÷ 5 = 2925
The result, 2925, is divisible by 5. Now, you can continue dividing by 5 until you can no longer divide:
2925 ÷ 5 = 585
585 ÷ 5 = 117
117 ÷ 5 = 23.4 (not divisible by 5)
At this point, you cannot divide further by 5. Now, you move on to the next prime number, which is 7:
117 ÷ 7 = 16.71 (not divisible by 7)
You continue this process by finding the successive prime numbers and dividing until you can no longer divide evenly. The prime factorization of 87750 is:
87750 = 2^1 * 3^3 * 5^3 * 7^2
So, the prime factorization of 87750 in exponent form is 2^1 * 3^3 * 5^3 * 7^2.