how to you compare 8 fractions with different denominators including improper fractions?
Either change them to equivalent decimals or to fractions with the same denominators.
1. make them the same denominator, or
2. find the decimal equivalents for each.
how do you change them into equivalent decimals and same denominators?
For decimals, divide the numerator by the denominator.
Example: 3/4 = 0.75
For fractions, find a common multiple of the denominators.
Examples: 2, 3, 4, >> the common multiple is 12.
so it's like you do this ->
2,4,6,8,10,12
3,6,9,12,15,18,21
4,8,12,16,20
and one more question, what about the numerators?
like if you're comparing 3/8 to 2/5 the common multiple is 40. the numerators?
Divide the new denominator by the old denominator.
40/5 = 8
Multiply the old denominator by the quotient.
2 * 8 = 16
2/5 = 16/40
http://www.mathsisfun.com/equivalent_fractions.html
so it would be like, 5/8 ? 6/7
8,16,24,32,40,48,56,64
7,14,21,28,35,42,49,56
LCD IS 56
so now i do 56/7=8*6=48 6/7=48/56
56/8=7*5=35 so, 5/8=35/56
5/8 (35/56) < 6/7 (48/56)
Comparing fractions with different denominators, including improper fractions, can be done using a common denominator. Here's a step-by-step guide on how to compare eight fractions with different denominators, including improper fractions:
Step 1: Find the Least Common Denominator (LCD)
To compare fractions with different denominators, you need to find the LCD, which is the least common multiple of all the denominators. For example, let's say we have the following fractions:
1/2, 3/4, 5/6, 7/8, 9/10, 11/12, 13/14, 15/16
To find the LCD, list the multiples of each denominator until you find a common multiple. In this case, the multiples of the denominators are:
Denominator 2: 2, 4, 6, 8, 10, 12, 14, 16
Denominator 4: 4, 8, 12, 16
Denominator 6: 6, 12, 18
Denominator 8: 8, 16
Denominator 10: 10, 20
Denominator 12: 12, 24
Denominator 14: 14, 28
Denominator 16: 16
The LCD in this case is 48 since it is the smallest common multiple of all the denominators.
Step 2: Convert all fractions to have the same denominator
Multiply the numerator and the denominator of each fraction by the necessary value to make their denominators equal to the LCD. For example, let's take the first fraction, 1/2:
(1/2) x (24/24) = 24/48
Repeat this process for all fractions:
1/2 = 24/48
3/4 = 36/48
5/6 = 40/48
7/8 = 42/48
9/10 = 43.2/48
11/12 = 44/48
13/14 = 45.6/48
15/16 = 46.8/48
Step 3: Compare the numerators
Now that all the fractions have the same denominator (in this case, 48), you can compare them by looking at their numerators. The fraction with the greatest numerator will be the largest fraction, and vice versa.
In this example, by comparing the numerators, you can determine the order of the fractions from least to greatest:
24/48, 36/48, 40/48, 42/48, 43.2/48, 44/48, 45.6/48, 46.8/48
As you can see, the fractions are now in order from least to greatest.