Answer:
32 : 5
Explanation:
Change values to whole numbers.
Convert fractions to integers by eliminating the denominators.
Our two fractions have unlike denominators so we find the Least Common Denominator and rewrite our fractions as necessary with the common denominator
List all prime factors for each number.
Prime Factorization of 8 is:
2 x 2 x 2 => 23
Prime Factorization of 256 is:
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 => 28
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 2, 2, 2, 2, 2
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256
In exponential form:
LCM = 28 = 256
LCM = 256
Therefore,
LCM(8, 256) = 256
Rewriting input as fractions if necessary:
3/8, 15/256
For the denominators (8, 256) the least common multiple (LCM) is 256.
Therefore, the least common denominator (LCD) is 256.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
3/8 = 3/8 × 32/32 = 96/256
15/256 = 15/256 × 1/1 = 15/256
Our two fractions now have like denominators so we can multiply both by 256 to eliminate the denominators.
We then have:
3/8 : 15/256 = 96 : 15
Try to reduce the ratio further with the greatest common factor (GCF).
- The factors of 15 are: 1, 3, 5, 15
- The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Then the greatest common factor is 3.
The GCF of 96 and 15 is 3.
Divide both terms by the GCF, 3:
96 ÷ 3 = 32
15 ÷ 3 = 5
The ratio 96 : 15 can be reduced to lowest terms by dividing both terms by the GCF = 3 :
96 : 15 = 32 : 5
Therefore:
3/8 : 15/256 = 32 : 5