Answer:
5/9, 3/5, 5/8, 3/4
Explanation:
In order to arrange the fractions in ascending order, we first need to find the least common denominator (LCD). The LCD is the smallest number that the denominators of each fraction is divisible by. Changing fractions to make them have the same denominator makes it easier to compare them as well as performing operations on them. To find the LCD, we can list out the multiples of the denominators of each fraction until we find the smallest multiple that each denominator shares.
- 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80...
- 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40...
- 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90...
- 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50...
Eventually, we see that each denominator shares a common multiple of 360. Now that we have a denominator of 360, we have to multiply each numerator by the appropriate factor so that the value of each respective fraction will be equivalent.
- Multiply 5/8 by 45/45: 225/360
- Multiply 3/4 by 90/90: 270/360
- Multiply 5/9 by 40/40: 200/360
- Multiply 3/5 by 72/72: 216/360
Now that the fractions share a common denominator, we can put them in ascending order by looking at their numerators.
Thus, the fractions arranged in ascending order is 5/9, 3/5, 5/8, 3/4.