Arrange the following fractions in ascending order
7/15,5/12,3/7
2/5 3/10 4//15
Arrange the following fractions in descending order: $\frac{3}{5},\frac{1}{4},\frac{3}{10}$
3
5,
1
4,
3
10
To arrange the fractions in ascending order, we need to compare the fractions and determine which one is the smallest, which one is the next smallest, and so on.
One way to compare fractions is by finding a common denominator. In this case, we can find a common denominator by finding the least common multiple (LCM) of the denominators.
The denominators in the fractions are 15, 12, and 7. The LCM of these numbers is 420.
Now, we need to convert each fraction to have a denominator of 420.
To convert 7/15 to a fraction with a denominator of 420, we multiply both the numerator and denominator by 28. This gives us: (7/15) * (28/28) = 196/420.
To convert 5/12 to a fraction with a denominator of 420, we multiply both the numerator and denominator by 35. This gives us: (5/12) * (35/35) = 175/420.
To convert 3/7 to a fraction with a denominator of 420, we multiply both the numerator and denominator by 60. This gives us: (3/7) * (60/60) = 180/420.
Now that all the fractions have a common denominator of 420, we can compare their numerators.
The fractions in ascending order are:
175/420, 180/420, 196/420
To simplify the fractions further, we can divide the numerator and denominator by their greatest common divisor (GCD).
The GCD of 175 and 420 is 5, so we can simplify 175/420 by dividing both the numerator and denominator by 5. This gives us 35/84.
The GCD of 180 and 420 is 60, so we can simplify 180/420 by dividing both the numerator and denominator by 60. This gives us 3/7.
The GCD of 196 and 420 is 28, so we can simplify 196/420 by dividing both the numerator and denominator by 28. This gives us 7/15.
So, the fractions in ascending order are:
35/84, 3/7, 7/15