How to arrange fractions in ascending and descending order?
Fractions represent the equal parts of a whole or a collection of items. So if we have a collection of items and we divide them into parts, then each part is a fraction of the whole.
Answer: The fractions can be first expressed as like fractions and then be arranged in ascending and descending order.
Like fractions are fractions with the same denominator. We will convert the fractions to like fractions to arrange them in order.
Arranging in decreasing order means arranging the fractions from 'greatest to smallest' in value. Similarly, arranging in increasing order means arranging the fractions from 'smallest to greatest' in value.
Let's take a few fractions to see how we can arrange fractions in ascending and descending order:
1/2, 2/3, 1/5, 3/7
To express these fractions as like fractions, we must make all the denominators the same by taking the LCM of all the denominators, that is, 2, 3, 5, and 7.
LCM of 2, 3, 5, 7 = 2 × 3 × 5 × 7 = 210
Now let's make the denominators as 210 for all the fractions:
1/2 = 1/2 × 105/105 = 105/210
2/3 = 2/3 × 70/70 = 140/210
1/5 = 1/5 × 42/42 = 42/210
3/7 = 3/7 × 30/30 = 90/210
Since the denominators of all the fractions are the same now, we will arrange the fractions in order using the numerators.
Let's now arrange the above fractions in descending order:
140/210 > 105/210 > 90/210 > 42/210 or 2/3 > 1/2 > 3/7 > 1/5
Let's now arrange the fractions in ascending order:
42/210 < 90/210 < 105/210 < 140/210 or 1/5 < 3/7 < 1/2 < 2/3
Therefore, to arrange any set of fractions in decreasing or increasing order, we must first express them as like fractions.