Arrange rational numbers in ascending order -
2/4,2/3,8/21
using a common denominator of 84, they are
42/84, 56/84, 32/84
so, what do you think?
To arrange rational numbers in ascending order, you need to compare their values and place them in increasing order.
Let's start with the given rational numbers: 2/4, 2/3, and 8/21.
1. First, we can simplify these fractions by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD for 2 and 4 is 2, for 2 and 3 is 1, and for 8 and 21 is 1. Simplifying the fractions, we get:
2/4 = 1/2
2/3 = 2/3
8/21 = 8/21
2. Now that the fractions are simplified, we can compare their values. To do this, we can either convert them to decimals or compare them directly by cross-multiplying.
- Converting to decimals:
1/2 ≈ 0.5
2/3 ≈ 0.66666667
8/21 ≈ 0.38095238
- Cross-multiplying:
Multiply the numerator of one fraction by the denominator of the other fraction to compare.
For simplicity, let's compare 1/2 with 8/21.
(1/2) * (21/8) = 21/16 ≈ 1.3125
3. Comparing the fractions:
- By comparing decimals, we see that the order is: 0.38095238, 0.5, 0.66666667.
- By comparing cross-products, we see that the order is: 8/21, 1/2, 2/3.
Putting it all together, the rational numbers in ascending order are:
8/21, 1/2, 2/3.