which of the following shows the numbers in order from least to greatest
a)2 /15,2 1/6,2 1/7
b)2 1/8,2 1/4, 2.4
c)2.4,2 1/5,2.6
d)2.2,2.5,2.25
Ans B
To determine the correct answer, we need to arrange the numbers in each option from least to greatest.
a) 2 15/16, 2 1/6, 2 1/7
To compare mixed numbers, we convert them to improper fractions first.
2 15/16 = (2 * 16 + 15)/16 = 47/16
2 1/6 = (2 * 6 + 1)/6 = 13/6
2 1/7 = (2 * 7 + 1)/7 = 15/7
Now we can compare the fractions:
47/16, 13/6, 15/7
To compare the fractions, we can find a common denominator and compare the numerator values directly:
Multiply the first fraction by 6/6 to get: 141/48
Multiply the second fraction by 8/8 to get: 104/48
Multiply the third fraction by 16/16 to get: 240/112
Comparing the fractions:
104/48 < 141/48 < 240/112
So the order from least to greatest is:
2 1/6, 2 15/16, 2 1/7
b) 2 1/8, 2 1/4, 2.4
To compare these numbers, we can convert the mixed numbers to decimals:
2 1/8 = 2 + 1/8 = 2.125
2 1/4 = 2 + 1/4 = 2.25
Now we have:
2.125, 2.25, 2.4
Comparing the decimals, we can see that:
2.125 < 2.25 < 2.4
So the order from least to greatest is:
2 1/8, 2 1/4, 2.4
c) 2.4, 2 1/5, 2.6
These numbers are already in decimal and mixed number form, so we can directly compare them:
2.4, 2 1/5, 2.6
Comparing the decimals:
2.4 < 2.6
Since 2 1/5 is between 2.4 and 2.6, the final order is:
2.4, 2 1/5, 2.6
d) 2.2, 2.5, 2.25
These numbers are already in decimal form, so we can directly compare them:
2.2, 2.5, 2.25
Comparing the decimals:
2.2 < 2.25 < 2.5
So the order from least to greatest is:
2.2, 2.25, 2.5
Based on the comparisons made, the correct answer is:
Option d) 2.2, 2.25, 2.5