 Question:

# Order the following fractions from least to greatest: – 5/6; 1/6; 1/2; -1/9

A -5/6 ; -1/9 ; 1/6 ; 1/2
Explaination

Remember that when we are dealing with negative numbers, the greater its absolute value (a number’s distance from zero), the smaller the number itself.
Step 1: Organize and sort our numbers into groups
Since none of these numbers has any whole number in front, we will sort these numbers into positive and negative numbers.
Positive Numbers: 1/6 and 1/2
Both 1/6 and 1/2 are greater than any of the negative fractions. We will compare these fractions using common denominators. (Step 2)
Negative Numbers: -5/6 and – 1/9
These two we will also compare using common denominators. (Step 3)
Step 2: Compare positive fractions using Common Denominators & Equivalent Fractions
We are comparing the fractions 1/6 and 1/2
Let’s first find the Least Common Multiple of 6 and 2:
Multiples of 6: 6, 12, 18, 24
Multiples of 2: 2, 4, 6, 8, 10
LCM: 6
Now we create equivalent fractions with 6 as the new denominator.
Since 2 × 3 = 6, we also multiply the numerator by 3
(1×3)/(2×3) = 3/6
1/6 has already the denominator of 6
Now we can compare:
3/6 is larger than 1/6 therefore 1/2 is larger than 1/6
Step 3: Compare negative fractions using Common Denominators & Equivalent Fractions
We are comparing the fractions 5/6 and 1/9
Let’s first find the Least Common Multiple of 6 and 9:
Multiples of 6: 6, 12, 18, 24
Multiples of 9: 9, 18, 27, 36, 45
LCM: 18
Now we create equivalent fractions with 18 as the new denominator.
First Up: 5/6
Since 6 × 3 = 18, we also multiply the numerator by 3
(5×3)/(6×3)= 15/18
Second Up: 1/9
Since 9 × 2 = 18, we also multiply the numerator by 2
(1×2)/(9×2) = 2/18
Now we can compare:
15/18 is larger than 2/18 therefore -5/6 is further from zero than -1/9 which means -5/6 / is less than -1/9
Step 4: Organize our fractions from least to greatest.
-5/6 is smaller than -1/9
1/6 is smaller than 1/2
The order of the fractions from least to greatest is -5/6 ; – 1/9; 1/6 ; 1/2