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

Question:

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.

Start with 1/2

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

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