Problem 34 - Introductory Algebra for College Students

Question

Find each sum without the use of a number line. $$-\frac{5}{6}+\frac{1}{3}$$

Step-by-Step Solution

Answer

-1/2

Step 1: Find the less/common multiple

In order to add fractions, they must have the same denominator. To find the least common multiple for denominators 6 and 3, the multiples of each are enumerated until a common value is found. In this case, 6 is also a multiple of 3, hence, 6 is the least common multiple (LCM).

Step 2: Convert fractions to use same denominator

The aim is to convert 1/3 to have 6 as a denominator. To do this, both numerator and denominator are multiplied by the same number, so as not to change the value of the fraction. For 1/3, multiply numerator and denominator by 2, which makes it 2/6.

Step 3: Add fractions

Now -5/6 and 2/6 have the same 6 denominator. The numerators can then be added, so that’s -5 + 2 = -3. The result thus is -3/6.

Step 4: Simplify the result

The result (-3/6) can be reduced to its simplest form by dividing both numerator and denominator by their greatest common divisor (GCD). The GCD of 3 and 6 is 3. Thus, the simplified form of the fraction is -1/2.