Question

Find the sum. $$\frac{5}{8}+\frac{1}{3}$$

Short answer

\(\frac{5}{8}+\frac{1}{3}=\frac{23}{24}\

Step-by-step solution

Find the Least Common Denominator (LCD)

First, we need to find the least common denominator (LCD), also known as least common multiple (LCM) for 8 and 3. The LCD for 8 and 3 is 24. This means that we need to convert both fractions so that they have 24 as the denominator, before we can add them

Convert Fractions to Have the Same Denominator

To convert \(\frac{5}{8}\) to a fraction with 24 as the denominator, we multiply the numerator and the denominator by 3. Therefore, \(\frac{5}{8}\) becomes \(\frac{15}{24}\). To convert \(\frac{1}{3}\) to a fraction with 24 as the denominator, we multiply the numerator and the denominator by 8. Therefore, \(\frac{1}{3}\) becomes \(\frac{8}{24}\). So, \(\frac{5}{8}+\frac{1}{3}\) becomes \(\frac{15}{24}+\frac{8}{24}\)

Add the Fractions

Now that we have the same denominator for both fractions, we can add them. We add the numerators and keep the denominator. Therefore, \(\frac{15}{24}+\frac{8}{24}=\frac{23}{24}\)