Question

question 21 of 42
what is the sum of the fractions below?
3/4 + 6/7

a. 9/28
b. 15/11
c. 15/28
d. 9/11

Explanation:

Step1: Find a common denominator

The denominators are 4 and 7. The least common denominator (LCD) of 4 and 7 is \(4\times7 = 28\) since 4 and 7 are coprime.

Step2: Rewrite the fractions with the LCD

For \(\frac{3}{4}\), multiply numerator and denominator by 7: \(\frac{3\times7}{4\times7}=\frac{21}{28}\)
For \(\frac{6}{7}\), multiply numerator and denominator by 4: \(\frac{6\times4}{7\times4}=\frac{24}{28}\)

Step3: Add the fractions

Now add the two fractions with the common denominator: \(\frac{21}{28}+\frac{24}{28}=\frac{21 + 24}{28}=\frac{45}{28}\)

Answer:

C. \(\frac{45}{28}\)