What fraction should be added to the sum of $5 \frac{3}{4}$, $4 \frac{4}{5}$ and $7 \frac{3}{8}$ to make the result a whole number?

### Concept & Strategy To make a sum a whole number by *addition*, calculate the fractional remainder of the sum, then subtract that value from 1 to determine the missing component needed to complete the next whole integer. ### Step-by-Step Solution * **Isolate fractional components:** We only need to evaluate the addition of the fractions: $\frac{3}{4} + \frac{4}{5} + \frac{3}{8}$ * **Find the common denominator:** The LCM of 4, 5, and 8 is 40. $$\text{Fraction Sum} = \frac{30}{40} + \frac{32}{40} + \frac{15}{40}$$ $$\text{Fraction Sum} = \frac{30 + 32 + 15}{40} = \frac{77}{40}$$ * **Convert to mixed fraction:** $$\frac{77}{40} = 1 \frac{37}{40}$$ * **Calculate value to add:** The remaining fraction value is $\frac{37}{40}$. To complete the whole integer balance, calculate: $$\text{Value to add} = 1 - \frac{37}{40} = \frac{3}{40}$$ ### Exam Strategy & Shortcut Once you determine the improper sum numerator is 77 over a base of 40, find the next highest multiple of 40, which is 80. The amount required to reach that perfect integer value is simply $80 - 77 = 3$. Hence, $\frac{3}{40}$ is the immediate answer. ### Common Pitfall Students often compute $\frac{37}{40}$ and select it directly or forget to subtract the fractional residue from 1 when an addition step is required rather than subtraction. ### Final Answer **Therefore, the correct answer is 3/40.**