Explain why, when we add $\frac{1}{4}+\frac{3}{8}$, we can change both fractions to a common denominator in order to find the sum.

Choose the correct answer below.

AWe can change both fractions to a common denominator so that they have equal-sized parts. We can't add different-sized parts. In this case, we can make the parts the same size. We have $\frac{1}{4}=\frac{2}{8}$ and so $\frac{1}{4}+\frac{3}{8}=\frac{2}{8}+\frac{3}{8}=\frac{2+3}{8}=\frac{5}{8}$.
BWe can change both fractions to a common numerator so that they have equal-sized parts. We can't add different-sized parts. In this case, we can make the parts the same size. We have $\frac{1}{4}=\frac{3}{12}$ and so $\frac{1}{4}+\frac{3}{8}=\frac{3}{12}+\frac{3}{8}=\frac{3}{12+8}=\frac{3}{20}$.
CWe can change both fractions to a common denominator so that they have equal-sized parts. We can't add different-sized parts. In this case, we can make the parts the same size. We have $\frac{1}{4}=\frac{1}{8}$ and so $\frac{1}{4}+\frac{3}{8}=\frac{1}{8}+\frac{3}{8}=\frac{1+3}{8}=\frac{4}{8}=\frac{1}{2}$.
DWe can change both fractions to a common denominator so that they have equal-sized parts. We can't add different-sized parts. In this case, we can make the parts the same size. We have $\frac{1}{4}=\frac{2}{8}$ and so $\frac{1}{4}+\frac{3}{8}=\frac{2}{8}+\frac{3}{8}=\frac{2+3}{8+8}=\frac{5}{16}$.

Question

addisonlong04 addisonlong04

01-11-2026
Mathematics

Answered

Explain why, when we add $\frac{1}{4}+\frac{3}{8}$, we can change both fractions to a common denominator in order to find the sum.

Choose the correct answer below.

AWe can change both fractions to a common denominator so that they have equal-sized parts. We can't add different-sized parts. In this case, we can make the parts the same size. We have $\frac{1}{4}=\frac{2}{8}$ and so $\frac{1}{4}+\frac{3}{8}=\frac{2}{8}+\frac{3}{8}=\frac{2+3}{8}=\frac{5}{8}$.
BWe can change both fractions to a common numerator so that they have equal-sized parts. We can't add different-sized parts. In this case, we can make the parts the same size. We have $\frac{1}{4}=\frac{3}{12}$ and so $\frac{1}{4}+\frac{3}{8}=\frac{3}{12}+\frac{3}{8}=\frac{3}{12+8}=\frac{3}{20}$.
CWe can change both fractions to a common denominator so that they have equal-sized parts. We can't add different-sized parts. In this case, we can make the parts the same size. We have $\frac{1}{4}=\frac{1}{8}$ and so $\frac{1}{4}+\frac{3}{8}=\frac{1}{8}+\frac{3}{8}=\frac{1+3}{8}=\frac{4}{8}=\frac{1}{2}$.
DWe can change both fractions to a common denominator so that they have equal-sized parts. We can't add different-sized parts. In this case, we can make the parts the same size. We have $\frac{1}{4}=\frac{2}{8}$ and so $\frac{1}{4}+\frac{3}{8}=\frac{2}{8}+\frac{3}{8}=\frac{2+3}{8+8}=\frac{5}{16}$.

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-01T21:40:23-05:00

To add fractions, convert them to a common denominator to ensure parts are of equal size.
$\frac{1}{4}$ converts to $\frac{2}{8}$.
Add the numerators of the common-denominator fractions: $\frac{2}{8} + \frac{3}{8} = \frac{2+3}{8} = \frac{5}{8}$.
Option A is the only choice that reflects this correct logic and calculation.
Final Answer: $\boxed{A}$

Explanation

Understanding the Need for a Common Denominator

To add fractions like $\frac{1}{4}$ and $\frac{3}{8}$, it is essential that the parts we are adding are of the same size. A fraction represents parts of a whole, and the denominator tells us how many equal-sized parts the whole is divided into. Here, $\frac{1}{4}$ means 1 part out of 4, while $\frac{3}{8}$ means 3 parts out of 8. Because these "parts" (fourths and eighths) have different sizes, we cannot add them directly. We must first convert them into a common unit of measurement, which is done by finding a common denominator.

Converting and Adding the Fractions

The denominators are 4 and 8. The least common multiple of 4 and 8 is 8. Therefore, we want both fractions to have 8 as the denominator. We already have $\frac{3}{8}$. For $\frac{1}{4}$, we can multiply both the numerator and the denominator by 2 to keep the value the same:
\[\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}\]
Now both fractions have the same denominator, allowing us to combine the parts:
\[\frac{1}{4} + \frac{3}{8} = \frac{2}{8} + \frac{3}{8}\]
When the denominators are the same, we simply add the numerators and keep the denominator constant:
\[\frac{2 + 3}{8} = \frac{5}{8}\]

Conclusion

Comparing our result and reasoning with the provided options:

Option A correctly states that we need equal-sized parts, performs the conversion $\frac{1}{4} = \frac{2}{8}$, and correctly adds the numerators while keeping the denominator the same to get $\frac{5}{8}$.
Option B suggests using a common numerator and performs an incorrect addition.
Option C uses an incorrect conversion ($\frac{1}{4} = \frac{1}{8}$).
Option D correctly converts the fraction but uses an incorrect addition rule ($8+8=16$).

Therefore, Option A is the correct answer. The smallest possible value is $\boxed{A}$.

Examples

Adding fractions with different denominators is like trying to add different currencies without converting them to a common base. For example, if you have 1/4 of a dollar (25 cents) and 3/8 of a dollar (37.5 cents), you can't just add "1" and "3" to get 4. Instead, you convert them both to the same unit (cents) to get 25 + 37.5 = 62.5 cents, or 5/8 of a dollar. This process of finding a "common denominator" ensures that you are adding comparable values, just like converting different units into a standard, universal unit in measurement or finance.