what common fraction is one third the way from 1/4 to 1/3

To find the fraction that is one-third of the way from \( \frac{1}{4} \) to \( \frac{1}{3} \), we can use the following approach:

### Step 1: Find the difference between \( \frac{1}{3} \) and \( \frac{1}{4} \)
We subtract \( \frac{1}{4} \) from \( \frac{1}{3} \):

\[
\frac{1}{3} - \frac{1}{4} = \frac{4}{12} - \frac{3}{12} = \frac{1}{12}
\]

### Step 2: Find one-third of that difference
Next, we calculate one-third of \( \frac{1}{12} \):

\[
\frac{1}{3} \times \frac{1}{12} = \frac{1}{36}
\]

### Step 3: Add that to \( \frac{1}{4} \)
Finally, we add \( \frac{1}{36} \) to \( \frac{1}{4} \) to find the point one-third of the way from \( \frac{1}{4} \) to \( \frac{1}{3} \).

To do this, we first need a common denominator between \( \frac{1}{4} \) and \( \frac{1}{36} \). The least common denominator (LCD) between 4 and 36 is 36.

\[
\frac{1}{4} = \frac{9}{36}
\]

Now, add \( \frac{9}{36} \) and \( \frac{1}{36} \):

\[
\frac{9}{36} + \frac{1}{36} = \frac{10}{36}
\]

### Step 4: Simplify the fraction
Finally, simplify \( \frac{10}{36} \):

\[
\frac{10}{36} = \frac{5}{18}
\]

### Final Answer:
The fraction that is one-third of the way from \( \frac{1}{4} \) to \( \frac{1}{3} \) is \( \frac{5}{18} \).

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Would you like more details or clarification? Here are some additional related questions you might find interesting:

1. How do you calculate the midpoint between two fractions?
2. What is the process for converting fractions to decimals?
3. How do you add or subtract fractions with different denominators?
4. Can this method be used to find the fraction halfway between two numbers?
5. How do you find a fraction that is a specific proportion between two other fractions?

**Tip**: When adding or subtracting fractions, always make sure you have a common denominator before combining the numerators!

What common fraction is one third the way from 1/4 to 1/3?

Learn how to calculate the fraction that is one-third of the way from 1/4 to 1/3 using step-by-step methods. This problem involves fraction subtraction, finding a portion of a difference, and adding fractions with different denominators. Suitable for students in Grades 5-7.

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