$5 \frac{1}{4}-2 \frac{3}{4}=3 \frac{2}{4}=3 \frac{1}{2}$

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Tascha914 Tascha914

04-11-2026
Mathematics

Answered

$5 \frac{1}{4}-2 \frac{3}{4}=3 \frac{2}{4}=3 \frac{1}{2}$

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-04T20:04:14-05:00

Convert the mixed numbers $5 \frac{1}{4}$ and $2 \frac{3}{4}$ to improper fractions: $\frac{21}{4}$ and $\frac{11}{4}$.
Subtract the improper fractions: $\frac{21}{4} - \frac{11}{4} = \frac{10}{4}$.
Simplify the resulting fraction to $\frac{5}{2}$.
Convert back to the mixed number form, resulting in $\boxed{2 \frac{1}{2}}$.

Explanation

Problem Analysis

We need to evaluate the difference between two mixed numbers: $5 \frac{1}{4} - 2 \frac{3}{4}$. The objective is to find the correct result and simplify it to its simplest form. To subtract mixed numbers efficiently, we can either subtract the whole parts and fractional parts separately or convert both to improper fractions. In this case, since the fractional part of the first number is smaller than the fractional part of the second, converting to improper fractions is the most straightforward approach.

Converting and Subtracting Fractions

First, we convert both mixed numbers into improper fractions.
For $5 \frac{1}{4}$:
\[5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}\]
For $2 \frac{3}{4}$:
\[2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}\]
Now, we perform the subtraction:
\[\frac{21}{4} - \frac{11}{4} = \frac{21 - 11}{4} = \frac{10}{4}\]

Simplifying the Result

Finally, we simplify the improper fraction $\frac{10}{4}$. Dividing both the numerator and the denominator by their greatest common divisor, which is 2, we get:
\[\frac{10 \div 2}{4 \div 2} = \frac{5}{2}\]
Converting the fraction $\frac{5}{2}$ back into a mixed number:
\[\frac{5}{2} = 2 \frac{1}{2}\]
Thus, the correct value of $5 \frac{1}{4} - 2 \frac{3}{4}$ is $2 \frac{1}{2}$.

Examples

This type of subtraction is common in everyday situations, such as cooking or construction. For instance, if you have a board that is $5 \frac{1}{4}$ inches long and you need to cut off a piece that is $2 \frac{3}{4}$ inches, calculating the remaining length is a practical application of subtracting mixed numbers. Accurate calculation ensures you have the right amount of material for your project.