Write $\frac{23}{5}$ as a mixed number.

Question

05-11-2026
Mathematics

Answered

Write $\frac{23}{5}$ as a mixed number.

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T20:01:31-05:00

Understand that the improper fraction $\frac{23}{5}$ requires division to convert it into a mixed number.
Divide $23$ by $5$ to obtain the quotient $4$ and the remainder $3$.
Use the quotient as the whole number part and the remainder as the numerator of the proper fraction.
Conclude that the mixed number is $\boxed{4 \frac{3}{5}}$.

Explanation

Problem Analysis

To convert the improper fraction $\frac{23}{5}$ into a mixed number, we first identify the components of the fraction. An improper fraction is one where the numerator is greater than or equal to the denominator. A mixed number consists of a whole number part and a proper fraction part. Here, the numerator is $23$ and the denominator is $5$.

Division of Numerator by Denominator

We perform long division to see how many times the denominator $5$ goes into the numerator $23$. Dividing $23$ by $5$:
$23 \div 5 = 4$ with a remainder.
To find the remainder, we calculate $23 - (4 \times 5) = 23 - 20 = 3$.
Thus, $23$ divided by $5$ gives a quotient of $4$ and a remainder of $3$.

Forming the Mixed Number

With the quotient of $4$ and the remainder of $3$, we can express the fraction as a mixed number. The quotient becomes the whole number part, and the remainder becomes the numerator of the fractional part, while the denominator remains $5$.
So, $\frac{23}{5} = 4 \frac{3}{5}$.

Final Answer

The improper fraction $\frac{23}{5}$ converted to a mixed number is $\boxed{4 \frac{3}{5}}$.

Examples

Imagine you are baking a batch of cookies and the recipe calls for $\frac{23}{5}$ cups of flour. Since standard measuring cups usually measure in whole units and small fractions, it is much easier to work with a mixed number. By converting $\frac{23}{5}$ to $4 \frac{3}{5}$, you can quickly measure out 4 full cups of flour and then add an extra $\frac{3}{5}$ cup, making the baking process more intuitive and straightforward.