Write $\frac{10}{3}$ as a mixed number.

Question

05-11-2026
Mathematics

Answered

Write $\frac{10}{3}$ as a mixed number.

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T20:00:57-05:00

Divide the numerator (10) by the denominator (3) to find the quotient and remainder.
The quotient is 3 and the remainder is 1.
Write the mixed number as the quotient followed by the remainder over the denominator: $\boxed{3 \frac{1}{3}}$.

Explanation

Problem Analysis and Methodology

To convert an improper fraction $\frac{10}{3}$ to a mixed number, we perform integer division of the numerator (10) by the denominator (3). A mixed number is represented as $q \frac{r}{d}$, where $q$ is the quotient, $r$ is the remainder, and $d$ is the original denominator.

Performing Integer Division

We divide 10 by 3:
\[10 \div 3 = 3 \text{ with a remainder of } 1\]
This is because $3 \times 3 = 9$, and $10 - 9 = 1$. Therefore, the quotient $q = 3$ and the remainder $r = 1$.

Final Result Representation

Using the quotient $q = 3$ and the remainder $r = 1$, we place them into the format $q \frac{r}{d}$:
\[\frac{10}{3} = 3 \frac{1}{3}\]
Thus, the improper fraction $\frac{10}{3}$ written as a mixed number is $3 \frac{1}{3}$.

Examples

Imagine you are baking cookies and the recipe calls for $\frac{10}{3}$ cups of flour. Since measuring cups usually come in whole units and fractions, it is much easier to visualize this as $3 \frac{1}{3}$ cups. You would fill your measuring cup three times completely, and then fill it one-third of the way for the last measurement, making your task in the kitchen simpler and more precise.