Write $8 \frac{4}{17}$ as an improper fraction.

Question

mitajo21 mitajo21

05-11-2026
Mathematics

Answered

Write $8 \frac{4}{17}$ as an improper fraction.

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T20:05:41-05:00

Identify the parts of the mixed number: integer part $A=8$, numerator $B=4$, and denominator $C=17$.
Apply the conversion formula: $A \frac{B}{C} = \frac{A \times C + B}{C}$.
Calculate the numerator: $8 \times 17 + 4 = 136 + 4 = 140$.
State the resulting improper fraction: $\boxed{\frac{140}{17}}$.

Explanation

Analysis of the Mixed Number

A mixed number is composed of an integer part and a fractional part. For any mixed number of the form $A \frac{B}{C}$, where $A$ is the whole number, $B$ is the numerator, and $C$ is the denominator, it represents the sum $A + \frac{B}{C}$. Our objective is to convert the mixed number $8 \frac{4}{17}$ into an improper fraction, which is a fraction where the numerator is greater than or equal to the denominator. To do this, we use the identity $A \frac{B}{C} = \frac{A \cdot C + B}{C}$. Here, we have $A = 8$, $B = 4$, and $C = 17$.

Converting to an Improper Fraction

To convert the mixed number to an improper fraction, we first multiply the integer part by the denominator of the fractional part:
\[8 \times 17\]
Calculating this product, we find that $8 \times 10 = 80$ and $8 \times 7 = 56$, so:
\[8 \times 17 = 80 + 56 = 136\]
Next, we add the numerator of the fractional part, which is $4$, to this product:
\[136 + 4 = 140\]
Finally, we place this sum over the original denominator, which is $17$, to get the improper fraction:
\[\frac{140}{17}\]

Final Conclusion

The mixed number $8 \frac{4}{17}$ is equivalent to the improper fraction $\frac{140}{17}$. We have successfully represented the sum as a single fraction where the numerator is 140 and the denominator is 17. The final result is $\boxed{\frac{140}{17}}$.

Examples

Converting mixed numbers to improper fractions is a fundamental skill in arithmetic, especially when performing operations like addition or multiplication with fractions. For instance, if you are following a recipe that calls for $8 \frac{4}{17}$ cups of flour and you need to scale the recipe, working with the improper fraction $\frac{140}{17}$ makes it much easier to multiply by a scaling factor. This mathematical foundation allows for seamless calculations in everyday measurements, cooking, or engineering tasks where precise quantities are essential.