Problem 40 Convert to a mixed numeral. $$... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 3: Problem 40

Convert to a mixed numeral. $$ \frac{89}{10} $$

Short Answer

Expert verified

8 \frac{9}{10}

Step by step solution

Divide the Numerator by the Denominator

Perform the division $\frac{89}{10}$. 89 divided by 10 equals 8 with a remainder of 9. This tells us that the whole number part of the mixed numeral is 8.

Write the Remainder Over the Denominator

The remainder from the division in Step 1 is 9. Write this remainder over the original denominator (10), forming the fraction $\frac{9}{10}$.

Combine the Whole Number and the Fraction

Combine the whole number from Step 1 (which is 8) with the fraction from Step 2 $\frac{9}{10}$ to form the mixed numeral. The mixed numeral is $8 \frac{9}{10}$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

fractions

Fractions are a way to represent parts of a whole. They consist of two parts: a numerator and a denominator. The numerator is the number on top and it represents the part of the whole we are focusing on. The denominator is the number on the bottom and it indicates how many equal parts the whole is divided into.
For example, in the fraction $ \frac{89}{10} $, 89 is the numerator and 10 is the denominator. Here, we are dividing 89 into 10 equal parts.
Understanding fractions is crucial for converting improper fractions (where the numerator is larger than the denominator) to mixed numerals, which show a whole number combined with a proper fraction.

division

Division is a mathematical process where you split a larger number into equal smaller parts. When dealing with fractions, especially improper fractions, division helps to find how many whole parts are there and what is left over.
In our example of converting $ \frac{89}{10} $ into a mixed numeral, we first divide 89 by 10. When we perform this division, 89 divided by 10 equals 8. This tells us that we have 8 whole parts.
But the division doesn鈥檛 always result in a clean break; often, there is something left over, which we refer to as the remainder.

remainder

The remainder is what is left after performing a division. It represents a portion of the whole that isn't enough to form another complete part.
For example, after dividing 89 by 10, we get a quotient of 8, but there is a remainder of 9. This remainder becomes the numerator of the fraction part when writing a mixed numeral.
So, our remainder 9 goes over our original denominator 10, forming the fraction $ \frac{9}{10} $.
Combining this fraction with the whole number 8, we get the mixed numeral $ 8 \frac{9}{10} $. Understanding remainders is key to working with mixed numerals efficiently.

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91影视

Convert to a mixed numeral. $$ \frac{89}{10} $$

Short Answer

Step by step solution

Divide the Numerator by the Denominator

Write the Remainder Over the Denominator

Combine the Whole Number and the Fraction

Key Concepts

fractions

division

remainder

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