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Chapter 3: Problem 46

Convert to a mixed numeral. $$ \frac{39}{9} $$

Short Answer

Expert verified
4 \frac{3}{9}

Step by step solution

01

- Divide the numerator by the denominator

Divide 39 by 9. The quotient will be the whole number part of your mixed numeral.
02

- Find the remainder

Determine the remainder of the division. This will be the numerator of the fractional part of your mixed numeral.
03

- Write the mixed numeral

Combine the quotient (the whole number part) with the remainder over the original denominator.

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Key Concepts

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

fraction division
Fraction division is the process of dividing one fraction by another. However, in some cases, like our example, we start with an improper fraction (a fraction where the numerator is greater than the denominator). To convert this improper fraction, \(\frac{39}{9}\), into a mixed numeral, we need to perform division.
quotient and remainder
When you divide 39 by 9, you get a quotient and a remainder. The quotient is the whole number part of your mixed numeral. In this case, 39 divided by 9 is 4 with a remainder of 3.
The division looks like this:

$$ 39 \div 9 = 4 \quad remainder \quad 3. $$

The quotient (4) will be the whole part, and the remainder (3) will be used in the fractional part.
converting improper fractions
To convert the improper fraction \(\frac{39}{9}\) to a mixed numeral, you combine the quotient and the remainder you got from division. The mixed numeral will have the quotient as the whole number part and the remainder over the original denominator as the fractional part.

The mixed numeral is then:

$$ 4 \frac{3}{9} $$

Simplify the fraction \(\frac{3}{9}\) by dividing both the numerator and denominator by their greatest common divisor (3):

$$ \frac{3}{9} = \frac{1}{3} $$

So, the mixed numeral becomes:

$$4 \frac{1}{3}.$$

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