Problem 11 Write the improper fraction as a... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 4: Problem 11

Write the improper fraction as a mixed number. $$-\frac{77}{6}$$

Short Answer

Expert verified

-12 \frac{5}{6}

Step by step solution

- Divide the Numerator by the Denominator

First, divide the numerator (-77) by the denominator (6). This will give the whole number part of the mixed number. Perform the division: $\frac{-77}{6} = -12 \text{ remainder } 5$

- Write the Mixed Number

The quotient (-12) is the whole number part of the mixed number, and the remainder (5) is the numerator of the fractional part over the original denominator (6). Therefore, the mixed number is: $-12 \frac{5}{6}$

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Key Concepts

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

Fractions

Fractions are a fundamental concept in mathematics representing a part of a whole. They consist of two parts: the numerator and the denominator. The numerator is the top number that signifies how many parts of the whole you have. The denominator is the bottom number that indicates the total number of equal parts the whole is divided into.

Understanding fractions is crucial as they are used in various real-life contexts such as measuring ingredients in a recipe, understanding time, and sharing things equally. In an improper fraction, the numerator is larger than the denominator, indicating that the fraction is greater than one whole unit.

Mixed Numbers

Mixed numbers are an essential concept when working with fractions. A mixed number is a combination of a whole number and a proper fraction (where the numerator is less than the denominator).

For example, the mixed number $-12 \frac{5}{6}$ means there are 12 whole parts and an additional part that is $\frac{5}{6}$ of the whole. Mixed numbers provide a more intuitive way to express quantities greater than one when dealing with improper fractions.

Division

Division is a mathematical operation used to determine how many times one number, called the divisor, can be subtracted from another number, called the dividend. This concept is vital when converting improper fractions to mixed numbers.

To change an improper fraction like $-\frac{77}{6}$ into a mixed number, divide 77 by 6. The integer part of the result becomes the whole number in the mixed number, and the remainder becomes the numerator of the fraction. This process helps simplify improper fractions and makes them easier to understand and work with.

Remainders

Remainders play a crucial role in division, especially when converting improper fractions to mixed numbers. A remainder is what is left over after division when the divisor does not evenly go into the dividend.

In the division of $-77 \div 6$, the remainder is 5. This remainder forms the numerator of the fractional part of the mixed number, while the original divisor (6) remains the denominator. Consequently, converting $-\frac{77}{6}$ to a mixed number involves writing the integer quotient (-12) and then expressing the remainder as a fraction over the original divisor, resulting in $-12 \frac{5}{6}$.

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91影视

Write the improper fraction as a mixed number. $$-\frac{77}{6}$$

Short Answer

Step by step solution

- Divide the Numerator by the Denominator

- Write the Mixed Number

Key Concepts

Fractions

Mixed Numbers

Division

Remainders

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