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Chapter 4: Problem 69

Convert the improper fraction to a mixed number. $$-\frac{27}{10}$$

Short Answer

Expert verified
The mixed number is \(-2\frac{7}{10}\).

Step by step solution

01

Divide the Numerator by the Denominator

To convert the improper fraction \(-\frac{27}{10}\) into a mixed number, first divide 27 by 10. This gives a quotient and a remainder. So, 27 divided by 10 equals 2 with a remainder of 7.
02

Write the Quotient as the Whole Number Part

Since the quotient is 2, this will be the whole number part of the mixed number.
03

Form the Fraction Part

The remainder becomes the numerator of the fractional part. The denominator remains the same. Hence, the fractional part will be \(-\frac{7}{10}\).
04

Combine the Whole Number and Fraction Parts

The improper fraction \(-\frac{27}{10}\) is converted to the mixed number \(-2\frac{7}{10}\).

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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 essential for converting improper fractions to mixed numbers. An improper fraction has a numerator larger than its denominator, such as \(-\frac{27}{10}\). To start, divide the numerator by the denominator. For \(-\frac{27}{10}\), this means dividing 27 by 10. This step helps us break down an improper fraction into more manageable parts. Important points to remember:
  • The quotient represents the whole number part of the mixed number.
  • The remainder will form the numerator of the fractional part.
Mastering this division technique is key to understanding other related mathematical concepts.
Quotient and Remainder
Understanding quotient and remainder is vital for fraction division. When dividing 27 by 10, we get:
  • Quotient: 2 (as 10 goes into 27 two times)
  • Remainder: 7 (since 10 times 2 equals 20, and 27 minus 20 is 7)
The quotient (2) tells us how many whole units we have. The remainder (7) indicates what's left over. This leftover part turns into the numerator of our fraction in the mixed number form. For our example, \(-\frac{27}{10}\) becomes \(-2\frac{7}{10}\). Remember, quotient and remainder are two fundamental aspects of working with fractions and mixed numbers.
Mixed Numbers
A mixed number is a way to express an improper fraction. It consists of a whole number part and a fractional part. In our example, the improper fraction \(-\frac{27}{10}\) converts to the mixed number \(-2\frac{7}{10}\).
  • Whole Number Part: The quotient (2) becomes the whole number part.
  • Fractional Part: The remainder (7) forms the numerator while the denominator remains the same (10).
Putting it together: the negative sign means we鈥檙e dealing with negative values, making our final answer \(-2\frac{7}{10}\). Mixed numbers simplify improper fractions and make them easier to understand and work with.

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Most popular questions from this chapter

Simplify to lowest terms by first reducing the powers of 10. $$\frac{720}{800}$$

Simplify to lowest terms by first reducing the powers of 10. $$-\frac{2000}{1500}$$

Simplify the expression. $$\frac{16 a b}{10 a}$$

Label the fraction as proper or improper. $$\frac{2}{3}$$

True or false? Suppose \(m\) and \(n\) are nonzero numbers, where \(m>n .\) Then \(\frac{n}{m}\) is a proper fraction.
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