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Chapter 2: Problem 95

Find 8 less \(1 \frac{7}{12}.\)

Short Answer

Expert verified
The result of subtracting 8 from \(1 \frac{7}{12}\) is \(-6\frac{5}{12}\)

Step by step solution

01

Convert Mixed Fraction to Improper Fraction

The mixed number \(1 \frac{7}{12}\) is converted to an improper fraction. An improper fraction is obtained by multiplying the denominator and the whole number, and then adding the numerator. Therefore, for our problem, the mixed fraction \(1 \frac{7}{12}\) will then be \(12*1 + 7 = 19\), giving us \(\frac{19}{12}\)
02

Convert Subtracted Number to Fraction

The number 8 that needs to be subtracted should be converted to a fraction with the same denominator. Here, 8 is equivalent to \(\frac{96}{12}\) as \(8*12 = 96\). Now the two fractions can be compared.
03

Subtract Fractions

Now, the subtraction can be performed. When subtracting fractions, subtract the numerators and keep the denominator the same. So, \(\frac{19}{12} - \frac{96}{12} = \frac{-77}{12}\). This equates to \(-6\frac{5}{12}\).

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Key Concepts

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

Improper Fraction
An improper fraction is a type of fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). Understanding improper fractions is essential when you're dealing with mixed numbers in mathematical operations because very often mixed numbers need to be converted into improper fractions to simplify calculations.

For example, if you have a fraction like \( \frac{5}{3} \), this is an improper fraction because 5 (the numerator) is larger than 3 (the denominator). Improper fractions may seem more complicated at first, but they actually make it easier to perform operations such as addition, subtraction, multiplication, and division.
Subtracting Fractions
Subtracting fractions involves taking one fraction away from another. The most important thing to remember is that to subtract fractions, they must have the same denominator. If the denominators are different, you must find a common denominator before you can subtract the numerators. Once the denominators are the same, subtract the numerators and keep the denominator unchanged.

  • Identify if fractions have the same denominator.
  • If they do not, convert them to equivalent fractions with a common denominator.
  • Subtract the numerators, keeping the denominator the same.
The result may be an improper fraction, which can be left as-is or converted into a mixed number for ease of understanding and interpretation.
Mixed Number to Improper Fraction Conversion
Converting a mixed number to an improper fraction is a pivotal step in subtracting mixed fractions. A mixed number includes both a whole number and a fraction. To convert it to an improper fraction, follow this process:

  • Multiply the whole number by the denominator of the fraction part.
  • Add the result to the numerator of the fraction part.
  • Write this new number as the numerator and keep the original denominator.
For example, to convert \(1 \frac{7}{12}\) to an improper fraction, multiply the whole number 1 by the denominator 12 to get 12. Then add the numerator 7 to obtain 19. The improper fraction is then \(\frac{19}{12}\). This process simplifies complex fractional arithmetic by turning it into simpler improper fractions that are easier to manage.

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