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Chapter 4: Problem 457

In the following exercises, find the difference. $$2 \frac{5}{12}-1 \frac{7}{12}$$

Short Answer

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Step by step solution

01

Convert Mixed Numbers to Improper Fractions

Convert the mixed numbers to improper fractions. For denom + numerator

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Key Concepts

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

Mixed Numbers
A mixed number is a combination of a whole number and a fraction. For example, in the mixed number \(2 \frac{5}{12}\), 2 is the whole number, and \(\frac{5}{12}\) is the fraction.
Mixed numbers are often used in everyday situations, like measuring ingredients or dividing objects. To work with fractions in mathematical problems, it's easier to first convert mixed numbers to improper fractions. Understanding this will help you simplify subtraction, addition, and other operations involving fractions.
Improper Fractions
An improper fraction is when the numerator (the top number) is larger than or equal to the denominator (the bottom number). For example, \(\frac{17}{12}\) is an improper fraction.
To convert a mixed number to an improper fraction, follow these steps:
  • Multiply the whole number by the denominator.
  • Add the result to the numerator.
  • Place this sum above the original denominator.

For example, to convert \(2 \frac{5}{12}\) to an improper fraction:
  • Multiply 2 (the whole number) by 12 (the denominator): \(2 \times 12 = 24\).
  • Add the numerator: \(24 + 5 = 29\).
  • Place the result over the original denominator: \(\frac{29}{12}\).

Doing this for the other mixed number in your problem \(1 \frac{7}{12}\) gives:
  • Multiply 1 by 12: \(1 \times 12 = 12\).
  • Add the numerator: \(12 + 7 = 19\).
  • Place the result over the original denominator: \(\frac{19}{12}\).
By converting both mixed numbers, we can now easily work with improper fractions for subtraction or any other operations.
Finding Difference
To find the difference between two fractions, make sure they have the same denominator. In our example, both fractions \(\frac{29}{12}\) and \(\frac{19}{12}\) already have the same denominator, which is 12.
Now, follow these steps to subtract them:
  • Subtract the numerators: \(29 - 19 = 10\).
  • Keep the same denominator: \(12\).
  • The result is the improper fraction: \(\frac{10}{12}\).

Simplify the fraction if possible. Both 10 and 12 can be divided by 2:
  • Divide the numerator by 2: \(10 \rightarrow 5\).
  • Divide the denominator by 2: \(12 \rightarrow 6\).
  • The simplified fraction is \(\frac{5}{6}\).

So, the difference between \(2 \frac{5}{12}\) and \(1 \frac{7}{12}\) is \(\frac{5}{6}\). Simplifying fractions will give you the most precise and easy-to-understand answer.

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Most popular questions from this chapter

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(\frac{m+n}{p}\) when \(m=-6, n=-2, p=4\)

In the following exercises, solve the equation. $$ n+\frac{9}{11}=\frac{4}{11} $$

In the following exercises, simplify. $$ \frac{2}{5}+\left(-\frac{7}{5}\right) $$

In the following exercises, solve the equation. $$ \frac{m}{-2}=-16 $$

In the following exercises, perform the indicated operations and simplify. $$-\frac{11}{36}-\frac{11}{20}$$
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