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Chapter 4: Problem 10

Write the mixed number as an improper fraction. $$2 \frac{7}{10}$$

Short Answer

Expert verified
\(\frac{27}{10}\)

Step by step solution

01

Understand the Mixed Number

A mixed number consists of a whole number and a fractional part. In this case, the mixed number is \(2 \frac{7}{10}\).
02

Convert the Whole Number to a Fraction

To convert the whole number to a fraction, multiply the whole number by the denominator of the fractional part. Here, \(2\) multiplied by \(10\) equals \(20\). So, \(2\) can be represented as \( \frac{20}{10} \).
03

Add the Fractional Part

Next, add the fractional part \(\frac{7}{10}\) to the fraction obtained from the whole number. So, \(\frac{20}{10} + \frac{7}{10}\).
04

Combine the Fractions

When adding fractions with the same denominator, simply add the numerators while keeping the denominator the same. \(\frac{20}{10} + \frac{7}{10} = \frac{27}{10}\).

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Key Concepts

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

Improper Fractions
To understand how to convert a mixed number to an improper fraction, you first need to know what an improper fraction is. An improper fraction has a numerator that is greater than or equal to its denominator. This makes it top-heavy.

For example, in the fraction \(\frac{27}{10}\), the numerator 27 is greater than the denominator 10. This qualifies it as an improper fraction. Improper fractions are useful in various mathematical operations, such as addition and subtraction of fractions. They help keep expressions simpler and uniform.
Mixed Numbers
A mixed number combines a whole number and a fraction. Examples include \(2 \frac{7}{10}\).
Mixed numbers are often easier to understand because they clearly indicate the quantity of whole items along with the part.

To convert a mixed number like \(2 \frac{7}{10}\) to an improper fraction:
  • First, multiply the whole number (2) by the denominator (10) to turn it into a fraction. This gives you \( \frac{20}{10}\).
  • Next, add the fractional part \( \frac{7}{10} \) to \( \frac{20}{10} \).
  • Finally, you get \( \frac{27}{10} \) as the improper fraction.
This conversion is essential for adding or subtracting fractions effectively.
Fraction Addition
Adding fractions is straightforward when they have the same denominator.

For example, when converting \(2 \frac{7}{10}\) to an improper fraction, you deal with \( \frac{20}{10} \) and \( \frac{7}{10} \). Because the denominators are the same (10), you simply add the numerators: 20 + 7.

Here鈥檚 how:
  • Keep the denominator the same.
  • Add the numerators: 20 + 7 = 27.
So, \( \frac{20}{10} + \frac{7}{10} = \frac{27}{10}\).
This rule applies to any fraction addition where the denominators match. If they don鈥檛, you must first find a common denominator.

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