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Chapter 3: Problem 10

Convert to fraction notation. $$ 20 \frac{1}{5} $$

Short Answer

Expert verified
\(\frac{101}{5}\)

Step by step solution

01

Identify the Mixed Number Components

The given mixed number is 20 \(\frac{1}{5}\). Identify the whole number and the fractional part. Here, the whole number is 20 and the fractional part is \(\frac{1}{5}\).
02

Convert the Whole Number to a Fraction

Convert the whole number 20 to a fraction with the same denominator as the fractional part. Since the fraction part has a denominator of 5, convert 20 to \(\frac{20 \times 5}{5} = \frac{100}{5}\).
03

Add the Fractions Together

Add the two fractions together: \(\frac{100}{5}\) from the whole number and \(\frac{1}{5}\) from the fractional part. \(\frac{100}{5} + \frac{1}{5} = \frac{100 + 1}{5} = \frac{101}{5}\).

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Key Concepts

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

fraction notation
Fraction notation is a way of representing numbers that are not whole. It shows how many parts of a whole we have. A fraction is written as \(\frac{a}{b}\), where 'a' is the numerator and 'b' is the denominator. The numerator represents how many parts we have, while the denominator shows how many equal parts the whole is divided into. Understanding fraction notation is key for working with mixed numbers and adding fractions.
mixed numbers
A mixed number is a combination of a whole number and a fraction. For example, in 20 \(\frac{1}{5}\), 20 is the whole number, and \(\frac{1}{5}\) is the fractional part. To convert a mixed number to a fraction, we need to handle both parts. We turn the whole number into a fraction with the same denominator as our fractional part before adding them together. Mixed numbers are convenient but sometimes need converting to fractions for operations like addition.
fraction addition
Adding fractions involves combining fractions with the same denominator or making the denominators the same. In our exercise, we first converted 20 to a fraction \(\frac{100}{5}\) which has the same denominator as \(\frac{1}{5}\). Then we added the numerators, leaving the denominator the same: \[ \frac{100}{5} + \frac{1}{5} = \frac{101}{5}. \] Always remember, the key is to have common denominators before adding the numerators together.
denominator
The denominator is the number below the fraction line, telling us how many equal parts the whole is divided into. In our exercise, the fraction \(\frac{1}{5}\) has a denominator of 5. The whole number 20 needs to be converted to a fraction with this same denominator to combine it properly. Ensuring both fractions have the same denominator is essential for accurate fraction operations. Here, we did \[ 20 \times \frac{5}{5} = \frac{100}{5} \] to match the denominator.

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Most popular questions from this chapter

Simplify. Classify the given numbers as prime, composite, or neither. \([2.1 \mathrm{c}]\) $$ 1,5,7,9,14,23,43 $$

Simplify. $$ 5 \cdot 2^{2} \div 10 \quad[1.9 \mathrm{c}] $$

A tile \(\frac{5}{8}\) in. thick is glued to a board \(\frac{7}{8}\) in. thick. The glue is \(\frac{3}{32}\) in. thick. How thick is the result?

Use a calculator to arrange the following in order from smallest to largest. $$ \frac{3}{4}, \frac{17}{21}, \frac{13}{15}, \frac{7}{9}, \frac{15}{17}, \frac{13}{12}, \frac{19}{22} $$

Simplify. $$ \left(\frac{3}{4}\right)^{2}+3 \frac{1}{2} \div 1 \frac{1}{4} $$
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