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Chapter 3: Problem 20

Convert to fraction notation. $$ 1 \frac{3}{5} $$

Short Answer

Expert verified
\( \frac{8}{5} \)

Step by step solution

01

Identify the Mixed Number Components

The mixed number given is 1 \( \frac{3}{5} \). This consists of a whole number part (1) and a fractional part ( \( \frac{3}{5} \) ).
02

Convert the Whole Number to a Fraction

Convert the whole number 1 to a fraction with the same denominator as the fractional part. Thus, 1 becomes \( \frac{5}{5} \) since any number divided by itself is 1.
03

Combine the Fractional Parts

Add the fractions together: \( \frac{5}{5} + \frac{3}{5} \). They have the same denominator, so we can add the numerators directly: \[ \frac{5 + 3}{5} = \frac{8}{5} \].

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Key Concepts

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

Mixed Number
A mixed number is a number that consists of both an integer (whole number) and a proper fraction. For example, in the problem given, we have the mixed number 1 \( \frac{3}{5} \). The number 1 represents the whole part, and \( \frac{3}{5} \) represents the fractional part.
Mixed numbers are used to express quantities that are larger than one but not whole. Some everyday examples include saying 'one and a half hours' or 'two and three-quarters cups of flour.' These mixed numbers are easier to understand and visualize compared to improper fractions.
Fraction Addition
Adding fractions is especially important when handling mixed numbers like 1 \( \frac{3}{5} \). To add fractions, they must have the same denominator. This makes it easier to combine them.
For example, let's consider the fractions \( \frac{5}{5} \) and \( \frac{3}{5} \) from our solution. Since both fractions have the same denominator (5), we simply add their numerators: \[ \frac{5}{5} + \frac{3}{5} = \frac{8}{5} \].
Remember these key steps while adding fractions:
  • Ensure the denominators are the same.
  • Add only the numerators.
  • Keep the denominator unchanged.
If the denominators are not the same, you may need to find a common denominator first.
Improper Fraction
Once we convert a mixed number to a fraction, it often becomes an improper fraction. An improper fraction has a numerator larger than its denominator.
In our example, after converting 1 \( \frac{3}{5} \) to a fraction, we got \( \frac{8}{5} \). Here, 8 (the numerator) is greater than 5 (the denominator), making it an improper fraction.
Improper fractions are helpful in various calculations because they make mathematical operations more straightforward, especially in algebra.
Always remember:
  • A mixed number can always be converted to an improper fraction.
  • Improper fractions help in performing arithmetic operations easily.
  • You can also convert an improper fraction back to a mixed number if needed.

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Most popular questions from this chapter

Add and simplify. $$ \frac{8}{10}+\frac{7}{100}+\frac{4}{1000} $$

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

A cubic meter of concrete mix contains \(420 \mathrm{~kg}\) of cement, \(150 \mathrm{~kg}\) of stone, and \(120 \mathrm{~kg}\) of sand. What is the total weight of a cubic meter of the mix? What part is cement? stone? sand? Add these fractional amounts. What is the result?

Simplify. $$ \frac{4}{7} \cdot \frac{7}{15}+\frac{2}{3} \div 8 $$

Simplify. $$ \frac{3}{4}-\frac{2}{3} \cdot\left(\frac{1}{2}+\frac{2}{5}\right) $$
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