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Chapter 4: Problem 62

How many fifths are in \(2 \frac{3}{5} ?\)

Short Answer

Expert verified
There are 13 fifths in 2\( \frac{3}{5} \).

Step by step solution

01

Convert the Mixed Number to an Improper Fraction

To convert the mixed number to an improper fraction, multiply the whole number by the denominator of the fractional part and add the numerator. Thus, for the mixed number 2\( \frac{3}{5} \), multiply 2 by 5 and add 3: \[ 2 \times 5 + 3 = 10 + 3 = 13 \]. The improper fraction is \( \frac{13}{5} \).
02

Identify the Denominator (Fifths)

The goal is to determine how many fifths are in the improper fraction. Here, since the fraction is \( \frac{13}{5} \), the number of fifths is represented by the numerator, which is 13.

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Key Concepts

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

mixed numbers
Mixed numbers combine a whole number and a fraction. They are used when a value is more than one but not a whole number. For example, 2 3/5 consists of 2 (a whole number) and 3/5 (a fraction). Using and understanding mixed numbers helps in everyday life, like measuring ingredients for a recipe. Converting mixed numbers to improper fractions simplifies mathematical operations.
improper fractions
An improper fraction has a numerator larger than its denominator, such as 13/5. Converting mixed numbers to improper fractions is helpful because it can make calculations easier. Here's how you do it: multiply the whole number by the denominator of the fraction, then add the numerator. For example, to convert 2 3/5, you do 2 * 5 + 3 = 13. The result is the improper fraction 13/5.
fraction conversion
Fraction conversion involves changing one form of a fraction to another. Converting mixed numbers to improper fractions is a common type of fraction conversion. This step is important for performing arithmetic operations like addition, subtraction, multiplication, and division more easily. Once an improper fraction is achieved, it can often be simplified or converted back to a mixed number if needed.
denominator and numerator
Fractions are made up of a numerator and a denominator. The numerator is the top number and represents how many parts are considered. The denominator is the bottom number and shows the total number of equal parts in the whole. For example, in the fraction 13/5, 13 is the numerator and 5 is the denominator. In the conversion exercise, we identified the fifths as the denominator, and the numerator told us how many fifths (13) there are. Understanding these components is crucial for fraction conversion.

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Most popular questions from this chapter

Write three fractions equivalent to \(\frac{3}{4}\)

Convert the improper fraction to a mixed number. $$\frac{13}{7}$$

Simplify to lowest terms by first reducing the powers of 10. $$-\frac{2000}{1500}$$

Convert the mixed number to an improper fraction. $$10 \frac{3}{5}$$

Simplify. $$\left|\frac{3}{20}\right|$$
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