Problem 4 Use $=$ or $\neq$ to make a ... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 6: Problem 4

Use $=$ or $\neq$ to make a true statement. $$\frac{2}{5} \square \frac{21}{55}$$

Short Answer

Expert verified

$ \frac{2}{5} eq \frac{21}{55} $

Step by step solution

- Compare fractions

To compare the fractions $ \frac{2}{5} $ and $ \frac{21}{55} $, find a common denominator or convert each fraction to decimal form.

- Convert to decimal

Convert each fraction to decimal form:\[\frac{2}{5} = 0.4\] and \[\frac{21}{55} = \frac{21}{55} \approx 0.3818\]

- Compare decimal values

Now compare the decimal values: $0.4$ and approximately $0.3818$. Since $0.4 > 0.3818$, we establish the inequality.

- Conclude the comparison

Write the statement with the correct symbol: $ \frac{2}{5} eq \frac{21}{55}$

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Key Concepts

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

common denominator

When comparing fractions, one helpful method is finding a common denominator. This means converting the fractions so they have the same bottom number. For example, to compare $\frac{2}{5}$ and $\frac{21}{55}$, we find a common denominator for 5 and 55. In this case, 55 can be the common denominator because 5 multiplies evenly into 55.

Converting $\frac{2}{5}$ with a denominator of 55 involves multiplying both the numerator and the denominator by 11:
$\frac{2 \times 11}{5 \times 11} = \frac{22}{55}$.

Now we can directly compare $\frac{22}{55}$ and $\frac{21}{55}$. It's clear $\frac{22}{55}$ is greater because 22 is more than 21.

decimal form

Another method to compare fractions is converting them to their decimal forms. This involves performing the division described by the fraction.

For instance:

$\frac{2}{5}$ as a decimal is $2 \div 5 = 0.4$.
$\frac{21}{55}$ as a decimal is approximately $\frac{21}{55} = 0.3818$.

With the decimals available, we can easily see that 0.4 is greater than 0.3818. This method can be especially useful when dealing with more complex fractions or when a common denominator is not readily apparent.

inequality

Inequality symbols are used to compare values, indicating if one is greater than, less than, or equal to another. Common inequality symbols include:

$>$ (greater than)
$<$ (less than)
$=$ (equal to)

In our original exercise, we compare $\frac{2}{5}$ and $\frac{21}{55}$. By finding that $\frac{2}{5}$ is greater than $\frac{21}{55}$, we would use the symbol $>$. Thus, the true statement is $\frac{2}{5} > \frac{21}{55}$.

Using inequality symbols clearly communicates the relationship between the fractions.

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91影视

Use \(=\) or \(\neq\) to make a true statement. $$\frac{2}{5} \square \frac{21}{55}$$

Short Answer

Step by step solution

- Compare fractions

- Convert to decimal

- Compare decimal values

- Conclude the comparison

Key Concepts

common denominator

decimal form

inequality

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