Fractions Review: Videos & Practice Problems

To compare fractions, convert them to decimals by dividing the numerator by the denominator. For example, \( \frac{3}{4} = 0.75 \) and \( \frac{4}{5} = 0.8 \), making \( \frac{4}{5} \) larger. This method simplifies identifying larger fractions, as seen with \( \frac{2}{17} \) (0.118) and \( \frac{3}{29} \) (0.103), where \( \frac{2}{17} \) is greater. In cases like \( \frac{25}{40} \) and \( \frac{60}{96} \), both equal 0.625, indicating they are equivalent. Understanding these comparisons aids in grasping concepts like market equilibrium and competition.

Comparing Fractions

When comparing fractions, a straightforward method is to convert each fraction into a decimal by dividing the numerator (the top number) by the denominator (the bottom number). This approach simplifies the comparison, as it is often easier to evaluate decimal values than to compare fractions directly.

For example, to compare the fractions \( \frac{3}{4} \) and \( \frac{4}{5} \), you would perform the following calculations:

1. \( \frac{3}{4} = 3 \div 4 = 0.75 \)

2. \( \frac{4}{5} = 4 \div 5 = 0.80 \)

Since \( 0.80 \) is greater than \( 0.75 \), it follows that \( \frac{4}{5} \) is the larger fraction.

Continuing with another example, consider \( \frac{46}{15} \) and \( \frac{13}{4} \):

1. \( \frac{46}{15} = 46 \div 15 \approx 3.07 \)

2. \( \frac{13}{4} = 13 \div 4 = 3.25 \)

Here, \( 3.25 \) is greater than \( 3.07 \), indicating that \( \frac{13}{4} \) is the larger fraction.

For the fractions \( \frac{2}{17} \) and \( \frac{3}{29} \):

1. \( \frac{2}{17} = 2 \div 17 \approx 0.118 \)

2. \( \frac{3}{29} = 3 \div 29 \approx 0.103 \)

In this case, \( 0.118 \) is greater than \( 0.103 \), so \( \frac{2}{17} \) is the larger fraction.

Lastly, when comparing \( \frac{25}{40} \) and \( \frac{60}{96} \):

1. \( \frac{25}{40} = 25 \div 40 = 0.625 \)

2. \( \frac{60}{96} = 60 \div 96 = 0.625 \)

Both fractions yield the same decimal value, indicating that they are equal.

This method of converting fractions to decimals is a reliable technique for determining which fraction is larger or if they are equal, enhancing your ability to compare fractions effectively.

Here’s what students ask on this topic:

How do you compare fractions to determine which is larger?

To compare fractions, convert them to decimals by dividing the numerator by the denominator. For example, for the fractions $\frac{3}{4}$ and $\frac{4}{5}$, you would perform the divisions: $\frac{3}{4}=\; 0.75$ and $\frac{4}{5}=\; 0.8$. Since 0.8 is greater than 0.75, $\frac{4}{5}$ is the larger fraction. This method simplifies the comparison process, making it easier to identify which fraction is larger.

What is the decimal equivalent of the fraction $\frac{2}{17}$?

To find the decimal equivalent of the fraction $\frac{2}{17}$, divide the numerator by the denominator: $\frac{2}{17}=\; 0.118$. This means that $\frac{2}{17}$ is approximately 0.118 when expressed as a decimal.

How can you tell if two fractions are equal?

To determine if two fractions are equal, convert both fractions to their decimal forms by dividing the numerator by the denominator. If the resulting decimals are the same, the fractions are equal. For example, for the fractions $\frac{25}{40}$ and $\frac{60}{96}$, both convert to 0.625. Since the decimals are equal, the fractions $\frac{25}{40}$ and $\frac{60}{96}$ are equivalent.

Why is it easier to compare fractions by converting them to decimals?

Converting fractions to decimals simplifies the comparison process because it allows you to work with a single number rather than a ratio. Decimals are easier to compare directly, especially when dealing with fractions that have different denominators. For example, comparing $\frac{3}{4}$ (0.75) and $\frac{4}{5}$ (0.8) is straightforward because you can see that 0.8 is greater than 0.75. This method eliminates the need for finding a common denominator, making it a quicker and more intuitive approach.

What is the decimal form of the fraction $\frac{13}{4}$?

To convert the fraction $\frac{13}{4}$ to its decimal form, divide the numerator by the denominator: $\frac{13}{4}=\; 3.25$. Therefore, the decimal equivalent of $\frac{13}{4}$ is 3.25.