Fractions Review - Online Tutor, Practice Problems & Exam Prep

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

Alright, guys. So let's continue with a video on comparing fractions. So when we have 2 fractions, how do we tell which one is larger than the other? The easiest way is you just literally do the division. You take the numerator, the top number, divide it by the bottom number, get a decimal, and then it's a lot easier to compare the decimals than just looking at fractions. So let's go ahead and start with this first one here, and then, why don't you guys pause the video and try these other ones. Cool.

So the first fraction we've got here is three-fourths. 34, we put that in our calculator. 3÷4 and we're going to get 0.75. 0.75. Alright. How about four-fifths? 4÷5 is going to give us 0.80. I'll put here and 0.8 is bigger than 0.75, so I'm gonna put our less than sign there. 0.8 is bigger. Four-fifths is the larger fraction. Alright. So why don't you guys try these ones and then we will continue together. Alright.

So, I'm assuming you tried it. Let's go on with 46 over 15. That comes out to be 3.07. I'm going to round it off to 3.07 there, and let's do 134, and we get 3.25. Alright. So 134 looks bigger. 3.07. So 134 is the bigger fraction. Let's try this one. Two seventeenths and three twenty-ninths. So 217 divided by 171 will give us approximately 0.118. I will round it off to there. And how about 329 gives us 0.103. Alright, so in this case, 0.118 is bigger, so two seventeenths is the bigger fraction here.

Let's go ahead and do this last one. 25÷40 gives us 0.625 and 60÷96 also gives us 0.625. So in this one, they are equal. Alright. So these are equal. There's no larger one. Cool. Alright. Let's move on here.

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.