Comparing Fractions
Which fraction is larger, or ? Don't be fooled into thinking that is larger just because it has the larger bottom number. There are several ways to compare two fractions, and they can be best explained by example.

Use your intuition: "pizza" fractions. Visualize the fractions in terms of two pizzas, one cut into 8 slices and the other cut into 5 slices. The pizza that's cut into 5 slices has larger slices. If you eat 3 of them, you're eating more pizza than if you eat 3 slices from the other pizza. Thus, is larger than .  

Compare the fractions to known fractions like . Both and are close to . However, is more than , while is less than . Therefore, is larger than . Comparing fractions to is actually quite simple. The fraction is a little less than , which is the same as ; in a similar fashion, is a little more than , which is the same as . ( may sound like a strange fraction, but you can easily see that it's the same as by considering a pizza cut into 5 slices. If you were to eat half the pizza, you'd eat slices.)  

Change both fractions to decimals. Remember the fraction definition at the beginning of this lesson? A fraction means divide: Divide the top number by the bottom number. Changing to decimals is simply the application of this definition.  
Because 0.6 is greater than 0.375, the corresponding fractions have the same relationship: is greater than .  

Raise both fractions to higher terms. If both fractions have the same denominator, then you can compare their top numbers.  
Because 24 is greater than 15, the corresponding fractions have the same relationship: is greater than .  

Shortcut: cross multiply. "Cross multiply" the top number of one fraction with the bottom number of the other fraction, and write the result over the top number. Repeat the process using the other set of top and bottom numbers.  
Since 24 is greater than 15, the fraction under it, , is greater than . 
TipIt's time to take a look at your pocket change again! Only this time, you need less than a dollar. So if you found extra change in your pocket, now is the time to be generous and give it away. After you gather a pile of change that adds up to less than a dollar, write the amount of change you have in the form of a fraction. Then reduce the fraction to its lowest terms. You can do the same thing with time intervals that are less than an hour. How long till you have to leave for work, go to lunch, or begin your next activity for the day? Express the time as a fraction, and then reduce to lowest terms. 
Converting Fractions Sample Questions
 Reduce to lowest terms.
 Raise to 16ths.
Solutions
Question 1
Divide by 3:
Question 2
1.  Divide the old bottom number (8) into the new one (16):  
2.  Multiply the quotient (2) by the old top number (3):  2 ×3=6 
3.  Write the product (6) over the new bottom number (16):  
4.  Check: Reduce the new fraction to make sure you get back the original. 
Find practice problems and solutions for these concepts at Converting Fractions Practice Questions.
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