Standard 4NF2 I can compare 2 fractions with different numerators and different denominators.

What you should already know Fractions represent parts of a whole The numerator is the top number Represents the number of pieces in question The denominator is the bottom number Represents the number of equal pieces that make the whole One of you has a booger hanging out of his nose!

Comparing like fractions with different numerators When 2 fractions have the same denominators, they are called like fractions. It’s easy to compare them, all you have to do is compare the numerators.

For Example… ¼ is less than 2/4 because 1 is less than 2 4/5 is greater than 2/5 because 4 is greater than 2 Got it? Good Here’s a dancing lizard

Showing your work This is what a comparison problem usually looks like in math class: > Easy peasy

Unlike Unit Fractions When 2 fractions have different denominators, they are called unlike fractions. When a fraction has a 1 for the numerator, it’s called a unit fraction. It’s easy to compare these too. Remember: the bigger the number on bottom, the smaller the piece it represents. Makes sense: Would you rather have half of a cake or 1/12 of a cake? If you like cake, I know which one you’re going for

Example… ½ is bigger than 1/8 1/3 is less than ½ 1/100 is less than 1/10 (think pennies and dimes)

Show your work… This is what it would look like in math class: <

Are you getting it? So far, I’ve been taking it easy on you… We’ve got like fractions, Easy We’ve got unlike unit fractions, Easy Now we’ve got unlike fractions with different denominators, Easy??

You can Benchmark it! Okay, you’ve got to compare these two fractions… 4/8 and 5/6 Use ½ as a benchmark 4/8 is equal to ½ 5/6 is only 1 little sixth away from 1 whole, so… 4/8 is less than 5/6 This is useful, but it doesn’t work all the time

Now for something completely different… Cross multiplying does work all the time, It’s also called the butterfly method, but don’t let the name fool you. It can be a vicious monster, like your sister! Here’s what you do… Multiply the numerator on the left by the denominator on the right. Write the product to the left of the numerator. Now multiply the numerator on the right by the denominator on the left. Write that product down to the right of that numerator. Compare the 2 products. This works every time, but sometimes you could end up with some big multiplication problem, so put on your big boy pants! Or big girl pants! Whatever, just be sure to wear pants. No shirt, No shoes, No service… Funny, they never mention pants.

Example Comparing ¾ to 4/7 Multiply 3 x 7 to get 21, put it by the 3 Multiply 4 x 4 to get 16, put it by the 4 (numerator) 21 is greater than 16, so ¾ is greater than 4/7

Work it out This is what the problem should look like in math class > Note: It’s called the butterfly method because you can draw a circle from the 3 to the 7 and from the 4 to the other 4 making a butterfly shape. Some teachers are so girly :-P

Model It! Drawing a model can be very helpful

Model for Comparing Like fractions. Comparing ¼ to 2/4 Notice only one box is filled in the top model, 2 boxes filled in the bottom model Easy to see, easy to compare ¼ is less than 2/4 *****************

Model for comparing Unlike Unit Fractions Let’s compare 1/3 to 1/7 Notice that sevenths are smaller pieces than thirds Easy to see, easy to compare 1/3 is greater than 1/7 *********** ****

Modeling Unlike fractions with different denominators Let’s compare ¾ to 2/10 This model may be a little harder to draw Be sure both models are the same size because they both represent 1 whole ¾ is greater than 2/10 ******** **

Your Turn… Compare the following fractions Compare 3/8 to 5/8 Compare 1/8 to 1/5 Compare 2/5 to 3/7 Take your time I’m in no hurry I’ve got all day Don’t mind me

How did you do? 3/8 is less than 5/8 1/8 is less than 1/5 2 x 7 = 14 3 x 5 = is less than 15, so… 2/5 is less than 3/7 Here’s a picture of you at a party You’re a real party animal