Standard 4NF2

Standard 4NF2I can compare 2 fractions with different numerators and different denominators.

What you should already knowFractions represent parts of a wholeThe numerator is the top numberRepresents the number of pieces in questionThe denominator is the bottom numberRepresents the number of equal pieces that make the wholeOne of you has a booger hanging out of his nose!

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

For Example is less than 2/4 because 1 is less than 24/5 is greater than 2/5 because 4 is greater than 2Got it?GoodHeres a dancing lizard

4Showing your workThis is what a comparison problem usually looks like in math class:2 1--- > ---6 6Easy peasy

Unlike Unit FractionsWhen 2 fractions have different denominators, they are called unlike fractions.When a fraction has a 1 for the numerator, its called a unit fraction.Its 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 youre going for

Example is bigger than 1/81/3 is less than 1/100 is less than 1/10 (think pennies and dimes)

Show your workThis is what it would look like in math class:1 1--- < ---4 2

Are you getting it?So far, Ive been taking it easy on youWeve got like fractions,EasyWeve got unlike unit fractions,EasyNow weve got unlike fractions with different denominators,Easy??

You can Benchmark it!Okay, youve got to compare these two fractions4/8 and 5/6Use as a benchmark4/8 is equal to 5/6 is only 1 little sixth away from 1 whole, so4/8 is less than 5/6This is useful, but it doesnt work all the time

Now for something completely differentCross multiplying does work all the time,Its also called the butterfly method, but dont let the name fool you. It can be a vicious monster, like your sister!Heres what you doMultiply 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 serviceFunny, they never mention pants.

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

12Work it outThis is what the problem should look like in math class.21 163 4--- > ---4 7Note: Its 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 to 2/4Notice only one box is filled in the top model, 2 boxes filled in the bottom modelEasy to see, easy to compare is less than 2/4***************************************************Model for comparing Unlike Unit FractionsLets compare 1/3 to 1/7Notice that sevenths are smaller pieces than thirdsEasy to see, easy to compare1/3 is greater than 1/7***************Modeling Unlike fractions with different denominatorsLets compare to 2/10This model may be a little harder to drawBe sure both models are the same size because they both represent 1 whole is greater than 2/10

****************************Your TurnCompare the following fractionsCompare 3/8 to 5/8Compare 1/8 to 1/5Compare 2/5 to 3/7Take your timeIm in no hurryIve got all dayDont mind me

How did you do?3/8 is less than 5/81/8 is less than 1/52 x 7 = 143 x 5 = 1514 is less than 15, so2/5 is less than 3/7Heres a picture of you at a partyYoure a real party animal