3434 Fractions By Mr. Walker

What is a Fraction? A fraction is just a smaller part of something else. If you have one piece of the pizza, you are only eating a fraction of the pizza, not the whole thing.

What do Fractions look like?

Parts of a Fraction The top part of the fraction is called the Numerator The bottom part of the fraction is called the Denominator 1 4 _

How Fractions Work This is a whole circle with 4 pieces. If you shade or take one piece of the circle away, you are taking 1 of the 4 pieces. That fraction looks like this… If you take away 1 of the 4 pieces you will be left with 3 of the 4 pieces. That fraction looks like this… So the numerator (top #) is the part or parts that you are working with… 1 and the denominator (bottom #) is the number of total parts the object has or used to have. 4

Try it Out What fraction of the objects are shaded? Remember that the part you are working with (the shaded part) goes on top and the total number of parts goes on the bottom.

Comparing Fractions With like denominators >,, <, or = If the two fractions you are comparing have like denominators (the same), your job is easy. Just look at the numerator and see which one is bigger < The 3 is bigger than the 1. So the answer is … > The 7 is bigger than the 5. So the answer is … The denominators are the same, so just compare the numerators. Try it Out < > = Answer

Comparing Fractions With unlike denominators >,, <, or = If the two fractions you are comparing have unlike denominators (different), you need to do a little more work using multiplication The problem The Denominators are different Starting on the bottom Multiply diagonally up across the middle 4X3=125X3= > 1512 Which is bigger the 15 or the 12 ? Answer

Comparing Fractions With unlike denominators Try it Out >,, <, or = > Answer = < > > < = >

Adding & Subtracting Fractions Adding fractions with like Denominators means adding the same size pieces to the circle Adding fractions with unlike denominators means adding different size pieces to the circle

Adding & Subtracting Fractions With like denominators If the denominators are the same then adding and subtracting fractions is easy = 3 5 Try it Out = = = Answer Denominators are the same so you just use that number in your answer on the bottom. Then you just add or subtract the numerators (top numbers).

Adding & Subtracting Fractions With unlike denominators = If the denominators are different then we need to do some work before we can add these two fractions. 1. Rewrite the problem so it looks like this = = 2. Add some of these lines to make your work nice and neat 3. Take the denominators and count them both out to find a number that they both have in common 5, 10, 15, 20, 25 3, 6, 9, 12, They both have a 15 in common 15 So we will use that number as the new denominator

Adding & Subtracting Fractions With unlike denominators continued = = 15 X 3 = 5. Now ask yourself how many times 5 goes into Now ask yourself how many times does 3 go into 15 X 5 = 3 times, 5x3=15 5 times, 3x5=15 6. For the top fraction you used a X 3 on the denominator Whatever you do to the denominator, you also have to do to the numerator So multiply the numerator by a 3, which looks like this… X 3 = 6 8. For the bottom fraction you used a X 5 on the denominator Whatever you do to the denominator, you also have to do to the numerator So multiply the numerator by a 5, which looks like this… X 5 = 5 9. Now just add the numerators and you are done 11

Adding & Subtracting Fractions Try it Out = = 12 X 3 = X 4 = X 3 = 3 X 4 = 4 7 4, 8, 12, 16, 20 3, 6, 9, 12, = = 35 X 5 = X 7 = X 5 = 10 X 7 = , 14, 21, 28, 35 5, 10, 15, 20, 25, 30, = = X 3 = X 2 = X 3 = 3 X 2 = 4 7 2, 4, 6, 8, 10 3, 6, 9, 12, 15

Reducing Fractions Whenever possible you should reduce your fractions To Reduce means to make the numbers in the fraction smaller. The actual fraction does not change but the numbers do. You reduce a fraction by dividing both the numerator and the denominator by the same number. Remember… Whatever you do to the denominator, you also have to do to the numerator 3636 = 2 3 = 1 : _ : _ 2424 = 2 2 = 1 : _ : _ As you can see by the bars, the numbers got smaller (reduced) but the fraction shaded (amount) stayed the same.

Reducing Fractions Try it Out 6868 = 4 2 = 3 : _ : _ Hints 1. When you divide both the numerator and the denominator it has to come out perfect, no remainders. 2. When you divide you can never divide by 1 because they would just be the same numbers 3. If they are both even numbers you can always use 2 to divide 4. If you can use a bigger number to divide it is better, if not, you may have to reduce several times to get the smallest numbers 5 15 = 3 5 = 1 : _ : _ 7878 = 8 ? = 7 : _ : _ 4848 = 2 4 = 1 : _ : _ 4848 = 4 2 = 2 : _ : _ or 2 = 2 1 : _ : _ Can’t, so it is already as small as it can get

Changing Fractions Improper to Mixed Some fractions are improper. Improper means that the numerator is bigger than the denominator. They are top heavy with a bigger number on top They need to be changed so they will not fall over To change it, you just divide the top by the bottom. A fraction is really just a division problem. 7 5 ) R2 The denominator stays the same. 5 The remainder becomes the numerator 2 The answer on top of the division problem goes in front of the fraction. It’s the whole number. 1 5

Changing Fractions Improper to Mixed Try it Out 3 2 ) R == 3 2 ) R == 3232 ) R ==

Changing Fractions Mixed to Improper To change this mixed fraction to an improper is as easy as 1, 2, 3. Some fractions are mixed. Mixed means that the fraction also has a whole number in front of it. Think, the whole number and fraction are mixed up together to get a job done. Whole number The fraction 1. Keep the bottom number the same To get the top number, just take the denominator (bottom #) and multiply it by the whole number in front. 3. Then add the numerator (top number) to your answer. Mixed and improper are just two ways to say the same fraction 5X1=5 x 5+2=7 + =

Changing Fractions Mixed to Improper Try it Out x + = 2 5 Answer x + = 5 18 Answer x + = 7 13 Answer = 7 17 Answer = = 3 9 =3