1. FRACTIONS! DELGADO ADULT EDUCATION UNIT ON FRACTIONS

2. What are fractions good for? Fractions express a part of a whole. That whole could be one thing, like a pizza, that has been divided up into parts, or a group. For an introduction to what fractions are, and to how useful they are, click the following link: https://www.khanacademy.org/math/arithm etic/fractions/understanding_fractions/v/intr oduction-to-fractions https://www.khanacademy.org/math/arithm etic/fractions/understanding_fractions/v/intr oduction-to-fractions

3. Addition Addition: When adding two fractions, what is the first thing you look at? The denominator (the bottom number)! You cannot add fractions until you have written them so that each has the same denominator on the bottom. How do you find the Least Common Denominator (or Multiple)? You look for the smallest number that both numbers go into: For instance, if you want to add 2/3 + 3/4, you first need to find the Least/Lowest Common Denominator. You do this by 1) listing the numbers that 3 goes into, 2) listing the numbers that 4 goes into, and then 3) finding the smallest number (other than 0) that both go into. Click the next slide for a demonstration of how to do this.

4. Finding the Least Common Denominator Finding the Least/Lowest Common Denominator for 2/3 and 3/4: 1) list the numbers that 3 goes into, 2) list the numbers that 4 goes into, and 3) find the smallest number (other than 0) that both go into.

5. Addition, continued Now, you will rewrite 2/3 and 3/4 so that 12 is the denominator. 2 x 4 = 8 3 x 4 12 + = 17/12 3 x 3 = 9 4 x 3 12 AN UNBREAKABLE RULE: WHEN DOING THIS, YOU MUST ALWAYS MULTIPLY THE TOP AND BOTTOM BY THE SAME NUMBER! Click the following link for a short lesson! https://www.khanacademy.org/math/arithmetic/fractions/Equivalent_fra ctions/v/finding-common-denominators https://www.khanacademy.org/math/arithmetic/fractions/Equivalent_fra ctions/v/finding-common-denominators When you have finished the lectures, do the exercises (listed in the left- hand column and marked with a star) to practice. For more practice, go to: http://www.mathsisfun.com/fractions_addition.html http://www.mathsisfun.com/fractions_addition.html At the above site, you will find another lesson and exercises at the bottom of the page.

6. Practice adding fractions Solve the following problems, and reduce them to their lowest terms: 1/3 + 1/4 1/5 + 3/20 6/10 + 2/6 7/9 + 1/18 How do you know when a fraction has been reduced to lowest terms? When you are rewriting fractions so that they have a common denominator, and when you are reducing or simplifiying fractions, you are just rewriting them in different terms. These are called equivalent fractions.

7. Equivalent fractions Notice how each of the fractions below represent ½ a pie? You can write ½ in as many ways as you like, as long as the numerator is ½ the denominator! Click below to see a short lesson on reducing fractions, and then recheck the answers above to make sure they are in lowest terms. https://www.khanacademy.org/math/arithmetic/fractions/ Equivalent_fractions/v/fractions-in-lowest-terms https://www.khanacademy.org/math/arithmetic/fractions/ Equivalent_fractions/v/fractions-in-lowest-terms

8. Subtracting fractions Subtraction generally follows the same rules and procedures as addition, with the exception of “mixed numbers”. Let’s take this opportunity to review mixed numbers. 1 ½ is a mixed number (a whole number plus a fraction). 1 ½ = 3/2. 3/2 is an “improper fraction,” which is any fraction in which the numerator (top number) is equal to or greater than the denominator (bottom number). You can convert any mixed number to an improper fraction, and vice versa. Remember how to do this? https://www.khanacademy.org/math/arithmetic/fracti ons/mixed_numbers/v/converting-mixed-numbers-to- improper-fractions https://www.khanacademy.org/math/arithmetic/fracti ons/mixed_numbers/v/converting-mixed-numbers-to- improper-fractions

9. Converting between improper fractions and mixed numbers Convert the following improper fractions to mixed numbers, and vice versa: 1 4/7 5/4 2 3/8 9/2 1 7/8 So, if you have a subtraction problem like: 3 3/7 – 1 4/7 You’ll notice that you can’t subtract 4/7 directly from 3/7. But if you convert both to improper fractions, 24/7 – 11/7 = 13/7 = ____________________________ (convert to a mixed number!) If you don’t remember how to convert an improper fraction to a mixed number, watch this short lesson: https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-fractions-topic/cc-4th-mixed- numbers/v/changing-an-improper-fraction-to-a-mixed-number https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-fractions-topic/cc-4th-mixed- numbers/v/changing-an-improper-fraction-to-a-mixed-number

10. Multiplying fractions Click below to watch a short Khan Academy video about multiplying fractions: https://www.khanacademy.org/math/arithmetic/frac tions/multiplying_fractions/v/multiplying-fractions https://www.khanacademy.org/math/arithmetic/frac tions/multiplying_fractions/v/multiplying-fractions Thankfully, multiplying and dividing fractions is a bit easier than adding and subtracting them. This is because you don’t have to worry about finding the lowest common denominator. You just multiple all the top numbers together, and multiply all of the bottom numbers together. For example: 3/7 x 1/2= 3/14

11. Cancelling before multiplying

12. Multiplying mixed numbers Click on the following link to review multiplying mixed numbers: https://www.khanacademy.org/math/arithmetic/fracti ons/mixed_number_mult_div/v/multiplying--mixed- numbers https://www.khanacademy.org/math/arithmetic/fracti ons/mixed_number_mult_div/v/multiplying--mixed- numbers Click on the following link to review dividing fractions: https://www.khanacademy.org/math/cc-sixth-grade- math/cc-6th-arithmetic-operations/cc-6th-dividing- fractions/v/dividing-fractions-example https://www.khanacademy.org/math/cc-sixth-grade- math/cc-6th-arithmetic-operations/cc-6th-dividing- fractions/v/dividing-fractions-example ***Please complete and check the Fractions Review Worksheet before moving on.***

13. Introduction to Percents

14. Converting a fraction to a decimal To find the percentage of apples that have worms in them, you express the problem as: 1 ÷ 3 =.333 (repeating). This rounds to.33 as a decimal. First, you convert the fraction to a decimal, which you do with a simple division problem. When you are dividing, you should take your answer out to the thousandths place, and if it does not end or begins repeating, round your answer to the hundredths place. Watch the short lesson below. https://www.khanacademy.org/math/arithmetic/decimals/decimal_to_fraction/v/converting-fractions- to-decimals To review rounding and place value, click here (or copy and paste this link): https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-place-value-decimals-top/cc-5th- rounding-decimals/v/rounding-decimals Once you have converted the fraction to a decimal, you convert the decimal to a percent by moving the decimal point two places to the right.

15. *percents, continued Back to the apples:.33 have worms in them, and when you move the decimal point, you can see that 33% have worms in them. To review converting from decimals to percents, click here: https://www.khanacademy.org/math/arithmetic/deci mals/percent_tutorial/v/converting-decimals-to- percents--ex-1 https://www.khanacademy.org/math/arithmetic/deci mals/percent_tutorial/v/converting-decimals-to- percents--ex-1 At this point, you’re ready to move on to PERCENTS! YAY!