VIEWS: 12 PAGES: 42 POSTED ON: 11/24/2011 Public Domain
Adding and Subtracting FRACTIONS!!!! A helpful slide show with good hints for you to learn. First of all, what makes up a Fraction? A fraction has two parts to it: A Numerator (the top number) And a Denominator (the bottom number) Which section do you need help with? Select an area to learn. Adding Fractions Subtracting Fractions How do you ADD FRACTIONS? First of all, you need ½+¾ a “common Cannot be added denominator”. This together... Yet. means the bottom numbers of each fraction must be the 2/4 + ¾ same. Can be added because the denominators are “common” (the same) Test Time!!!! See if you can get these correct, and you will be on your way! Can These Be Added? A. ¾+¼ A. YES B. ½ + 5/8 B. NO C. 3/16 + 5/16 C. YES D. 1½+3½ D. YES E. 10 3/16 + 3 5/8 E. NO F. 15/16 + 3 3/8 F. NO G. 2 7/8 + 2 3/8 G. YES How did you do? To start any problem, you first need to determine if you CAN add them together as they are. Or…if you need to change them somehow to add them. Making a Common Denominator How to make a common denominator. Here’s what you do if Find the common the denominators are denominator for: different: 2 and 4 ANSWER: 4 You first need to find a 16 and 4 number that BOTH ANSWER: 16 denominators can 4 and 8 divide into evenly. ANSWER: 8 HINT Did you notice that the common denominator was ALWAYS the bigger of the two denominators? Just remember that this rule ONLY applies in woodworking. Not in your math class. Converting the Fractions Step #1 Converting the Fraction Step #1 Let’s try an example together! ½+¾ The ½ needs to be converted to match the bigger denominator. So…(what number) x 2 = 4? Answer: 2 Simple huh? Converting the Fractions Step #2 Converting the Fraction Step #2 Take the answer (2) and multiply it by both the numerator and denominator. 2x½ (OR) 2 x 1 = 2 2x2 = 4 Do you agree that ½ = 2/4? So now…2/4 + 1/4 can be added together. Adding the Fractions Adding the Converted Fraction Now…what do we do with 2/4 + 1/4? All that’s left is adding ONLY the numerators. The denominator IS NOT added. It stays the same. So… 2/4 + 1/4 = 3/4 THE ANSWER!!! Conclusions All addition problems take the same steps to solve. The common denominator will ALWAYS be the bigger denominator of the two. Don’t be afraid of the problem if it has big numbers. It’s easy! Click here to go back to the beginning of the slide show. Subtracting Fractions Learn to Borrow Subtraction Subtracting fractions begins exactly the same way as adding fractions. The first thing you have to do is figure out if you CAN subtract them as they are. If not, you will need to convert a denominator so you can. Test Time!!! This should be a breeze. Can these be subtracted? 1½-¾ NO 15/16 – 3/16 YES 3 5/8 – 1 ½ NO 5 2/4 – 3 ¼ YES 10 5/8 – 7 15/16 NO 3¼-1¼ YES 7 7/8 – 3 13/16 NO How did you do? Remember that all you need to know is if they are able to be subtracted. If not, we need to convert one of the fractions. Make a common denominator Let’s do one together 1½-¼ You can see that one of them needs to be converted so you can subtract them. What will the common denominator be? ANSWER: 4 Step #1 Step #2 Identify the common Since ¼ already has a denominator. denominator of 4 you 1½-¼ don’t need to change ANSWER: 4 it. But ½ needs to be converted to 4’ths. Step #2 (continued) How do you convert ½ into 4ths? (what number) x 2 = 4? ANSWER: 2 Now, multiply both the numerator (top number) and the denominator (bottom number) by 2. 1x2=2 2x2=4 Step #3 So now ½ has been converted to 2/4. Now we have: 1 2/4 – ¼ Go ahead and subtract ONLY the numerators. What did you get? ANSWER: 1 ¼ Go again Did you get the right answer? If so, good job!!! If not, you had better go over it again. BORROWING!!! Generally, borrowing is the most difficult thing to do in subtracting fractions. There are 4 simple steps to follow and it works for ANY fraction in ANY problem. Don’t worry, it’s easy once you learn the steps. Here is the problem Let’s say that you got a problem like this: 3 ¼ - 15/16 First step: They can’t be subtracted as they are. Second step: What is the common denominator? ANSWER: 16 Third step: Convert a fraction. Let’s go through it With a common denominator of 4 we need to figure out: (what number) x 4=16? ANSWER: 4 SO: 4 x 1 = 4 4 x 4 = 16 Oops! What’s this? The problem now Normally you would reads like this: now subtract. The problem is that 4 – 15 would be a negative 3 4/16 – 15/16 number. We can’t have that! THUS, BORROWING IS NEEDED! Borrowing In this problem: 3 4/16 – 15/16 Borrowing is having to increase the value or amount of 4/16 so that it’s bigger than 15/16. In other words, we need to make 4/16 bigger so that we CAN subtract. Here’s how to do it 3 4/16 needs to be changed somehow. We’re going to take 1 whole number from the 3 and add it to 4/16. Would you agree that: 2 + 1 4/16 = 3 4/16? NOW COMES THE TRICKY PART. The tricky part 2 + 1 4/16 needs to We can write 1 as: be changed a bit 2/2 = 1 before we can 3/3 = 1 subtract from it. 4/4 = 1 Lets take 1 4/16 and And so forth up to: “fix” it. 16\16 = 1 Because 16 is the SO NOW: common denominator 16 + 4 = 20 we need to write 1 in 16 16 16 16ths. Recap 3 ¼ -15/16 = 3 4/16 – 15/16 = (2 +1 + 4/16) – 15/16 = (2 + 16/16 + 4/16) – 15/16 = (2 + 20/16) – 15/16 = All of these expressions are equal to each other. Let’s pause and try a couple problems. Ready for an easy test? What fraction would you turn 1 into to complete the problem? 1 + 3/16 16/16 1 + 1/8 8/8 1 + 9/16 16/16 1+½ 2/2 1+¾ 4/4 1 + 5/8 8/8 Back to the problem Now, instead of: 2 + 1 4/16 we have: 2 20/16 If we rewrite the problem now we have: 2 20/16 – 15/16 Now it’s just a simple subtraction problem! Don’t forget 2 20/16 – 15/16 Remember that you only subtract the numerator, not the denominator. The answer: 2 5/16 WHEW! If you’re not sure yet about how to borrow, click below to go through it again. Borrowing The End Is your brain turned into mush yet?