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Math-Fractions Unit Project 'Prezi' Presentation
Transcript of Math-Fractions Unit Project 'Prezi' Presentation
SO LET'S GET STARTED! Dividing Fractions Hi I'm Rakshintha, and I'm going to go through how to divide fractions, either its proper or improper fractions or even mixed numbers. The definitions have already been given to you so I'm just going to start with dividing fractions. Don't worry, its not too hard, in fact its easier than adding and subtracting fractions. Order of Operations HI GUYS, HOW ARE YOU DOING? YOU HAVE LEARNED THE BASICS OF FRACTIONS NOW YOU WILL COMBINE WHAT YOUVE LEARNED AND FIGURE OUT A SOLUTION USING THE NEXT FEW STEPS. DONT WORRY IF IT LOOKS HARD YOU WILL GET IT JUST TRY YOUR BEST!! Problem Solving HEY!! PROBLEM SOLVING IS NEXT AND LAST WITH FRACTIONS. THE FOLLOWING STEPS WILL GO THROUGH WHAT YOU NEED TO KNOW. HOW TO ADD, SUBTRACT, MULTIPLY, AND DIVIDE FRACTIONS HOW TO USE ORDER OF OPERATIONS HOW TO PROBLEM SOLVE BY: RAKSHINTHA, BETHANY, OLIVIA, AND NOAH. Definitions Denominator:
the bottom part of the fraction
the top part of the fraction
*numerator Definitions 2 Lowest Common Denominator (LCD):
the smallest whole number that has 2 or more given numbers as factors
ex: 12-LCD of 4 and 6
a fraction that has another fraction that has the same value as each other. to get equivalent fractions you have to multiply or divide the numerator and denominator by the exact same number.
ex: 1/2 = 2/4
1/3 = 2/6
3/4 = 6/8 Definitions 3 Reduce:
when you divide a number by another number( numerator or denominator) to get the lowest possible number. Also called "simplification"
ex: 4/2 = 2
10/2 = 5 Subtracting Fractions: How To 1. Write out the question.
2/3 - 3/4 = ?
2.Line up your equal signs vertically (min.1 ,max. ?)
3. Make sure the denominators are the same. If not, you have to find the lowest common denominator.
4. List all the multiples for the denominators until a common one comes up. In the example, the LCD is 12. Fractions 5. Create an equivalent fraction for each fraction using the common denominator(see line 2 in example).
6. Subtract the numerators but leave the denominator alone.
7. If possible, reduce fraction to lowest terms.
8. Box your answer. Mixed Fractions I will now teach you how to subtract fractions with whole numbers/mixed numbers. Don't worry! It's easy! Mixed Fractions: How To 1. Write out the question.
2. Line up your equal signs.
3. Subtract the whole numbers and "save" them for later.
4. Make sure the denominators are the same. If not, you have to find the lowest common denominator. List common multiples for both denominators.
5. Then follow what you did in subtracting proper fractions, but remember to also add in your whole number to your equation in the end. SUBTRACTING FRACTIONS Dividing Proper Fractions Question: 2/5 / 3/7 = ?
1. Write down your question
2. Whenever in a division question always remember to change it to a multiplication question and to do that you turn the second fraction into its reciprocal*. the reciprocal of 3/7 is 7/3.
3. Next rewrite the question. Remember to change the division sign to a multiplication sign. Now your question is 2/5 * 7/3 = ?
4. Now just multiply. Multiply the numerators together which are 2 and 7 and you get 14, your new numerator. Multiply the denominators which are 5 and 3 and get 15, your new denominator. Your answer is 14/15.
5. Next you have to see if your fraction can be simplified. In this case 14/15 cannot be simplified further therefore your final answer is 14/15.
6. Always remember to box your answer when your finished.
= 14/15 Reciprocal: Flipping the fraction upside down so that the denominator and numerator can switch places. In the question 2/5 the reciprocal is 5/2. Dividing Fractions My Mixed Fractions Mixed Fractions: How To Continued 6. Ask yourself, can the answer be positive? Is it a negative? If the answer is a negative, you have to borrow a whole number in 'fraction form' and add it to the first fraction so it becomes improper.
7. Then you need to subtract the numerators but keep the denominators the same.
8. Next, you have to reduce to lowest terms if possible.
9. Then, add on the whole numbers.
10. Finally, box your answer. As you have learned in the
subtracting lesson, you always
need common denominators to complete the question. Adding is almost exactly the same (obviously except with adding the numerators instead of the subtracting them) So lets get on with an example. :) 1. Simply write the question (lets say 4/5
plus 2/ 10 4/5 + 2/10 2. The second step is to find the lowest common denominator of 4/5 and 2/10. This is 10 because 5 goes in to 10, and so does 10. (5 goes in twice and 10 goes in once) We also must make the numerators equal to how many times we enlarged the denominators. So 4 becomes 8 because I also multiplied the denominator by two. 2 stays the same because I only had to multiply the denominator by 1. = 8/10 + 2/10 3. Next, we simply add the numerators. When ever you do addition with fraction, or as you learned earlier, subtraction, the denominators always stay the same. So, 8 + 2 = 10. = 10/10 4. Now, you would simplify and box your answer. As a small step in cases like this where your fractions numerator is equal to its denominator, you could simply by making it a whole number (1). = 1 Yay!!! Now you know the basics of addition
with fractions. In the next part, you will be
learning how to do more complex problems,
such as adding with mixed numbers or
improper fractions. MIXED NUMBERS 1. Write the question: 4 2/3 + 3 5/6 2. Add the whole numbers,
but save the answer for later 4 + 3 = 7 3. Like in the last section of
the tutorial, find the common
denominator, in this case, 6.
Also multiply the numerators
as needed. (2x2 5x1) =4/6 + 5/6 4. Add the numerators. =9/6 5. Since we have an improper
fraction, lets fix that by dividing 9
by six. (6 goes into nine once so the
whole number is 1, and the remainder
is 3 so that becomes the numerator.
The denominator stays the same) =1 3/6 6. Now we could simplify what we have now, but I prefer to do that at the end. Other than that, we must add the whole number that we saved at the beginning (7) 1 3/6 + 7 =8 3/6 7. Finally, we simplify the product. (3/3=1 and 6/3=2. So 1/2. WOO HOO! Now you know how to add fractions! The only other small thing that I would like to add is that when you are adding a fraction and a whole number, you must assume that whole number when changed to a fraction, the numerator is over one whole. (1 = 1/1,
2 = 2/1,
3 = 3/1,etc...) GOOD JOB, YOURE DONE WITH THE SIMPLEST TYPE OF DIVIDING WITH FRACTIONS NOW I THINK YOURE READY FOR SOME MORE HARDER QUESTIONS. 1. Write out the question.
2. Change the mixed fraction into an improper fraction, by multiplying the denominators with the whole number then adding the numerator with the product. (the denominator stays the same but the number you get after doing all that math is your new numerator.)
3. Turn your second fraction into its reciprocal. Then change the division sign to a multiplication sign.
4. To get the answer, multiply the numerators together and the denominators together. Question: 3/5 / 2 4/5 = 3/5 / 2 4/5
= 3/5 / 14/5
= 3/5 * 5/14
= 15/70 continued on the next slide Dividing Fractions By Mixed Fractions Part 2 5. Now see if the fraction can be simplified. If not that is your final answer. The final answer is 3/14 because 15/70 can be reduced.
6. 3/14 cannot be reduced anymore therefore it is the answer. don't forget to box your answer.
Always remember that when you have a whole number its always going to be out of one (3 = 3/1,
4 =4/1) = 15/70
= 3/14 = 3/14 YAY YOUVE FINISHED DIVIDING WITH FRACTIONS. Q) At Amy's party, the girls ate 3/21 pizzas and the boys ate 7/21 pizzas. how many pizzas in total were eaten at her party?
how to solve?
1. Separate your sheet into 3 sections. Now label them given, solve and statement. In the given section fill in what is important from the question and then restate the question in your own words. In your solve section solve your question with a formula. In your statement section you answer the question in a sentence form.
2. Pick out the important information from the question and figure out if the question is an adding, subtracting, multiplying, or division question. In this case its addition because total is the answer to an addition question. The important parts in this question is girls: 3/21 and boys:7/21. The question restated would in the forms of 'how many pizzas were eaten at the party?'
3. Now write down what you're going to do in your solve section just do usual steps of adding with fractions, if you YOU need help with that go back to adding fractions with Noah. the formula now would be g + b = total.(g stands for girls and b stands for boys). Now substitute: 3/21 + 7/21 = 10/21.
4. In the statement section write down your answer in a sentence form. The sentence should be around 'at Amy's party her guests ate 10/21 pizzas'. THERE YOU GO YOU FINISHED PROBLEM SOLVING WITH FRACTIONS!!!!! YAY!!:) HEY!!! GREAT WORK, YOU FINISHED EVERYTHING WITH FRACTIONS. NOW IF ANYONE ASKS YOU HOW TO DO ANYTHING YOU CAN GO HELP THEM BECAUSE YOURE AN EXPERT ON THIS STUFF. WELL THEN GOOD LUCK!!! ;) Q) 1/4 + 2/3(5) - 2 1/2
1. In an order of operation question you have to use BEDMAS : B - brackets, E = exponents, D - division, M - multiplication, A - addition, S - subtraction. This is what you have to keep in mind to do an order of operation question. This is the order in which you have to do the question. In this question what you have to do first is the multiplication. Then you do the question left to right so addition then subtraction.
2. To follow the BEDMAS rule you multiply 2/3 by 5 because the brackets right beside a number means that it is multiplied. So 2/3 * 5 is 10/3 [you don't want to change that to a mixed number just yet so replace that fraction in the place of 2/3(5)]. CONTINUED ON NEXT SLIDE 3. Next rewrite the question. so now its 1/4 + 10/3 - 2 1/2 = ?
4. Focus on the first part of the equation so you have to find the fraction for the question 1/4 + 10/3. Change the denominators because they aren't the same and the lowest common denominator for 4 and 3 is 12. 1/4 is now 3/12 and 10/3 is 40/12. This is because 4 times 3 is 12 and whatever you do to the bottom you have to do to the top, same thing applies to the other fraction. Now add those two together and you should get 43/12.
5. Now replace the answer to the place where you did the math and continue the equation.
43/12 - 2 1/2.
6. This is a mixed fraction so you can change it to a improper fraction 5/2. You get this by multiplying the denominator with the whole number and then adding the numerator to the product. Now your equation should look like 43/12 - 5/2 = ? continued on next slide 7. You have a subtracting question, you've got to change the denominators to match each other. The LCD of 2 and 12 is 1. So multiply the numerator of the fraction 5/2 by 6 and you get 30/12. The other fraction stays the same because the denominator times 1 is 12 so 43 times 1 is 43 also. The question becomes 43/12 - 30/12 = ?. So now you just subtract to get 13/12.
8. See if your answer can be reduced further. Yes, this answer can be reduced as 1 1/12. How did you get it you may ask? To change an improper fraction to a mixed number you see how many times the denominator goes into the numerator in this case its just once so the whole number is 1. Now subtract 12 from 13 and you get 1 that's your new numerator. so your final answer is = 1 1/12. THERE YOU GO YOU JUST FINISHED A PROBLEM SOLVING QUESTION WITH FRACTIONS. Multiplying Proper Fractions 1. Write your question out.
Example: 2/5 * 3/5
2. Then to get the answer, you multiply the numerators together then the denominators together. So in this case the numerators are 2 and 3 multiply those and the product is 6. The denominators multiplied is 25. Your new fraction is 6/25.
3. Now you see if your fraction can be reduced, if it can you have to remember that whatever you do to the bottom you have to do to the top. In this question you can't, so your answer is 6/25. YEAH!! YOU JUST FINISHED MULTIPLYING PROPER FRACTIONS ;) MULTIPLYING IMPROPER FRACTIONS: Even when you have an improper fraction you can still go through the same steps as multiplying the proper fractions, but don't forget to simplify in the end from an improper fraction to a mixed number.
1. Write the question. 4/3 * 5/3
2. Multiply the numerators (4 and 5) then the denominators together (3 and 3). Your new numerator is 20 and the new denominator is 9.
The fraction now is 20/9. 3. Now you have to see if 20/9 can be reduced or simplified to a mixed number. Yes it can in this situation. To get an improper fraction to a mixed number you see how many times the denominator goes into the numerator evenly. This denominator goes into its numerator 2 times evenly. The 2 is now your whole number. now what is 2*9? its 18. The difference between 20 and 18 is 2. the 2 you got now is your new numerator. Now your fraction is 2 2/20.
4. Now your answer is 2 2/20, box your answer and you're done. WAIT!! 2 2/20 can be reduced even further. So your final answer is 2 1/10.
YES!! You're done.
* Just remember that when you have a whole number there is an imaginary one as the denominator. For example: 3 = 3/1 or 4 = 4/1.* MULTIPLYING IMPROPER FRACTIONS PART 2: