fraction rules review
DESCRIPTION
Fraction Rules Review. Yes, you need to write it all down, including the examples. You will be graded on your notes. Why not just use decimals???. Because you are doing Algebra. Converting every fraction to decimals makes working with variables REALLY, REALLY difficult…. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/1.jpg)
Fraction Rules ReviewYes, you need to write it all down, including the examples.You will be graded on your notes.
![Page 2: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/2.jpg)
Why not just use decimals???Because you are doing Algebra.
Converting every fraction to decimals makes working with variables REALLY, REALLY difficult….
Especially when you start working with exponents (powers)….
Or multiple variables….So learn to love fractions!
![Page 3: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/3.jpg)
Adding Fractions1. Check for a common
denominator (the bottom #). If the denominators are the same, just add the top numbers across.
1/6+4/6=5/6
![Page 4: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/4.jpg)
2. If the denominators are different, find the least common denominator (LCD).
![Page 5: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/5.jpg)
Least Common Denominatora. First find the Least Common
Multiple of the two denominators.
1/6+3/4
LCM of 6 and 4 is 12, so the LCD of 1/6 and ¼ is 12
![Page 6: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/6.jpg)
b. Then multiply BOTH the top AND the bottom numbers of the fraction (the numerator and the denominator) by whatever number is needed to make the denominator the LCD
1/6 * 2/2=2/12¾*3/3=9/12
![Page 7: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/7.jpg)
Finally, you can…3. Add the top numbers (the
numerators) across; leave the bottom numbers alone.
2/12+9/12=11/12
4. Simplify if possible.
![Page 8: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/8.jpg)
Subtracting FractionsFollow the same process as
adding fractions. Remember that once the denominators are the same, you only need to subtract the top numbers (the numerators).
![Page 9: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/9.jpg)
Multiplying Fractions1. Line them up next to each other.2. Multiply top AND bottom
(numerator and denominator) straight across.
1/6*3/4=3/24
3. Simplify.3/24=1/8
![Page 10: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/10.jpg)
***Simplify Before MultiplyingA good idea; it saves time.Look for common factors to
reduce by.
1/6*3/4
The six and the three have 3 as common factor, so you can reduce them:
½*1/4=1/8 same answer as before!
![Page 11: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/11.jpg)
Dividing Fractions1. Reverse the second fraction (the
divisor) top-to-bottom (use the reciprocal), and reverse the operation (multiply instead of divide).
1/6 1/6¾ = * 4/3
![Page 12: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/12.jpg)
2. Remember to simplify wherever you can before multiplying.
Reduce first: 1/3*2/3Then multiply: 1/3*2/3=2/9
![Page 13: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/13.jpg)
Whole & Mixed Numbers
![Page 14: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/14.jpg)
Adding Whole/Mixed Numbers1. Check for LCD. If they already
have a common denominator, you can add the whole numbers together and add the fractions together. Remember to convert improper fractions into whole or mixed numbers before you stop.
2 2/3 +3 2/3=2+3= 5, and 2/3 + 2/3=4/3Add the results: 5+4/3= 6 1/3
![Page 15: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/15.jpg)
2. If there is no LCD, convert BOTH numbers into improper fractions:2 2/3 + 1 4/5
Multiply the denominator times the whole number; add the result to the top (numerator).
2 2/3: 2*3 +2=8, so 2 2/3=8/31 4/5: 5*1 +4=9, so 1 4/5=9/5
![Page 16: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/16.jpg)
3. Find the LCD of the improper fractions.
8/3 and 9/5 LCD of 3, 5=154. Convert each fraction into an
equivalent fraction, using the LCD.8/3*5/5=40/159/5*3/3=27/15
![Page 17: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/17.jpg)
5. Add the top numbers (the numerators) only.
40/15+27/15=67/15
6. Simplify the result.67 divided by 15=4 7/15
![Page 18: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/18.jpg)
Subtracting Whole/Mixed #’sFollow the same process as for
adding them.
IF there is a common denominator already, you may need to “borrow” from the whole numbers first. Sometimes, it’s easier to just use improper fractions anyway!
![Page 19: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/19.jpg)
“borrowing” to subtract mixed numbers10 1/6-2 3/6The first fraction is smaller than
the second, so you need to “borrow” from 10 (the whole number):
9 7/6-2 3/6 now you can subtract:9-2=7 and 7/6-3/6=4/67+4/6=7 4/6 Simplify: 7 2/3
![Page 20: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/20.jpg)
Multiplying Whole/Mixed #’s***Remember that a whole # can
be written as a fraction by writing itself over 1 (because any number divided by itself is still…itself.)
2=2/127=27/1234=234/1
![Page 21: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/21.jpg)
1. Convert both #’s to fractions.3 1/3*4= 10/3*4/1
2. Multiply the top and bottom (numerator and denominator) straight across.
10/3*4/1=40/3
![Page 22: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/22.jpg)
3. Simplify.40/3=13 1/3
4. THINK. If you estimate, will you be close to the same answer?
3*4=12…which is close to 13 1/3
![Page 23: Fraction Rules Review](https://reader035.vdocument.in/reader035/viewer/2022062323/5681610f550346895dd069c9/html5/thumbnails/23.jpg)
Dividing Whole/Mixed #’s9 1/32/6 becomes 28/3
2/6Use the reciprocal: 28/3*6/2Simplify first: 14/1*2/1= 28/1 =28
Follow all the same steps as for multiplying, but reverse the second fraction (use the reciprocal) and the operation (multiply).