Adding and Subtracting Fractions

-5/8 + (-3/8) =

-1 Steps: Switch the '+' with a '-'! Now treat the problem as if you were just adding, but remember to add the '-' to your answer! 5/8+3/8=8/8, or -1!

1/5 + (-2/3)=

-1/3 Steps: Switch '+' to '-'! Then subtract since they have the same denominator. 1/5 - 2/3 = -1/3

-3 2/3 - 2 1/3 =

-6 Steps: Change the mixed numbers into improper fractions using the triangle method for both sides. 3x3=9+2=11/3 3x2=6+1=7/3 set up your new equation: -11/3 - 7/3 add the negatives: 11+7=-18/3 Now make the answer a mixed number again! 3 can go into 18 six times without leaving a remainder, so your answer is -6!

10/100 simplified

1/10 Steps: divide the numerator by itself, then the denominator by the numerator. 10/10=1 100/10=10 Therefore, your answer is 1/10!

30/60 simplified

1/2 steps: divide the numerator by itself, then the denominator by the numerator. 30/30=1 60/30=2 therefore, your answer is 1/2.

7/9+(-4/9)=

1/3 Steps: ignore the '+'! Begin subtracting the numerators, keeping the denominators the same since they are both 9. 7-4=3, therefore your answer is 3/9 unsimplified. Now we must simplify since 3 is a factor of 9. 3/3=1 9/3=3. Therefore, your answer is 1/3.

143/5 made into a whole or mixed number.

28 3/5 steps: simply determine how many times 5 can go into 143. We know that there will be a remainder because 5 cannot go into 143 evenly, it can only go into 143 up until 140. so to find the exact number, we just divide 140 by 5, 140/5=28. and our whole number is 28. 143-140=3, therefore our numerator is 3, and our denominator stays the same. our answer would then be 28 3/5.

4/10+7/20=

3/4 Steps: The denominators are different, but they have a common factor, 10. So to make them the same, we must simply find what number multiplied by 10 equals 20. In this case, the answer is 2. multiply both the numerator and the denominator on the left side by 2. 4x2= 8 10x2= 20 so our new equation is: 8/20+7/20= now we just add numerators and simplify if needed. 15/20. To simplify we just find the greatest common factor. 1,(3),(5),15 1,2,(5),(4),10,20 The common factor is 5, so our numerator will be 3, since it is the number that is multiplied by 5 to get 15. The denominator is 4 since it is the number that is multiplied by 5 to get 20. our simplified answer is 3/4.

35/112 - 1/3 =

5/24 Steps: These denominators are not the same, so we must make them alike by multiplying both sides by their counterpart. (to check if they are alike divide the larger denominator by the smaller denominator, in this case: 112/3, and the answer isn't a whole number so they do not have a common factor.) 35x3= 105 112x3= 336 1x35= 35 3x112= 336 put together your new equation: 105/336 - 35/336. Now, simply subtract numerators! 105-35=70, or 70/336. Now to simplify, we must find the GCF. To do so, we need to list all of the combinations that get us to 70, and all the combinations that get us to 336. 1,2,(5),7,10,(14),35,70! Therefore, our numerator will be 5. 1,2,3,4,6,7,8,12,(14),16,21,(24),48,42,48,56,84,168,336! Therefore our denominator will be 24. The common number between the two is 14. our simplified answer is 5/24.

12/45 - 6/45 =

6/45 Steps: subtract the numerators! 12-6=6, since our denominators are the same, just leave your answer as 6/45!

152/2 made into a whole or mixed number.

76 Steps: divide 152 by 2 using long division. 152/2=76. To check your answer, simply multiply your answer by the denominator and see if it equals the numerator.

4/5 + 7/10 =

Steps: Make the denominators the same by multiplying the numerator and denominator on the left side by 2 to equal the right. 4x2/5x2 = 8/10 8/10 + 7/10 = 15/10 Simplify! How many times can 10 go into 15? Once! so our whole number is 1, and what's left is 5, which is our numerator. So our unsimplified answer is 1 5/10. Simplified, your answer is 1 and 1/2.

Describe the way that you can simplify more complicated fractions such as 114/570. Explain the steps to the best of your ability.

divide the numerator by the numerator, then the denominator by the numerator. if the answer to the bottom portion is not a whole number, you cannot simplify.

Describe the "sideways triangle method" or the way to make a mixed number into an improper fraction.

multiply the denominator by the whole number then add the numerator.

(+)+(-)

negative number

(-)+(-)=

negative number

(+)+(+)=

positive number