Add. A) -7/20+13/20 B) -2/5+3/7 C) -8+5+(-3)

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embizze | High School Teacher | (Level 2) Educator Emeritus

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(a) Add `-7/20+13/20` : To add fractions with a like denominator we add the numerators and keep the denominator the same.

`-7/20+13/20=(-7+13)/20=6/20` . Usually you are asked to simplify the answer; no common factors appearing in the numerator and denominator. So `6/20=(2(3))/(2(10))=3/10`

Thus `-7/20+13/20=3/10`

(b) Add `-2/5+3/7` :To add fractions with unlike denominators we must find a common denominator. Here is a method that is quick; the only drawback is that you occasionally have to simplify the answer.

To add `a/b+c/d` you get `(ad+bc)/(bd)` .

So `(-2)/5+3/7=((-2)7+5(3))/(5*7)=(-14+15)/35=1/35`

So `-2/5+3/7=1/35`

(c) Add -8+5+(-3): There are many methods. The key is to see that when adding two numbers of unlike sign, you take the difference between the numbers (disregarding sign) and then keep the sign of the larger. When adding numbers of like sign we add the numbers and keep the sign.

So -8+5: Take 8-5=3. Since 8>5 we make the answer negative and -8+5=-3.

Then -8+5+(-3)=(-8+5)+(-3)=-3+(-3)=-(3+3)=-6.

So -8+5+(-3)=-6

As a check, suppose you owed someone $8. If you paid back $5 and then borrowed $3 more, how much would you owe them?