Fractions

Question 1

Rule for adding and subtracting fractions

Answer 1

Denominator must ALWAYS be the same. So find the LCD

Question 2

Quick check for why
a/(b + c)
doesn’t equal
a/b + a/c

Answer 2

Replace everything with 1:

1/2 doesn’t equal 2/1

Question 3

To add or subtract two fractions

Answer 3

we use a common denominator:
a/b + c/d = ad + bc / bd

• multiply top and bottom by the other denominator to get the quickest common denominator fractions.
• ALWAYS PUT + - in parentheses

Question 4

Multiply fractions

a/b x c/d

Answer 4

ac / bd

Question 5

Negative sign rule for fractions

Answer 5

a
-a/b = - — = a/-b
b

Question 6

To divide two fractions…

Answer 6

invert and multiply:
a/b
—— = a/b x d/c = ad/bc =a/c x d/b
c/d

Question 7

Simplifying Complex Fractions Method 1

Answer 7

Method 1
Key steps:
1) Create a single fraction in the numerator and denominator.
2) Apply the division rule of fractions by multiplying the numerator by the reciprocal or inverse of the denominator.
3) Simplify, if necessary.

https://www.chilimath.com/lessons/advanced-algebra/simplifying-complex-fractions/

Question 8

Simplifying Complex Fractions Method 2

Answer 8

Method 2

Key steps:

1) Find the Least Common Denominator (LCD) of all the denominators in the complex fractions.
2) Multiply this LCD to the numerator and denominator of the complex fraction.
3) Simplify, if necessary.

Usually the fastest method

https://www.chilimath.com/lessons/advanced-algebra/simplifying-complex-fractions/

Question 9

Improper fraction

Answer 9

Numerator > denominator

Question 10

Turn a decimal into a fraction

Answer 10

Put it over the corresponding 10’s figure and simplify

Question 11

Find common denominators for fractions

Answer 11

• multiply top and bottom by the other denominator to get the quickest common denominator fractions.

Question 12

For fraction problems, always remember

Answer 12

1) ALWAYS PUT + - in parentheses, they’re always linked
2) multiplication follows the distributive, commutative and associative laws.

3) Use the two methods of nested fractions:
1. Multiply top and bottom but the common denominator of top and bottom
2. OR (slower) make one fraction too and bottom, flip and multiply.

Question 13

When canceling terms in the numerator and denominator, always…

Answer 13

Make sure you keep the answer (1) in the numerator for the final answer.

e.g., (a-x) / -xa (a-x) does NOT = -xa

It equals -1/xa! Keep the 1!