Algebraic Fractions

Question 1

What does reducing fractions mean?

Answer 1

Canceling out as many things as possible that are multiplied in the numerator and denominator.

Cancel anything you can. (Remember you can only cancel things that are multiplied by the whole numerator or whole denominator.)

Question 2

How do you reduce a fraction?

Answer 2

1. Factorise the numerator and denominator.
2. Cancel anything you can. (Remember you can only cancel things that are multiplied by the whole numerator or whole denominator.)

Question 3

Can this expression be simplified?

Answer 3

Nooooooo. That’s illegal canceling.

You can only cancel things that are multiplied by the whole top and the whole bottom.

Question 4

How do you add fractions?

For example:

Answer 4

You first have to get a common denominator. Then just add the numerators.

Question 5

How do you subtract fractions?

Answer 5

First, you have to get common denominators. Then you have to subtract the numerators.

BE CAREFUL! Make sure you distribute the negative to each term of the second numerator.

Question 6

How do you multiply fractions?

Answer 6

1. You multiply the numerators together and you multiply the denominators together.
2. Factorise the numerator and denominator.
3. Cancel anything you can. (Remember you can only cancel things that are multiplied by the whole numerator or whole denominator.)

Question 7

How do you divide fractions?

Answer 7

You multiply the reciprocal. This means you should do the following.

1. Flip over the second fraction.
2. Multiply the numerators together and multiply the denominators together.
3. Factorise the numerator and denominator.
4. Cancel anything you can. (Remember you can only cancel things that are multiplied by the whole numerator or whole denominator.)

Question 8

How do you expand this expression?

Answer 8

Question 9

When is a fraction undefined?

Answer 9

When the denominator is zero, since it’s impossible to divide by zero.

Question 10

When is a fraction equal to zero?

Answer 10

When the numerator is equal to zero, since anything divided by zero equals zero.

Question 11

How do you expand this expression?

Answer 11

Question 12

How do you factorise this expression?

Answer 12

Question 13

How do you factorise

ax²+bx+c?

Answer 13

1. Multiply a•c.
2. List all the numbers that multiply together to make ac.
3. Find which of these pairs add to equal b.
4. Rewrite ax²+bx+c with this pair instead of b. (So like ax²+dx+ex+c, where d and e are the numbers from the last step.)
5. Factorise the first two terms and the last two terms separately.
6. Rewrite so you have two sets of brackets mulitplied.

Question 14

How can you transform (x-y) into (y-x)? (In case you want it to cancel with something.)

For example:

Answer 14

Multiply by -1.

(x-y) = –1(y-x)

Question 15

What is a nested fraction?

Answer 15

It’s when there’s a fraction in the numerator or denominator.

Question 16

How do you simplify a nested fraction?

Answer 16

1. Simplify the numerator and denominator separately.
2. Divide the top fraction by the bottom fraction.