Math Study Guide: Topic 3: Fractions and Mixed Numbers (pages 18-24)

Question 1

How do you change a fraction to a decimal?

Answer 1

by dividing the denominator (bottom) into the numerator (top)

Example: 4/9 = 4 divided by 9 = 0.44444 repeating forever

Question 2

How do you change a decimal into a fraction?

Answer 2

by getting rid of the decimal point, and then putting the number over the correct power of 10

Example: 0.125 can be written as 125/1,000, which can be reduced to 1/8

Question 3

When you add or subtract fractions, what must always be true?

Answer 3

They must have the same denominator.

And don’t forget, whatever you multiply to get the same denominator, you have to multiply to the numerator (then add or subtract the numerators)

Question 4

How do you multiply fractions?

Answer 4

Multiply the numerators together and multiply the denominators together (do not cross multiply!)

Question 5

Before multiplying fractions, what should you try to do?

Answer 5

Reduce the fractions if there is a common factor that is in one numerator and one denominator

Example: ¾ x 8/9 = 1/1/ x ⅔ = ⅔

Question 6

How do you divide fractions?

Answer 6

Multiply by the inverse (upside down) of that fraction

Example: ¾ divided by 7/5 =

¾ x 5/7

Question 7

What is an “improper fraction?”

Answer 7

An “improper fraction” is one where the numerator is larger than the denominator.

Example: 15/7 is an improper fraction. This can be changed to 2 1/7

(This can be changed to a “mixed number,” which is a whole number plus a fraction)

Question 8

What is a “mixed number?”

Answer 8

A “mixed number” is a whole number plus a fraction.

Example: 2 1/7

Question 9

How do you change a “mixed number” to an “improper fraction?”

Answer 9

Multiply the whole number by the denominator, then add the numerator.

Example: 5 ¾ is a mixed number. Multiply 5 by 4 and then add 3 = 22/4

Question 10

What should you do first before multiplying or dividing mixed numbers?

Answer 10

Change them into improper fractions.

Question 11

What can you do before adding or subtracting mixed numbers?

Answer 11

You can change them to improper fractions, but you don’t have to.

Example: For 3 ⅔ + 4 ¼, add 3 to 4 to get 7, and then add ⅔ + ¼ = 11/12, equaling 7 11/12

Question 12

In adding or subtracting mixed numbers, what do you do if the fraction of the larger number is smaller than the fraction of the smaller number?

Answer 12

You “borrow” from the whole number.

• Example: 8 ¼ - 3 3/5 =*
• 7 5/4 - 3 3/5 =*
• 4 13/20*