Add, subtract, multiply, divide fractions

1. • 1. GED Practice (Writing Decimals as
Fractions)
• 2. Basic Review of fractions
• 3. A/S/M/D Fractions

2. • At his job, Peter fills out a time sheet every Friday.
This week, Peter spent 27.5 hours out of 40 hours, or
0.6875 of his time, working on Project A.
• Which fraction is the best estimate of the time Peter
spent on Project A?
“seven tenths”
(1) 2/3
(2) 3/4
(3) 3/10
(4) 7/10
(5) 7/25

3. • Summary:
– Divide the denominator into the numerator
– Write the remainder as a fraction
•Example 1: Change to a mixed number.
4
•Step 1: Divide 3 into 14.
3) 14
- 12
2
•Step 2: Write the remainder (2) over the divisor
(3) to form the fraction part of the answer.

4. •Example 2: Change to a mixed number.
1
•Step 1: Divide 8 into 12.
8) 12
- 8
4
•Step 2: Write the remainder (4) over the divisor
(8) to form the fraction part of the answer.
•Step 3: Reduce the fraction

5. • Summary:
– Multiply the whole number by the denominator
– Add to the numerator
– Place over the current denominator
•Example 1: Change to an improper fraction.
•Step 1: Multiply the whole number by the
denominator .
•Step 2: Add the numerator to the product.
• Step 3: Write the answer over the denominator
to form the fraction part of the answer.

6. • Summary: Reducing changes the numbers in
a fraction, but it does not change the VALUE
of a fraction.
Example: Reduce
To reduce a fraction,
you divide both the •Step 1: Divide
numerator and both 14 and 16
denominator by a
by a number
number that goes
into them both that goes evenly
evenly. into both of
them.

7. • You will need to know how to set up fractions
and reduce them.
Example: John makes $800 a month. He pays $200 a
month to rent a room. What fraction of his income does
John pay for rent?
• Step 1: Find the whole.
Write it in the denominator.
• Step 2: Find the part. Write
it in the numerator.
• Step 3: Reduce.

8. • Summary: Reducing changes the numbers in
a fraction, but it does not change the VALUE
of a fraction.
•Step 1: Divide Example: Reduce
both 30 and 45
by a number
that goes evenly
into both of
them.

9. • Summary: Later when you add and subtract fractions,
you will often need to raise fractions to higher terms.
This is the opposite of reducing.
Example: Raise the fraction to higher terms by
finding the missing numerator.
•Step 1: Divide the 4
new numerator by the 6) 24
old denominator.
•Step 2: Multiply both
the old denominator
and numerator by 4.

10. • Summary: To compare fractions, you must have the
same denominators. Raise each fraction to higher
terms, then the new compare numerators.
Example: Which fraction is bigger,
•Step 1: Find a
common denominator ×7 21
for 5 and 7 and raise to 7
higher terms. ×7 5) 35
•Step 2: Look at the
numerators and
decide which one is
×5 25 5
×5 7) 35
bigger.

11. • Step 1: Look at the
denominators. If they are
different, find a common
denominator for the two
x4
7 8
numbers.
x4
• Step 2: Rewrite the problem
with new common
denominators.
• Step 3: Rewrite the
numerators.
• Step 4: Add the numerators.
• Step 5: Reduce answer to
lowest terms.

12. •Step 1: Find the Lowest ×3
Common Denominator 21
•Step 2: Add numerators ×3
×8 16
•Step 3: Change the
improper fraction to a
mixed number ×8
•Step 4: Add the whole
-24 13
number part of the
answer to the mixed number.

13. Step 1: Find a
common
denominator.
Step 2: Since you
×3 8 6 cannot take 7 from 6,
you must borrow
ONE from the whole
×3 number and add it to
the fraction.
Step 3: Subtract the
numerators, keep the
denominator.
Step 4: Subtract the
whole numbers.

14. • Step 1: Multiply the numerators together
• Step 2: Multiply the denominators together.
• Step 3: Reduce the answer if possible.
21

80

15. • To cancel, find a number that divides evenly
into the numerator of one fraction and the
denominator of the other.
1 2 •Step 1: Divide 3 and 15 by 3
2 •Step 2: Divide 4 and 8 by 4
•Step 3: Multiply the new
1 5
5 numerators and
denominators.

16. • A whole number can be written as a fraction
with a denominator of 1.
• Remember: a fraction of means to multiply.
Find ¾ of 24.
•Step 1: Write 24 as a fraction.
•Step 2: Divide 4 and 24 by 4.
•Step 3: Multiply across.
•Step 4: Change the improper
fraction to a whole number.

17. • Step 1: Change to an
improper
fraction.
• Step 2: Divide 4 and
6 by 2.
• Step 3: Multiply
across.
• Step 4: Change the
improper
fraction to a
mixed number.

18. • In division problems with fractions
or mixed numbers, you must invert
the divisor. The fraction ½ is the
reciprocal, or the inverse of the
improper fraction 2/1.

19. • Step 1: Write each number in fraction form.
• Step 2: Invert the divisor and change the
to a sign. (KSF!)
• Step 3: Follow the rules for multiplying
fractions.

20. • Change to an improper fraction and then
proceed as usual.