The document discusses key concepts for fractions including changing improper fractions to mixed numbers and vice versa, equivalent fractions through reducing and raising to higher terms, and comparing fractions by finding a common denominator. It provides examples for how to change fractions between improper and mixed number form, reduce fractions, raise fractions to higher terms, and compare fractions.

1. • 1. Review: Data
• 2. Introduction to Fractions (vocabulary)
• 3. Changing Improper Fractions to Whole or
Mixed Numbers
• 3. Changing Mixed Numbers to Improper
Fractions
• 4. Equivalent Fractions (Reducing and Raising to
Higher Terms)
• 5. Practice

2. The process of making the
• Numerator denominators the same in two or
• Denominator more fractions through division or
multiplication.
• Part
• Whole
• Mixed number
• Greatest common The opposite of reducing. The goal
factor is to make the denominators the
same so you can compare, add, or
• Lowest Common subtract.
denominator
• Reducing
• Higher Terms
• Equivalent Fractions

3. part
whole
Since the part is smaller than
the whole, we consider this a
PROPER fraction.

4. • 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.

5. •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

6. In order to multiply or
This represents divide mixed numbers, you
4 wholes plus must be able to turn them
into improper fractions.
one part out of
three parts.

7. • 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.

8. • Equivalent fractions have the same value.
• Equivalent fractions are equal. When you add or
subtract fractions with
different denominators,
you will have to find a
common denominator.

9. • Summary: Later when you add and subtract fractions, you
will often need to raise fractions to higher terms. To raise
to higher terms, you will need to multiply the top and
bottom by a number that will equal the same product.
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: 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.

11. • 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.

12. • 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.

14. • 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.