Unit 4 –
Rational Numbers and Operations
Name: ___________________
Lesson 4.1 – Equivalent Fractions
Simplest Form:
 Smallest name for a fraction
 Numerator and denominator have only one factor in common – “1”
 Numerator is smaller than the denominator
Finding simplest form
1. Find greatest common factor (GCF) -Largest factor found in two numbers
2. Divide the numerator and denominator by the GCF
60
÷
12 = 2
60 ÷
12 = 5
3. Check: Is there another common factor?
Lesson 4.2 - Comparing Fractions
Ways to compare fractions:
 Same denominators
 Same numerators
(larger value = larger numerator)
(larger value = smaller denominator)
 Compare to ½: Are the fractions less than, equal to, or greater than ½
 QCD - Quick Common Denominator (multiply denominator)
 Change to a decimal form and compare (calculator)
 Draw a picture
Least Common Denominator
1. Find the least common multiple (LCM)
2. List the multiples of the two denominators
3. Find the smallest one they have in common (this can be one of the
denominators)
12 = 12 24 36 48 60
20 = 20 40 60 80 100
Divisibility Rules Review
Divisible
by
When…
Examples
2
3
4
5
6
The ones digit is an even number.
The sum of the digits is divisible by 3.
The last 2 numerals are divisible by 4.
The ones digit is either a zero or a 5.
When the number ends in an even
numeral and the sum of the numerals is
divisible by 3.
You strike out the last numeral, double
that number and subtract that number
from the remaining digits, and the answer
is divisible by 7
The sum of the numbers is divisible by 9.
The ones digit is a zero.
244, 58, 7890
621, 999, 2082
424, 216, 7836
50, 975, 8090
354, 72, 5796
7
9
10
343
864, 324, 9738
80, 570, 3230,
Lesson 4.3 – Adding and Subtracting Fractions
Directions:
1. Find a common denominator
2. Write an equivalent fraction for each fraction
3. Add or subtract the numerator
4. Keep the denominator the same
5. Simplify
1
2
+
3
4
=
2
4
+
3 = 5 =
4
4
1¼
Lesson 4.4 - +/- Mixed numbers (like denominators)
Proper fraction - Numerator is smaller than the denominator
3
2
1
4
3
8
Improper fraction- Numerator is equal to or larger than the denominator
5
4
3
1
124
2
Simplest Form of a Mixed Number- The fraction part is in simplest form
Lesson 4.5 - +/- Mixed numbers (unlike denominators)
Add Mixed Numbers
1. Find a common denominator
2. Add the whole numbers
3. Add the fractions
4. Simplify
Subtract Mixed Numbers
1. Find a common denominator
2. Subtract the bottom whole number from the top whole number
3. Subtract the bottom fraction from the top fractions
(You may need to trade)
4. Simplify
Lesson 4.6 – Fraction Multiplication
Fraction Multiplication
1. Multiply the numerators
2. Multiply the denominators
3. Simplify the answer
3 * 5 = 15 =
4
6
24
7 * 2 = 14 =
3
3
9
5
8
4
2
3
Lesson 4.7 – Multiplication of Mixed Numbers
Multiply Mixed Numbers
1. Rename Mixed Numbers as Fractions
2. Multiply across
3. Reduce to simplest form
Lesson 4.8 – Fractions, Decimals, Percents
Fractions = The part of a whole
84 / 100
Decimals = The part of one
0.84
Percent = The part of 100
84 %
84 out of 100
Lesson 4.9 –Conversions
Decimal to a Percent
1. Move the decimal point two places to the right
2. Write the percent sign (%) after the number
Decimal to a Fraction
1. Write the decimal with a denominator of a power of ten (10, 100, 1000)
2. Find the simplest form of the fraction
Percent to a decimal
1. Move the decimal point two places to the left and leave off the percent sign
Percent to a fraction
1. Convert the percent to a fraction with a denominator of 10 or 100
2. Simplify the fraction
Lesson 4.11 – Percent of a Number
Regular Price - price to be paid
Discount
- the amount that you save in dollars and cents
Sale Price
- paid after the discount
Regular Price – Discount = Sale Price
Interest
-Amount paid to use someone else’s money
30 percent
of
60
=
x
.3
*
60
=
x
1/10
of
60
=
x
So 3/10
of
60
=
x
Unit 4 Study Zone
Test Date: ___________________
Parent’s Signature: ____________________
My plan to prepare for this test is:
Ideas to try…
Skill
Write fractions in
simplest form
Vocabulary/Process
Simplest form can be:
 Divide the numerator and denominator
by the Greatest Common Factor
 Improper fraction to a mixed number
Rename numbers as
fractions, decimals,
and percents
Review notes
Remember:
 Decimals are in tenths and hundredths
 Fractions may go up or be simplified to
get a denominator of 100
Add and subtract
mixed numbers
 Find a common denominator
 Add/Subtract the fractions first
 Add/Subtract the whole numbers
 Simplify to a mixed number
Note: You may convert both to improper
fractions and then solve and simplify
Estimate answers by
comparing to 1/2
Multiply fractions
Determine percents
using a calculator
Draw a circle graph for
chart data
 Round each number to the nearest half
(you may draw or visualize)
 Add to estimate the answer
 Compare estimate to question
To multiply fractions:
 Write both numbers as proper or improper
fractions
 Multiply across- numerators
 Multiply across-denominators
 Simplify
To find percents
 Write the part and whole as a fraction
 Divide the numerator by the denominator
 Round to nearest whole percent
 If it is more than one whole, then the
answer will be over 100%
To draw a circle graph
 Draw a circle and center point
 Draw sectors for each piece of data
 Label the sector and percent
 Check for a total of 100%
 Add a title
How to Study
Create any fraction (roll dice or use cards)
and simplify
Use examples from your study links and
journal to simplify and check
1. Use any or all of the items on an attached
page
2. Naming practice/races
 Write a fraction, decimal, or percent
 Write the number in other 2 formats
1. Use any or all of the items on an attached
page
2. Think of two numbers (with different
denominators) and subtract the smaller
from the larger. Use your answer in a fact
family addition problem to check your work.
Look at the fractions on an attached
worksheet. Classify them as less than ½,
equal to ½ or greater than ½.
1. Use any or all of the items on an attached
page
2. Choose two numbers (fractions, mixed, or
one of each) and multiply them. Check your
work on a calculator.
1. Choose two cards and create a fraction.
Either number may be in the numerator.
2. Divide the numerator by the
denominator.