Download Unit_4_Math_Study_Guide_6th_01

Revised 11/8/01
Name ___________________________________________________
6th – Everyday Math
Date ____________________
Page 1
Study Guide for Unit 4 Assessment
1)
Numerator
2)
Denominator in a fraction is the bottom number or the number of equal parts in all.
Example:
3)
in a fraction is the top number or the number of equal parts you are talking about.
5
8
5 is the numerator
8 is the denominator
Common Denominator
of two fractions is any nonzero number that is a multiple of the
denominators of both fractions.
Example:
1
5
multiples are:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
5
12
multiples are:
12, 24, 36, 48, 60
60 is the common
denominator.
1x(12)=12
5x(12)=60
5 x(5)=25
12x(5)=60
4)
Equivalent Fractions Two fractions that name the same number.
To find an equivalent fraction multiply or divide both the numerator and denominator by the same
number. Example:
6 x (2) = 12
6 / (3) = 2
9 x (2) = 18
or
9 / (3) = 3
5)
To compare, add, or subtract fractions, you will need to be able to find common denominators.
Find the common denominator for 3/5 and 7/12.
Rewrite 3/5 and 7/12 using the common denominator you named above in number 3.
3/5 = __________
6)
Simplest Form A fraction is in simplest terms if the numerator and denominator cannot be divided by a
common whole number greater than 1.
Example:
7)
7/12 = ___________
6/8 can be divided by 2/2 so it is not in its simplest form.
6/8 divided by 2/2 equals 3/4. This fraction, 3/4 , is now written in its simplest terms.
Improper or Top-heavy Fractions
A fraction that names a number greater than or equal to 1 ; a
fraction whose numerator is greater than or equal to its denominator.
Examples are: 7/3,
5/4,
9/9,
16/4.
To change to mixed numbers think of:
5/4 is 5 divided by 4.
5 divided by 4 equals 1 remainder 1 or 1 1/5.
7/3 as 7 divided by 3.
7 divided by 3 equals 2 remainder 1 or 2 1/3.
Name _______________________________________________________
6th – Everyday Math
Unit 4
Date ________________
Page 2
Practice by converting each improper (top heavy) fraction to a mixed number.
a.
17/4 = __________
b.
12/5 = ___________
c.
35/6 = __________
d.
18/7 = ___________
e.
24/4 = __________
f.
138/10 = ___________
8) To change a mixed number to an improper (top heavy) fraction – You need to do three steps
Change
2 1/2 to a fraction.
1/2
2
+
= 5/2
1) Multiply the whole number by the denominator,
(2 * 2 = 4)
2) Add on the numerator to that answer. (1 + 4 = 5).
3) Then, place that number over the denominator. (5 over 2 = 5/2).
*
So,
9)
2 1/2 = 5/2
To Add or Subtract Fractions – Make sure the denominators are the same then add or subtract the
numerators.
Example 1:
3
5
11 + 11
Example 2:
3
8
Example 3:
1
2
+
4 4/9
=
=
8
11
First find a like denominator by finding an equivalent fraction.
1/2 is equal to 4/8, so 3 + 1 = 3 + 4 = 7
8 2
8 8
8
+ 5/9 =
4 9/9
You can convert 9/9 to 1,
so 4 9/9 = 5.
Practice adding. Write all answers greater than 1 as a mixed or whole number. Write in simplest terms.
a.
2 1/8 + 5/8 = __________
b.
3/4 + 1/8 = __________
c.
2/5 + 1/10 = __________
d.
1/6 + 1/3 = __________
e)
2
2/3 +
1
2/9 +
3 5/18
= __________
Name ___________________________________
6th – Everyday Math
Date ________________
Page 3
Subtraction Example:
4 4/9 - 5/9 = You can’t take 5/9 from 4/9, so you will need to borrow from the 4.
Take 1 from 4 4/9 and change it to 9/9, so you have 3 4/9 + 9/9.
Add the 9/9 onto your 4/9 = 13/9.
So,
4 4/9 = 3 13/9
3 13/9 - 5/9 = 3 8/9
10)
11)
12)
13)
Subtract. Write in simplest terms.
a)
5/6 – 1/6 =
c)
2 2/3 – 1 2/9 =
e)
6 5/12 -
________
________
11/12 = ________
b)
3/4 - 1/4 =
________
d)
4 – 2 4/5 =
________
f)
3 3/4
- 5/6 = ________
Rename each as a fraction or mixed number. Write in simplest terms.
(percent means per hundred so, 12% means 12/100)
a)
35% = ________
b)
80% = ________
c)
0.4 = ________
d)
3.6 = ________
Rename each as a decimal. Write in simplest terms.
(One way to make into a decimal is to divide the numerator by the denominator)
a)
17/50
c)
16% = ________
= ________
b)
3 1/5
d)
99% = ________
= ________
Rename each as a percent. Write in simplest terms.
(Make each equivalent to a fraction with the denominator in the 100ths, and then change to percent)
________
a)
0.4 =
c)
32/100 =
________
b)
3/4 =
d)
4.32 =
________
________
Name ___________________________________________________________
6th – Everyday Math
14)
Date ________________
Page 4
You will need to be able to compare two fractions, tell which is greater, and tell why it is greater.
a)
Is 5/16 greater than or less than 1/4?
_______
Why? ________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
b)
Is 3/4 + 1/8 greater than or less than 1?
________
Why? ________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
15)
You’ll be asked to complete number stories using the addition or subtraction of fractions.
a)
Joe was making tacos. He had 7/8 cup of sharp cheddar cheese, but the recipe called for 1 3/4
cups of sharp cheddar cheese.
How much more cheddar cheese does Joe need?
b)
Sarah is building a shelf. She needs three boards.
One board needs to be 14 3/4 inches long.
The other two each need to be 5 1/4 inches long.
How much wood does she need in all? ________
________
Name __________________________________________________________
6th – Everyday Math
Unit 4
16)
To Multiply Fractions – Use this formula.
Example 1:
Example 2:
1/4 of 64 =
1/3 of 3/8 =
1
4
*
64
1
1
3
*
3
8
=
=
a c
b*d
=
a*c
b*d
1 * 64
4 * 1
1 * 3
3 * 8
Date ________________
Page 5
=
=
64
4
64 / 4 = 16
=
3
24
3 can be reduced by dividing both the numerator and denominator by 3.
24
So . . .
3
24
Example 3:
2 1/2 * 1 3/4
+
1/2
2
=
=
3 / 3
24 / 3
=
1
8
=
You first need to change each mixed number into a fraction.
To change, multiply the whole number by the denominator,
(2 * 2 = 4)
Add on the numerator to that answer. (1 + 4 = 5).
Then, place that number over the denominator. (5 over 2 = 5/2).
5/2
*
2 1/2 = 5/2
So . . .
and
1 3/4 = 7/4
Now multiply. 5
2
*
7
4
=
5 * 7
2 * 4
To change 35/8 back to a mixed number, 35 divided by 8 equals 4 with 3 left over.
Place the 3 over the denominator 8, so your answer is
35/8 = 4 3/8.
Solve. Write each answer in simplest form.
If possible, write your answers as mixed numbers or whole numbers.
18
a)
1/3 of
= ________
c)
1/3 of
e)
3/5 * 7/8 = ________
3 1/2
= ________
b)
1/4 of 1/2 = ________
d)
2/5 of
f)
3 1/4 * 2 3/2
15
= ________
= ________
=
35
8
Name ___________________________________________________________
6th – Everyday Math
17)
Date ________________
Page 6
You will be given data and asked to figure the percents for that data
You will then be asked to use a percent circle to record that data on a circle graph.
Example:
A survey asked 6th grade students to name their favorite sport.
Favorite Sport of
sixth graders
Football
Number of
Students
12
Percent of Total
Hockey
3
%
Soccer
9
%
Baseball
6
%
Total Students
30
100 %
%
To find the percents:
1)
Make each into a fraction of the whole amount.
For football, 12 out of 30 students picked it as their favorite sport,
so the fraction would be 12/30.
2)
One way to find the percent of a fraction is to divide the numerator by the denominator and
multiply by 100.
So, 12 divided by 30 equals 0.4 multiplied by 100 = 40 or 40%.
a)
Complete the table above.
b)
Then use your Percent Circle to display the data on the circle graph below.