Download Unit_6_Math_Study_Guide_6th_01

Name _________________________________________
Date ___________________
6th – Everyday Math
Page 1
Study Guide for Unit 6 Assessment
1) Multiplying Mixed Numbers and Fractions
Example:
3 1/2 * 2/3
First, changed the mixed number 3 1/2 to a fraction.
+
3
1/2
= 7/2
*
Second, multiply the numerators and multiply the denominators.
7
2 = 14
2 * 3 = 6
Third, Change back to a mixed number and reduce. 14/6 = 14 divided by 6 = 2 2/6 = 2 1/3
Solve:
a)
5 1/2 * 3/4 = _____
b)
3 2/5 * 1/2 = _____
2) Dividing Fractions by Fractions - Multiply the first fraction by the reciprocal of the second fraction.
*Reciprocal fractions are upside down fractions of the original.
The reciprocal fraction of 2/3 is 3/2.
Example: 7/2 divided by 2/3.
So,
7
2
2
3
a)
4/5
7 3 = 21
2 * 2 = 4
Solve:
2/3 = _____
b)
2/3
1/2 = _____
3) Adding and Subtracting Negative Numbers When adding two numbers, think of the first addend as a starting
point on a number line, the second addend as a move away from that starting point to the sum or difference.
(Start at 1, Add –5)
Example:
-6 –5 –4 –3 –2 –1
0 1
2 3
1 + (-5) = -4
4 5 6
6th
Unit 6 Study Guide
page 2
Solve:
a)
-3 + 5 = _____
c)
-8 – (-3) = _____
b)
5 + (-3) = _____
d)
(OPP) (OPP) -9 + (-3) = _____
(the two negatives make a plus)
4) Multiplying and Dividing Negative Numbers
Rule 1: If the numbers are both positive or both negative, the result is a positive number.
Rule 2: If one of the numbers is negative and the other is positive, the result is a negative number.
(Neg) (Neg) (Pos)
(Pos) (Neg) (Neg)
Example 1: -6 * (-2) = 12
(Neg) (Pos) (Neg)
Example 2: 6 * (-2) = -12
Example 3:
-12 / 2 = -6
Solve:
a)
-3 * 8 = _____ b)
64 / (-8) = _____
c)
-5 * (-5) = _____
Working with Expressions Involving Positive and Negative Numbers
Compare the Add/Sub. Chart with the Mult./Div. Chart below.
Remember when Adding or Subtracting to think
of it as putting together positives and negatives
Remember when Multiplying & Dividing
some rules are different from add/sub.
Pos. & Pos. / Add / answer is Pos.
Neg. & Neg. / Add / answer is Neg.
Pos. & Neg. / Sub. / answer is the sign of larger #
Pos. & Pos.
Neg. & Neg.
Pos. & Neg
answer is Pos.
answer is Pos.
answer is Neg
When adding two negative numbers your answer is always negative, but...
When multiplying or dividing two negative numbers the answer is always positive.
When adding a positive and negative number, the sign depends on which number is larger (pos or neg.) but...
When multiplying or dividing a positive and negative number the sign is always negative.
5) The Order of Operations – Please Excuse My Dear Aunt Sally. or PEMDAS
Parenthesis,
Exponents,
( Multiply “or”
Example: 52 + (3 * 4 – 2) / 5 =
Parenthesis first.
(multiply)
(subtract)
Exponents next.
Divide then add.
Answer:
Divide), (Add
“or”
Subtract). (Work left to right.)
52 + (3 * 4 – 2) / 5 = ?
52 + ( 12 – 2) / 5 =
52 +
10
/5 =
25 +
10
/5 =
25 +
2
= 27
52 + (3 * 4 – 2) / 5 = 27
6th
Unit 6 Study Guide
page 3
Solve: Follow the rules for the order of operations. (Show each step.)
(You would multiply here)
a)
6 + 3(14 – 6) = _____
b)
(6 + 14) / 5 * 8 = _____
c)
4 * 7 + 16 / 4 = _____
d)
2 * 62 + (27 / 3 – 4) = _____
e)
(42 / 2) + (14 / 2 – 5)3 = ____
f)
0.4 * (-6) = _____
g)
2 + 24 / 4 = ____
h)
102 * (21 / 3)
i)
(-3 + 5) 9 / 3 = _____
j)
(12/4 + 7)3 + (24/6 –2)4 = _____
= _____
6) Insert parenthesis to make each number sentence true.
a)
7 * 3 - 3 = 18
b)
9.2 * 2 - 2 > 10
c)
3 * 4 - 2 = 3 + 0 * 2
d)
6 / 2 + 3 > 6
e)
12 - 3 * 4
f)
6 * 9 = 46 + 4 * 2
= 36
6th
Unit 6 Study Guide
page 4
7)
Equations – Number sentences that contain the relation symbol “=” are called equations.
Example: 7 * 5 = 35
8)
Variables A variable is a letter or symbol that represents a number.
Example 1:
7*5=x
Example 2:
7 * b = 35
Find the solution to each equation. Show your steps.
(*Hint: When all else fails, try plugging in numbers to see if it makes the number sentence true – Guess & Test)
a)
c)
(1/4)t – 4 = 6
j + 6 = 23
b)
Operation
____
____________
Operation
____
____________
____
____________
Solution:
Solution: ____________
____________
(e – 7) + 6 = 24
d)
3x + 4 = 25 – 4x
Operation
____
____________
____
____________
Operation
____
____________
____
____________
____
____________
Solution:
Solution: ____________
____________
Evaluate each expression for x = 5.
a)
9)
6 + x = ______
b)
4 x – 7 = ______
Joe is giving each student in his class 2/5 of a bag of jellybeans for his birthday.
He has 20 students in his room.
a)
How many bags will he need to buy?
___________________
b)
Write down the equation you used to solve this.
___________________
6th
Unit 6 Study Guide
page 5
10) Pan Balance Problems – If several objects are placed in the pans and if the pans are in balance, then you
can find the weight of one kind of object in terms of the other kind of object.
Example:
1)
2)
3)
Here you see 2 blocks, 6 stars on one side and 1 block , 8 stars on the other side.
You have at least one block on each side that balance so they cancel each other out.
You have at least 6 stars on each side that balance so they cancel each other out.
That leaves one block which equals 2 stars.
Solve the pan balance problems.
a)
b)
1 circle = _____ cylinders
1 heart = _____ triangles
c)
1 star = ______ lightning bolts
11)
Circle each number sentence that is true.
a)
x–5>x
b)
42 >
c)
(42 * 65) + 12 = 12 + (65 * 42)
d)
r*0>0
e)
786.6 = 786.60
f)
sixty-two is half of thirty-one
g)
12 = 14
h)
x/1=x
i)
376 < 234
6th
Unit 6 Study Guide
page 6
12) Inequalities – are any number sentences that contain one of the relation symbols below.
=
<
>
>
<
An inequality that contains one or more variables is an open sentence.
Example:
The inequality x + 3 > 8 is an open sentence.
To graph this we would draw a closed circle beginning at 5 (since 5 + 3 = 8)
Then draw an arrow through all numbers greater than 5 on the number line.
-10 -9 -8 -7 -6 -5 -4 -3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
Graph the solution for each inequality.
a)
y
= 8
-10 -9
b)
-8
-10 -9
13)
-5
-4
-3
-2 -1
0
1
2
3
4
5
6
7
8
9
10
-5
-4
-3
-2 -1
0
1
2
3
4
5
6
7
8
9
10
-5
-4
-3
-2 -1
0
1
2
3
4
5
6
7
8
9
10
y > 8
-10 -9
c)
-7 -6
-8
-7 -6
y < 8
-8
-7 -6
Write >, <, or = to complete each number sentence.
a)
-34 + (-18) _____ 12 - 64
b)
5 * (-80) _____ - 800 / 2
c)
5/6 – 2/3 _____ 3/4 – 3/8
d)
1/2 + 5/12 _____
1