CUSTOMARY LENGTH
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page 12
12 inches (in) = 1 foot (ft)
36 inches = 3 feet or 1 yard (yd)
5,280 feet = 1 mile (mi)
To change from a
larger unit of
measure to a smaller
unit, MULTIPLY.
To change from a
smaller unit of
measure to a larger
unit, DIVIDE.
Length
American standard
Metric standard
1 mile = 1760 yards
= (5280 feet)
1 yard = 3 feet
1 foot = 12 inches
1 mil = 1/1,000 inch
1 kilometer = 1000 meters
1 meter = 10 decimeters
1 decimeter = 10 centimeters
( 1 meter = 100 centimeters)
1 centimeter = 10 millimeters
Conversion:
1 inch is defined to be exactly 2.54 cm in July, 1959.
(before this, the UK inch measures 2.53998 cm, while the US
inch was 2.540005 cm)
Length
American standard
Metric standard
1 mile = 1760 yards
= (5280 feet)
1 yard = 3 feet
1 foot = 12 inches
1 mil = 1/1,000 inch
1 kilometer = 1000 meters
1 meter = 10 decimeters
1 decimeter = 10 centimeters
( 1 meter = 100 centimeters)
1 centimeter = 10 millimeters
Conversion:
1 inch is defined to be exactly 2.54 cm in July, 1959.
(before this, the UK inch measures 2.53998 cm, while the US
inch was 2.540005 cm)
Length
American standard
Metric standard
1 mile = 1760 yards
= (5280 feet)
1 yard = 3 feet
1 foot = 12 inches
1 mil = 1/1,000 inch
1 kilometer = 1000 meters
1 meter = 10 decimeters
1 decimeter = 10 centimeters
( 1 meter = 100 centimeters)
1 centimeter = 10 millimeters
Conversion:
1 inch is defined to be exactly 2.54 cm in July, 1959.
(before this, the UK inch measures 2.53998 cm, while the US
inch was 2.540005 cm)
Length
American standard
Metric standard
1 mile = 1760 yards
= (5280 feet)
1 yard = 3 feet
1 foot = 12 inches
1 mil = 1/1,000 inch
1 kilometer = 1000 meters
1 meter = 10 decimeters
1 decimeter = 10 centimeters
( 1 meter = 100 centimeters)
1 centimeter = 10 millimeters
Conversion:
1 inch is defined to be exactly 2.54 cm in July, 1959.
(before this, the UK inch measures 2.53998 cm, while the US
inch was 2.540005 cm)
First we need to find he length of each side by
counting the squares.
8 cm
6 cm
6 cm
The distance
around the
outside of a shape
is called the
perimeter.
8 cm
The perimeter of the shape is 8 + 6 + 8 + 6 = 28cm.
Now find the
perimeter of these
shapes. They are
not drawn to
scale.
5cm
3cm
3cm
4cm
3cm
7cm
3cm
7cm
3cm
3cm
Perimeter = 18cm
4cm
3cm
3cm
3cm
3cm
4cm
4cm
3cm
Perimeter = 22cm
Perimeter = 28cm
Take a walk around the edge!
This is a regular
octagon with sides
4 cm
The perimeter
is…
32 cm !
28
1) SOLVE R + 16 = -7
1.
Draw “the river” to
separate the
equation into 2 sides
2.
Subtract 16 from
both sides
3.
Simplify vertically
4.
Check your answer
by substituting your
answer back into the
problem
- 16 -16
r
= -23
-23 + 16 = -7
2) SOLVE X + 2 = -3
GET THE VARIABLE BY ITSELF. WHAT IS
YOUR FIRST STEP?
1.
Add 2 to both sides
2.
Subtract 2 from both sides
3.
Add 3 to both sides
4.
Subtract 3 from both sides
Answer Now
3) SOLVE 8 = M - 3
1.
2.
3.
4.
m=5
m = 11
m = 24
m = 8/3
Answer Now
APPLICATION
Clare had 9 bears. After she gave away some bears to her
brother, Clare still had 3 bears. How many bears did Clare give
away?
9–?=3
Clare had some bears. After she gave away
3 bears to her cousin, she had 6 bears left. How many bears
did Clare have to begin with?
?–3=6
NEGATIVE NUMBERS - THIS TIME THE SCALE IS HORIZONTAL
-6 -5
-4
-3 -2
-1
0
1
2
3
4
5
6
CAN YOU ORDER THIS SET OF NUMBERS STARTING
WITH THE COLDEST?
20
- 15
- 20
5
-2
10
-7
-10
-5
+7
0
5
10
A number line has many functions. Previously, we learned
that numbers to the right of zero are positive and numbers to
the left of zero are negative. By putting points on the
number line, we can graph values.
If one were to start at zero and move seven places to the right,
this would represent a value of positive seven. If one were to
start at zero and move seven places to the left, this would
represent a value of negative seven.
-7
-10
-5
+7
0
5
10
Both of these numbers, positive seven (+7) and negative seven
(-7), represent a point that is seven units away from the origin.
The absolute value of a number is the distance between that
number and zero on a number line. Absolute value is shown by
placing two vertical bars around the number as follows:
5 The absolute value of five is five.
-3 The absolute value of negative three is three.
LET’S PRACTICE
1.
-1
2.
5
3.
6
4.
-19
5.
-179
6.
57
EXAMPLE 2: (-2) + 5
1. Our car starts from 0 facing right.
2. It then backs up 2 units (to the
left) because it sees the - sign.
EXAMPLE 3: 5 – 3
1. Our car still starts at 0 facing
right.
2. It then moves forward 5 units.
EXAMPLES OF ADDITION
Four more than eleven
4+11
14 increased by 2
14 + 2
The sum of 9 , 4, and 11
9 + 4 + 11
EXAMPLES OF SUBTRACTION
34 decreased by 11
34 -11
17 less than 30
30 - 17
27 take away 10
27 - 10
EXAMPLES OF EQUALS
The sum of 4 and 19 is 23
4 + 19 = 23
The difference of 14 and 5 is 9
14 - 5 = 9
15 less than 6 becomes 9
15 – 6 = 9
EXAMPLES OF EQUALS
The sum of 4 and 19 is 23
4 + 19 = 23
The difference of 14 and 5 is 9
14 - 5 = 9
15 less than 6 becomes 9
15 – 6 = 9
UNIT 2 REVIEW
Review Questions on page 84 and 85 #1-40