Simplify
1.
1
4
2.
2
3
2
3
3.
3
5
5
4. 4
1
4
5 Minute Check
Simplify
1.
1
4
2
5 Minute Check
5 Minute Check
Simplify
1.
1
4
2
1
÷
4
2
1
1
4
1
2
·
=
1
8
Simplify
2. 3
2
3
5 Minute Check
5 Minute Check
Simplify
2. 3
2
3
3
1
3
1
÷
2
3
·
3
2
=
9
2
1
2
=4
Simplify
3.
3
5
5
5 Minute Check
5 Minute Check
Simplify
3
5
3.
5
3
5
3
5
÷
5
1
·
1
5
=
3
25
Simplify
4. 4
1
4
5 Minute Check
5 Minute Check
Simplify
4. 4
1
4
4
1
1
4
÷
4
1
·
4
1
= 16
Tuesday, Jan 6
Lesson 7.1.3
Convert Unit Rates
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Solve One-Step Inequalities
Convert Unit Rates
Objective: To convert units of measure
between derived units to solve problems.
Convert Unit Rates
The relationships among some commonly used
customary and metric units are shown in the
tables below.
Convert Unit Rates
Each of the relationships in the tables can be
written as a unit ratio. A unit ratio, like a unit
rate, has a denominator of one unit.
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
How to Convert Unit Rates
Step 1 – Write the complete rate as a fraction
with units .
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft
1s
How to Convert Unit Rates
Step 1 – Write the complete rate as a fraction
with units .
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft
1s
How to Convert Unit Rates
Step 2 – Determine the units of the answer
and write as a fraction.
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft
in
Leave space for the
1s
1s
=
conversion rate.
How to Convert Unit Rates
Step 2 – Determine the units of the answer
and write as a fraction.
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft
in
Leave space for the
1s
1s
=
conversion rate.
How to Convert Unit Rates
Step 3 – Determine the units of the
conversion rate(s).
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
conversion rate .
10 ft
in
in
1s
ft
1s
=
How to Convert Unit Rates
Step 3 – Determine the units of the
conversion rate(s).
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
conversion rate .
10 ft
in
in
1s
ft
1s
=
The conversion rate units are determined by the
original rate units and the answer units.
In the above case, we need to cancel the “ft” units
and replace with “in” units. Notice the conversion
rate has “ft” in the denominator, so it will cancel the
“ft” of the original rate.
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft
in
in
1s
ft
1s
=
conversion rate.
How to Convert Unit Rates
Step 4 – Complete the conversion rate(s).
Eg. How many inches in how many feet?
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft 12 in
in
1s
1 ft
1s
=
conversion rate.
How to Convert Unit Rates
Step 4 – Complete the conversion rate(s).
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft 12 in
in
1s
1 ft
1s
=
How to Convert Unit Rates
Step 5 – Multiply and cancel units.
Convert Unit Rates
A remote control car travels at a rate of 10
feet per second. How many inches per
second is this?
10 ft 12 in
120 in
1s
1 ft
1s
=
How to Convert Unit Rates
Step 5 – Multiply and cancel units.
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
Step 1 - ?
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
60 mile
1h
Step 2 - ?
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
60 mile
1h
Step 3 – ?
=
ft
1h
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
60 mile
1h
ft
mile
=
ft
1h
Remember – we want to cancel the “mile” unit in the
numerator of the original rate. In order to do so,
the conversion rate must have a “mile” unit in the
denominator.
Step 4 – ?
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
60 mile
1h
5280 ft
1 mile
=
ft
1h
How many feet in how many miles?
Step 5 – ?
Convert Unit Rates
A swordfish can swim at a rate of 60 miles per
hour. How many feet per hour is this?
60 mile
1h
5280 ft
1 mile
=
316, 800 ft
1h
Convert Unit Rates
A gull can fly at a speed of 22 miles per hour.
How many feet per hour can the gull fly?
Do this on your own.
Convert Unit Rates
A gull can fly at a speed of 22 miles per hour.
How many feet per hour can the gull fly?
22 miles
1h
5280 ft
1 mile
=
116,160 ft
1h
Convert Unit Rates
An AMTRAK train travels at 125 miles per
hour. Convert the speed to miles per minute.
Round to the nearest tenth.
Do this on your own.
Convert Unit Rates
An AMTRAK train travels at 125 miles per
hour. Convert the speed to miles per minute.
Round to the nearest tenth.
125 miles
1h
1h
60 min
=
2.1 miles
1 min
Convert Unit Rates
Marvin is walking at a speed of 7 feet per
second. How many feet per hour is this?
Do this on your own.
Convert Unit Rates
Marvin is walking at a speed of 7 feet per
second. How many feet per hour is this?
7 ft
1s
420 ft
1 min
60 s
1 min
=
60 min
1h
420 ft
1 min
=
25,200 ft
1h
Or you can create one large conversion rate…
Convert Unit Rates
Marvin is walking at a speed of 7 feet per
second. How many feet per hour is this?
7 ft
1s
60 s · 60 min
1 min · 1 h
=
25,200 ft
1h
Convert Unit Rates
The average speed of one team in a relay race
is10 miles per hour. What is the speed in feet
per second? Round to the nearest tenth.
Do this on your own.
Convert Unit Rates
The average speed of one team in a relay race
is10 miles per hour. What is the speed in feet
per second? Round to the nearest tenth.
10 miles
1h
5280 ft
1 mile
=
52,800 ft
1h
52,800 ft 1 h
880 ft 1 min 14.7 ft
1h
60 min
1 min 60 s
1s
Or you can create one large conversion rate…
=
=
Convert Unit Rates
The average speed of one team in a relay race
is10 miles per hour. What is the speed in feet
per second? Round to the nearest tenth.
10 miles
1h
5280 ft · 1 h · 1 min
1 mile · 60 min · 60 s
=
14.7 ft
1s
Convert Unit Rates
Johanna’s parents give her $10 per week for lunch money.
When you convert 100 ft per second to inches
per second, will there be more or less than
100 inches? Explain.
Convert Unit Rates
Johanna’s parents give her $10 per week for lunch money.
When you convert 100 ft per second to inches
per second, will there be more or less than
100 inches? Explain.
More; Since inches are smaller than feet, it will
take more inches to make equivalent rates.
Convert Unit Rates
Johanna’s parents give her $10 per week for lunch money.
If 1 yard is equal to 0.91 meters, convert 7
meters per minute to yards per hour. Round to
the nearest tenth.
Convert Unit Rates
Johanna’s parents give her $10 per week for lunch money.
If 1 yard is equal to 0.91 meters, convert 7
meters per minute to yards per hour. Round to
the nearest tenth.
7 meter
.91 meter
? yd
1 yd
=
7 meters = 7.7 yds
7.7 yd
1 min
=
7.7 yd 60 min
462 yd
1 min
1h = 1 h
Convert Unit Rates
Agenda Notes
Homework –
Homework Practice 7.1.3
Due Wednesday, Jan 7
You can use the table in slide 22 , if needed.
Mid-Chapter 7.1 Quiz - Thursday, Jan 8