1. Changing Units in the Customary System
Lesson 3-6
Changing Units in the
Customary System

2. Review Why did King Henry die?
Write the metric units from kilo- to milli- in order in a single line in your notebook.

3. King Henry Died by Drinking Choc Milk
kilo hecto deka (m) deci centi milli
(liter)
(gram)
Each step to the right decreases the size by 10. This means you need more of each unit on the right to equal the same amount of a unit on the left.
Does 100 m = 1 cm, or does 1 m = 100 cm?

4. Four ways to solve conversion problems
Ladder method (if metric to metric)
SLD, LSM
Multiply by (a fraction equal to) 1
The Simple Rule of 3

5. 1. Ladder method This is what you learned in science.
Move the decimal point based on the units
Solve using the ladder method:
5.7 km = _____ m
King Henry Died by Drinking Choc Milk
5.7 km = 5,700 m

6. 2. SLD, LSM
When converting from smaller to larger units, divide. (SL?D)
Why?
The unit is larger, so you will need less of that unit to equal the value of the original unit.
Example: 82 dkl = ___ kl
King Henry Died by Drinking Chocolate Milk
dkl are 2 units smaller than kl, so SLD.
Divide by 100. (Why 100? Why not 1,000 or 10?)
82 dkl ÷ 100 = 0.82 kl

7. 2. SLD, LSM
When converting from larger to smaller units, multiply. (LS?M)
Why?
The unit is smaller, so you will need more of that unit to equal the value of the original unit.
Example: 82 kl = ___ cl
King Henry Died by Drinking Chocolate Milk
kl are 5 units larger than cl, so LSM.
Multiply by 10,000. (Why?)
82 kl • 10,000 = 8,200,000 cl

8. 3. Multiply by 1 Example: 57 km = ____ m
What fraction can I put in there that’s equal to 1 and has both units km and m?
Which one do I choose? The one where I can cancel the units (because we can cross cancel in multiplication).

9. 3. Multiply by 1 (continued)
That doesn’t look right. The units in my answer will be in km2/m, not in meters. Try the other fraction.
That’s better.

10. 3. Multiply by 1 (continued)
Solve:
5 weeks = ____ hours
Note: You will have to multiply by 1 twice!
5 weeks = 840 hours

11. Homework
Solve the following. Show all work, or specify if you used the ladder method.
3.65 mi = ___ km (Note: 1 mi = 1.61 km)
5 ft 11 in = ___ cm (Note: 1 in = 2.54 cm)
15 gal = ___ l (Note: 1 gal = l)
6,840 hours = ____ weeks
0.89 km = ___ mm

12. Homework Answers
Solve the following. Show all work, or specify if you used the ladder method.
3.65 mi = km
5 ft 11 in = cm
15 gal = l
6,840 hours = weeks
0.89 km = 890,000 mm

14. Problem of the Day
Question: You have a leaking bucket with 15 ¼ liters of water. Water drains out of the bucket at a rate of 1/3 liter per minute. In how many minutes will the bucket be empty?
Answer: 45 ¾ minutes
Setup: What method did I use?
15 ¼ liters • 1 minute
1/3 liter
Remember: improper fractions, reciprocal

15. Go over today’s quiz
Any questions about last night’s homework?

16. Homework
Use any method, but show your work. Refer to your textbook for conversion facts. (I will always give you the conversion facts on a quiz or test.)
Lesson 3-6, p. 150 #s 1-8 (all), (multiples of 3)
Quiz Monday on Lesson 3-5 Dividing Fractions and Mixed Numbers

17. 4. The Simple Rule of Three
This is a good way to solve problems with proportions, percents, and other situations where you are given three out of four pieces of information.

18. 4. The Simple Rule of Three (continued)
Example:
If there is a ratio of 3 boys to 2 girls in grade six, how many girls are there if there are 120 boys?
Step 1: Make a chart, filling in the information you are given.
Boys
Girls 3 2
120 x

19. 4. The Simple Rule of Three (continued)
Step 2: Multiply the items that are diagonal to each other, then divide to find x.
Boys
Girls 3 2
120 x
120 • 2 ÷ 3
= 240 ÷ 3
= 80
There are 80 girls in sixth grade.

20. 4. The Simple Rule of Three (continued)
If there are 15 items on a store shelf, and that is 20% of the total number of items being sold in the store, how many items does the store have?
Items %

21. 4. The Simple Rule of Three (continued)
If there are 15 items on a store shelf, and that is 20% of the total number of items being sold in the store, how many items does the store have?
Items % 15 20 x
100

22. 4. The Simple Rule of Three (continued)
If there are 15 items on a store shelf, and that is 20% of the total number of items being sold in the store, how many items does the store have?
Items % 15 20 x
100
15 • 100 ÷ 20 = 75
The store has 75 items for sale.

23. 4. The Simple Rule of Three (continued)
Now apply this rule to a conversion problem.
If there are 2.54 cm in one inch, how many inches are in 62 cm? Cm In
2.54 1 62 x
62 • 1 ÷ 2.54 = in
There are inches in 62 centimeters.