Study Guide
Unit Conversion & Ratio – Direct Proportion
Unit Conversion follows Ratio – Direct Proportion pattern, so set up Ratio – Direct proportion between two
Units you are converting.
For example, you want to convert 35 feet to yard;
𝟏𝒚𝒂𝒓𝒅
Step 1. Set up Ratio between feet and yard:
Step 2. Write Direct Proportion form:*
𝟑𝒇𝒆𝒆𝒕
𝟏𝒚𝒂𝒓𝒅
𝟑𝒇𝒆𝒆𝒕
(This is known 1 yard = 3 feet)
𝒙
= 𝟑𝟓𝒇𝒆𝒆𝒕 ,OR
𝟑𝒇𝒆𝒆𝒕
=
𝟏𝒚𝒂𝒓𝒅
𝟑𝟓𝒇𝒆𝒆𝒕
𝒙
Step 3. Apply Cross multiplying rule: 𝟑𝒙 = 𝟑𝟓,
𝟑𝒙
𝟑𝟓
= 𝟑
𝟑
𝒙 = 𝟏𝟏. 𝟕 𝒚𝒂𝒓𝒅 , so 35 feet = 11.7 yard
*
It is wrong if you set up
𝟏𝒚𝒂𝒓𝒅
𝟑𝒇𝒆𝒆𝒕
𝟑𝟓𝒇𝒆𝒆𝒕
=
𝒙
; this form shows the Inverse Proportion.
Let's look another example: Convert 19 cm to inches.
1 𝑖𝑛𝑐ℎ
Step 1. Because 1 inch = 2.45 cm, write this in ratio form: 2.45 𝑐𝑚
Step 2. Write direct proportion form:
1 𝑖𝑛𝑐ℎ
2.45 𝑐𝑚
𝑥
= 19 𝑐𝑚
Step 3. Apply cross multiplying rule: 2.45𝑥 = 1 × 19
𝟐.𝟒𝟓𝒙
𝟐.𝟒𝟓
𝟏𝟗
= 𝟐.𝟒𝟓 , 𝑥 = 7.76 𝑖𝑛𝑐ℎ𝑒𝑠
Now, you can try some practice questions on the following page, and answers are provided on the last page.
Academic Success Center
Created by Ming Xu
P1-3
Worksheet
Unit Conversion & ratio - Direct proportion
Use Ratios and proportions to complete the following Questions.
24 hours to minutes
267 milligrams to grams
18 Yards to feet
70 inches to feet
1500 milliliters to liters
25.7 Kg to Pounds
85 cm3 to mm3
963 grams to micrograms
20 grams to kilograms
3 hours to seconds
100 kilometers to miles
3120 Liters to Gallons (UK)
10 cups to liters
500 ft3 to m3
Academic Success Center
Created by Ming Xu
P2-3
Answers
Unit Conversion & ratio - Direct proportion
24 hours to minutes
267 milligrams to grams
1440 (min)
0.267 (g)
18 Yards to feet
70 inches to feet
54 (ft)
5.83 (ft)
1500 milliliters to liters
25.7 Kg to Pounds
1.5 (L)
56.66 (lb.)
85 cm3 to mm3
963 grams to micrograms
8.5×104 (mm3), OR 85,000 (mm3)
9.63 × 108 (µg), OR 963,000,000 (µg)
20 grams to kilograms
3 hours to seconds
2.0 ×10-2 (kg), OR 0.02 (kg)
1.08 ×104 (sec)
100 kilometers to miles
3120 Liters to Gallons (UK)
62.14 (mile)
6.863×102 gal(UK), OR 686.30 gal(UK)
10 cups to liters
500 ft3 to m3
2.5 (L) In metric
14.16 m3
Academic Success Center
Created by Ming Xu
P3-3