Speed Blueprint Organizer Speed Blueprint
Method: Complex Fraction to Unit Rate
Name:
Date:
The Problem
Yosef typed a 36-word paragraph in 2/3 minute. What is his typing speed, in words per minute?
1
The Blueprint: Set up the Unit Rate
Fill in the initial rate as a complex fraction compared to 1 minute.
36
2
3
Words Minutes
=
?
1
Words Minute
2
The Solve: Multiply by the Reciprocal
36
Words
×
Flip Units
=
WPM
Workspace
Multiply numerator by reciprocal
(e.g., 36 × 3 ÷ 2)
Yosef's speed is words per minute.
Unit Rate Strategy: Always label your units! By setting the denominator to 1, the result in the numerator tells you the speed for that single unit of time.
Speed Blueprint Answer Key Speed Blueprint
Answer Key: Unit Rate Method
ANSWER KEY
The Problem
Yosef typed a 36-word paragraph in 2/3 minute. What is his typing speed, in words per minute?
1
Set up the Unit Rate
36
2
3
Words Minutes
=
54
1
Words Minute
2
Multiply by Reciprocal
36
Words
×
3
2
Flip
= 54
Ratio Table Proof
Words Time 36 2/3 min 18 1/3 min 54 1 min
Logic Workspace
36 × 3 = 108
36 ÷ 2 = 18
Yosef's speed is 54 words per minute.
Speed Blueprint Slides Math Laboratory
Speed Blueprints
Building unit rates from Complex Fractions.
Tool
Complex Fractions
Method
Reciprocals
The Goal: Unit Rate
"Yosef typed 36 words in 2/3 minute."
Find
Words
Step 1: Set the Proportion
36
2
3
Words Minutes
=
?
1
Words Minute
Step 2: Clearing the Fraction
To change 2/3 minutes to 1 minute,
2
3
×
3
2
=
1
Step 3: Calculate the Words
36
Words
×
3
2
Flip
Option A
36 × 3 = 108
Option B
36 ÷ 2 = 18
Final Result
54 Words Per Minute
Knitting Blueprint Organizer Speed Blueprint
Method: Complex Fraction to Unit Rate
Name:
Date:
The Problem
Kelly is knitting a scarf. It took her 1/3 hour to knit 3/8 foot of the scarf. How fast is her knitting speed, in feet per hour?
1
The Blueprint: Set up the Unit Rate
Fill in the initial rate as a complex fraction compared to 1 hour.
3
8
1
3
Feet Hours
=
?
1
Feet Hour
2
The Solve: Multiply by the Reciprocal
3
8
Feet
×
Flip Hours
=
Feet / Hour
Workspace
Show your work: Multiply the fractions
Kelly's knitting speed is feet per hour.
Blueprint Strategy: A unit rate compares a quantity to 1. When you multiply the top fraction by the bottom's reciprocal, you find the rate for 1 whole hour!
Knitting Blueprint Answer Key Speed Blueprint
Answer Key: Knitting Speed
ANSWER KEY
The Problem
Kelly is knitting a scarf. It took her 1/3 hour to knit 3/8 foot of the scarf. How fast is her knitting speed, in feet per hour?
1
Set up the Unit Rate
3
8
1
3
Feet Hours
=
9
8
1
Feet Hour
2
Multiply by Reciprocal
3
8
Feet
×
3
1
Flip
=
9
8
FPH
Logic & Simplification
Multiplication
3/8 × 3/1 = 9/8
Mixed Number
9/8 = 1 1/8
Kelly's knitting speed is 1 1/8 feet per hour.
Painting Blueprint Organizer Speed Blueprint
Method: Complex Fraction to Unit Rate
Name:
Date:
The Problem
Stacy and Neil painted 280 ft² of their wall with 4/5 gallon of paint. How many square feet can they paint with 3 gallons?
1
Find the Unit Rate (per 1 gallon)
280
4
5
ft² Gallons
=
?
1
ft² Gallon
2
The Solve: Multiplying
280
ft²
×
Flip Units
=
Unit Rate
ft² / gal
3
The Goal: Scale to 3 Gallons
Unit Rate
×
3
Gallons
=
ft²
Workspace
Painting Blueprint Answer Key Speed Blueprint
Answer Key: Painting Area
ANSWER KEY
The Problem
Stacy and Neil painted 280 ft² of their wall with 4/5 gallon of paint. How many square feet can they paint with 3 gallons?
1
Find the Unit Rate
280
4
5
ft² Gallons
=
350
1
ft² Gallon
2
The Solve
280
ft²
×
5
4
Flip
= 350
ft² / gal
3
The Goal
350
Unit Rate
×
3
Gallons
=
1050
ft²
Calculations
Unit Rate: (280 ÷ 4) × 5 = 70 × 5 = 350
Final: 350 × 3 = 1,050
Harper Blueprint Organizer Speed Blueprint
Method: Complex Fraction to Unit Rate
Name:
Date:
The Problem
Harper is 50 yards from school. On his map, the school is 3/4 inch away. If home is 3 inches from his location on the map, how many yards is he from home?
1
Find the Map Scale (per 1 inch)
50
3
4
Yards Inches
=
?
1
Yards Inch
2
The Solve: Multiplying
50
Yards
×
Flip Inches
=
Unit Rate
Yds / Inch
3
The Goal: Scale to 3 Inches
Unit Rate
×
3
Inches
=
Yards
Workspace
Harper Blueprint Answer Key Speed Blueprint
Answer Key: Map Scale Distance
ANSWER KEY
The Problem
Harper is 50 yards from school. On his map, the school is 3/4 inch away. If home is 3 inches from his location on the map, how many yards is he from home?
1
Find the Unit Rate
50
3
4
Yards Inches
=
200/3
1
Yards Inch
2
The Solve
50
Yards
×
4
3
Flip
= 200/3
Yds / Inch
3
The Goal
200/3
Unit Rate
×
3
Inches
=
200
Yards
Calculations
Unit Rate: 50 × 4/3 = 200/3 yards per inch
Final Distance: (200/3) × 3 = 200 yards
