September 30, 2013
On-Core 2-1
Unit Rates with complex fractions!!!!
September 30, 2013
Essential Question:
How do you find and compare unit rates????
September 30, 2013
If I pay $4 for 2 lbs of apples, how much
per pound am I paying?
What if I pay $4.50 for 1 1/2 lbs of
apples?
September 30, 2013
$4.50 for 1 1/2 lbs:
September 30, 2013
Or...just do a unit rate!
September 30, 2013
Jeff hikes 1/2 mile every 1/4 hour. Lisa hikes 1/3 mile every 1/6
hour. How far do they each hike in 1 hour?
? miles
1/4 hour
1/4 hour
1/4 hour
1/4 hour
1/2 mile
a) How many 1/4 hours are in 1 hour?
How far does Jeff hike in 1 hour?
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Complete the table for Jeff's hike
Distance (mi) 1/2
Time (hr)
1/4
1/2
3/4
1
2
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c) Complete the bar diagram to help you determine how far Lisa
hikes. How many miles does she hike in one hour?
? miles
1/6 hour 1/6 hour 1/6 hour 1/6 hour 1/6 hour 1/6 hour
1/3 mile
d) complete the table for Lisa's hike.
Distance (mi) 1/3
Time (hr)
1/6
1/3
1/2
1
2
September 30, 2013
Reflect:
1. How did you find Jeff's distance for 3/4 hour?
2. Which hiker walks farther in one hour? What does this tell
you about the speeds at which they hike?
September 30, 2013
Remember: ratio compares two quantities.
Rate compares two quantities with different units
Unit Rate is a rate with denominator of 1. (divide)
Sometimes rates are expressed with complex fractions (a
fractions within a fraction). In other words, you are DIVIDING
FRACTIONS AGAIN! YAY!
KEEP, SWITCH, FLIP
September 30, 2013
Finding unit rates:
While remodeling his kitchen,. Arthur paints the cabinets. He
estimates that he paints 30 square feet every 1/2 hour. How many
square feet does Arthur paint per hour?
Step 1: Find his rate
Step 2: Find unit rate
30 square feet
1/2 hour
September 30, 2013
Try this:
Paige mows 1/6 acre in 1/4 hour. How many acres does Paige mow
per hour?
Reflect:
How could you find the unit rate by using a table?
Acres
Time (hr)
1/6
1/4
September 30, 2013
Two containers filled with water are leaking. Container A leaks at a
rate of 2/3 gallon every 1/4 hour. Container B leaks at a rate of 3/4
gallon every 1/3 hour. Determine which one is leaking more rapidly.
(hint: find the unit rates of each container)
September 30, 2013
Two liquid storage containers are being filled. Liquid enters the
first container at a rate of 2/3 gallon per 1/4 minute. Liquid pours
into the second container at a rate of 3/5 gallon every 1/6 minute.
Determine which one is being filled faster.
Reflect: How do you know which units to use as the numerator in
this question (or any "rate" question, really)
September 30, 2013
Practice:
Simplify: 1/7
3/14
Ms. Crane eats 6/7 box of cookies every 1/3 hour. How many boxes
of cookies can she eat per hour?
September 30, 2013
Journal Time:
How do you find and compare unit rates?
Write a complex fraction in your journal, and explain how to
simplify it.