Ratios and Rates
What is a ratio that compares two quantities with different units called?
Unit rate
What does it mean for two quantities to be proportional?
They have a constant ratio / constant of proportionality
In a proportional relationship, where does the graph cross the y-axis?
(0, 0) or the origin.
What does “percent” mean?
Out of 100
What is 10% of 50?
5
Write the ratio of 12 apples to 4 apples in simplest form.
3:1
True or False: If two quantities are proportional, their graph is a straight line through the origin.
True
What equation represents a proportional relationship between x and y?
y = kx
Write 25% as a fraction and a decimal.
1/4 and 0.25
Find 20% of 80.
16
If a car travels 180 miles in 3 hours, what is the unit rate in miles per hour?
60 miles per hour
If y = 4x, what is the constant of proportionality?
4
If the constant of proportionality is 2.5, write the equation.
y = 2.5x
What percent is equivalent to 0.6?
60%
A shirt costs $40 and is on sale for 25% off. How much is the discount?
$10
A recipe uses 2 cups of sugar for every 5 cups of flour. Write this as a unit rate.
5/2 cups of flour for every 1 cup of sugar, or 2/5 cups of sugar for every 1 cup of flour.
A table shows x = 1, 2, 3, and y = 5, 10, 15. Is this a proportional relationship? Why?
Yes, y is always 5 times x
A table shows that when x doubles, y also doubles. What does this tell you?
The relationship is proportional
A test has 40 questions. If a learner gets 30 correct, what percent did they score?
75%
After a 10% increase, a price goes from $50 to what new price?
$55
Which is the better buy: $6 for 3 notebooks or $9 for 5 notebooks? Explain using unit rates.
$1.80 per notebook vs. $1.80 per notebook → same deal
Give one real-world example of a proportional relationship.
Possible answers: cost per item, distance vs. time at constant speed, etc.
If a graph is a straight line but does NOT pass through the origin, is it proportional? Why or why not?
No, proportional graphs must pass through the origin
Is 150% more than or less than 1 whole? Explain.
More than 1 whole
Explain how finding 1% can help you find any percent.
Once you know 1%, you can multiply to find any percent