Understanding Ratios
Write the ratio of 3 apples to 6 oranges in simplest form.
1:2
Find the unit rate: 45 miles in 3 hours.
15 miles per hour
In y = m*x, what does m represent?
The constant of proportionality or unit rate
What does every proportional graph pass through?
The origin (0,0)
You buy 3 shirts for $27. What is the price per shirt?
$9
A recipe uses 5 cups of flour for every 2 cups of sugar. What is the ratio of sugar to flour?
2:5
A table shows 2 packs cost $4, and 5 packs cost $10. Is this proportional?
Yes, the unit rate is $2 per pack.
If y = 3x, what is the value of y when x = 12?
36
A graph shows y = 2x. What is the unit rate of the line?
2
If 4 notebooks cost $6, how much will 10 notebooks cost?
$15
If there are 12 girls and 8 boys, what fraction of the group are girls?
12 / (12 + 8) = 3/5
Complete the table: if y = 3x, what is y when x = 7?
21
A graph passes through (2, 10). Find the equation of the proportional relationship.
y = 5x
How can you tell from a graph that two quantities are not proportional?
The line does not pass through the origin or is not straight.
A recipe calls for 2 cups of flour for 3 batches of cookies. How many cups for 9 batches?
6 cups
The ratio of red to blue marbles is 4:7. If there are 28 blue marbles, how many red are there?
16
A car travels 120 miles in 2 hours, then 180 miles in 3 hours. Is the relationship proportional? Explain.
Yes, both have a rate of 60 mph.
If the constant of proportionality is 1/4, what happens to y when x = 12?
y = 3
If the constant of proportionality is 1/3, what does that mean on a graph?
For every 1 unit on x, y increases by 1/3 — the line is less steep.
A train travels 90 miles in 1.5 hours. Find its speed, then how far it goes in 4 hours.
60 mph → 4hrs = 240 miles
Explain how the ratio 3:4 is different from the fraction 3/4 in meaning.
The ratio compares two quantities; the fraction represents a part-to-whole relationship.
Write the equation that represents the table:
x = 1, 2, 3, 4
y = 2, 4, 6, 8
y = 2x
Write a real-world example modeled by y = 8x.
You earn $8 per hour worked.
Two graphs have equations y = 2x and y = 5x. Which is steeper and why?
y = 5x, larger unit rate means steeper line.
You make $18 for 2 hours of tutoring. Write and use an equation to find earnings for 7.5 hours.
y = 9x → y = $67.50