Ratio Language
Give the ratio of apples to oranges when there are 6 apples and 9 oranges. (Answer in simplest form and with ratio language.)
2:3; There are 2 apples for every 3 oranges.
Find the unit rate: 12 miles in 3 hours. State the unit rate as "___ miles per hour."
4 miles per hour.
Fill in the missing value in this equivalent-ratio table: (2, 5), (4, __).
10
On a coordinate grid, the relationship of the pounds of oranges to the price passes through (4, 1). What is the unit rate of dollar per pound?
If the ratio of pens to pencils in a box is 2:3 and there are 10 pens, how many pencils are there?
15
Write the ratio "For every 4 cats there are 15 kittens" in two ways: using a colon and using the phrase "___ to ___".
"4:15" and "4 to 15"
If 5 pencils cost $2.50, what is the unit price for one pencil?
$0.50 per pencil.
A tape diagram shows 3 equal parts representing 18 total. What is the value of one part? Then write a ratio that relates one part to the total.
One part = 6; ratio part:total = 6:18 = 1:3.
If points (2, 6) and (4, 12) are on a graph, is the relationship proportional? Explain and give the unit rate.
Yes proportional; unit rate 3 (since 6/2 = 3 and 12/4 = 3).
Sara can type 300 words in 15 minutes. At that rate, how many words in 1 minute? How many in 45 minutes?
3.5 * 15 = 52.5 miles.
Explain in one sentence what the ratio 3:1 means in context for a classroom where the ratio describes boys to girls.
"For every 3 boys there is 1 girl"
A car travels 180 miles on 6 gallons of gas. What is the unit rate in miles per gallon?
30 miles per gallon.
Use a table of equivalent ratios to decide whether the pairs (6, 10) and (9, 15) form a proportional relationship. Explain briefly.
Yes; 6/10 = 0.6 and 9/15 = 0.6, so proportional.
A line through the origin passes through (3, 9). Sketch (describe) the slope and write the equation. What does the slope represent in context?
Slope = 3, equation y = 3x; slope = unit rate (output per 1 input).
A map uses 1 inch to represent 15 miles. How many miles does 3.5 inches represent? Show your reasoning.
3.5 * 15 = 52.5 miles.
A recipe calls for 2 cups of flour for every 3 cups of sugar. Write a sentence using ratio language to describe this relationship and give the ratio in simplest form.
Ratio 2:3; sentence: "For every 2 cups of flour there are 3 cups of sugar."
A runner completes 10 kilometers in 50 minutes. Find the unit rate in minutes per kilometer and in kilometers per minute.
5 minutes per kilometer and 0.2 kilometers per minute.
Given this table: x: 2, 4, 6; y: 3, 6, __. Complete the table and explain how you know the relationship is proportional.
y values: 3, 6, 9 so missing is 9. Proportional since constant ratio y/x = 1.5.
Two lines on the same graph: one through (1, 3) and (2, 6), another through (1, 4) and (2, 8). Which is steeper? Which is proportional? Explain.
First line slope 3, second slope 4. Second is steeper. Both proportional (both pass through origin and have constant slopes).
A recipe for 8 muffins calls for 200 g of sugar. How much sugar is needed per muffin? How much sugar for 14 muffins?
200/8 = 25 g per muffin; for 14 muffins: 350 g.
The ratio of red marbles to blue marbles is 7:5. If there are 60 marbles total, how many are red? Show your ratio reasoning.
7/(7+5)=7/12 of 60 = 35 red marbles.
A machine produces 420 widgets in 7 hours. If operating continuously, how many widgets does it produce per minute? Show units and steps.
1 widget per minute
A bike travels proportionally: at 2 hours it goes 18 miles. Create a table for 0, 1, 2, 3, 4 hours and use it to find the distance at 7.5 hours. Explain steps.
Table: 0→0, 1→9, 2→18, 3→27, 4→36. Distance at 7.5 hours = 67.5 miles.
A proportional relationship models cost y (dollars) = kx where x is pounds of fruit. If the graph goes through (5, 12.5), determine k and interpret k as a unit rate. Then describe how the graph would change if the store doubled its price per pound.
k = 12.5/5 = 2.5 so unit rate $2.50 per pound. Doubling price: graph steeper with slope 5; equation becomes y = 5x.
A small business makes bracelets: the ratio of labor hours to bracelets produced is 5:20. If they need 1,200 bracelets, how many labor hours are required? Show proportional reasoning and any equations used.
labor rate 5/20 = 0.25 hours per bracelet. For 1,200 bracelets: 1,200 * 0.25 = 300 hours (or use proportion: 5:20 = h:1200 → h = 300).