Lesson 12

Find each product or quotient mentally.

\(\frac23 \boldcdot \frac12\)

\(\frac43 \boldcdot \frac14\)

\(4 \div \frac15\)

\(\frac96 \div \frac12\)

Diego, Lin, and Mai went from the ticket booth to the bumper cars. 

1. Use each description to complete the table representing that person’s journey.

• Diego left the ticket booth at the same time as Tyler. Diego jogged ahead at a steady pace and reached the bumper cars in 30 seconds.
• Lin left the ticket booth at the same time as Tyler. She ran at a steady pace and arrived at the bumper cars in 20 seconds.
• Mai left the booth 10 seconds later than Tyler. Her steady jog enabled her to catch up with Tyler just as he arrived at the bumper cars.

Diego's time (seconds)	Diego's distance (meters)
0
15
30	50
1

Lin's time (seconds)	Lin's distance (meters)
	0
	25
20	50
1

Mai's time (seconds)	Mai's distance (meters)
	0
	25
40	50
1

2. Using a different color for each person, draw a graph of all four people’s journeys (including Tyler's from the other day).

• Drag the names to the correct lines to label them.
• If you choose to, you can use the Paint Brush tool to change the color of each line. Select the tool, click on a color in the palette below the graph, and then click on a line. Click on the Move tool (the arrow) before changing to a new paint brush color.
• You can hide any points you create with the checkbox below the graph.

3. Which person is moving the most quickly? How is that reflected in the graph?

1. Meteoroid Perseid 245 and Asteroid x travel through the solar system.  Explore the applet to learn about the distance they had each traveled after a given time.

   Is Asteroid x traveling faster or slower than Perseid 245? Explain how you know.

2. The graph shows the price of different lengths of two types of rope.

   

   

   If you buy $1.00 of each kind of rope, which one will be longer? Explain how you know.

Here is a graph that shows the price of blueberries at two different stores. Which store has a better price?

We can also use the graphs to compare the constants of proportionality. The line representing store B goes through the point \((1, 4)\), so the constant of proportionality is 4. This tells us that at store B the blueberries cost \$4 per pound. This is cheaper than the \$6 per pound unit price at store A.