IM 7.2.4 Lesson: Proportional Relationships and Equations

Find each quotient mentally.

[math]645\div100[/math]

[math]645\div50[/math]

[math]48.6\div30[/math]

[math]48.6\div x[/math]

A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions below. Be prepared to explain your reasoning.

How many people will 1 cup of rice serve?

How many people will 3 cups of rice serve? 12 cups? 43 cups?

How many people will [math]x[/math] cups of rice serve?

A recipe says that 6 spring rolls will serve 3 people. Complete the table as you answer the questions below. Be prepared to explain your reasoning.

How many people will 1 spring roll serve?

How many people will 10 spring rolls serve? 16 spring rolls? 25 spring rolls?

How many people will [math]n[/math] spring rolls serve?

How was completing this table different from the previous table? How was it the same?

A plane flew at a constant speed between Denver and Chicago. It took the plane 1.5 hours to fly 915 miles. Complete the table.

How far does the plane fly in one hour?[br]

How far would the plane fly in [math]t[/math]hours at this speed?[br]

If [math]d[/math] represents the distance that the plane flies at this speed for [math]t[/math] hours, write an equation that relates [math]t[/math] and [math]d[/math].

How far would the plane fly in 3 hours at this speed? in 3.5 hours? Explain or show your reasoning.

A rocky planet orbits Proxima Centauri, a star that is about 1.3 parsecs from Earth. This planet is the closest planet outside of our solar system.

How long does it take light from Proxima Centauri to reach Earth? (A parsec is about 3.26 light years. A light year is the distance light travels in one year.)

There are two twins. One twin leaves on a spaceship to explore the planet near Proxima Centauri traveling at 90% of the speed of light, while the other twin stays home on Earth. How much does the twin on Earth age while the other twin travels to Proxima Centauri? (Do you think the answer would be the same for the other twin? Consider researching “The Twin Paradox” to learn more.)

A bakery uses 8 tablespoons of honey for every 10 cups of flour to make bread dough. Some days they bake bigger batches and some days they bake smaller batches, but they always use the same ratio of honey to flour. Complete the table.

If [math]f[/math] is the cups of flour needed for [math]h[/math] tablespoons of honey, write an equation that relates [math]f[/math] and [math]h[/math].

How much flour is needed for 15 tablespoons of honey? 17 tablespoons? Explain or show your reasoning.