EN
BuilderGrade 6⏱ 15 min

Ratios

Mix blue and yellow paint. Equivalent ratios make the same green, and a ratio table shows why.

Standards: 6.RP.A.16.RP.A.3a

1Wonder

You mixed 3 cans of blue paint with 1 can of yellow and got the perfect sea green. Now you need more of it. Do you add 3 more cans of each? Or something else?

2Explore

Paint mixer

This activity needs a bigger screen

Turn your phone sideways, or open this lesson on a tablet or computer. The explanation and quiz below work here.

BlueYellowYour mix3 : 2For every 3 blue, there are 2 yellow.Blue is 3/5 of the paint.BlueYellow32649612815101812SillyChili
Blue cans
3
Yellow cans
2
Try this
  • Make 3 : 2. Then make 6 : 4. Is the green the same?
  • Make 3 : 1. Then add 3 cans of each to get 6 : 4. Is it still the same green? What about 6 : 2?
  • Look at the ratio table. Which mixes make the same shade as 2 : 3?
  • Press Next challenge and solve all four.

3Explain

3 : 2SillyChili
Step 1 of 5

A ratio compares two amounts

For this green we use 3 cans of blue and 2 cans of yellow. We write the ratio of blue to yellow as 3 : 2 and say “3 to 2”.

Equivalent ratiosa:b  =  (a×k):(b×k)a : b \;=\; (a \times k) : (b \times k)

Multiplying or dividing both parts of a ratio by the same number gives an equivalent ratio.

4Practice

Question 1 of 5

What is the ratio of blue cans to yellow cans?

5Recap

  • A ratio compares two amounts, like 3 : 2 (“3 to 2”, “3 for every 2”).
  • The order matters: 3 : 2 is not the same as 2 : 3.
  • Equivalent ratios come from multiplying or dividing both parts by the same number.
  • A ratio table lists equivalent ratios.
  • Adding the same amount to both parts does not keep the ratio.