Ratios
(worked examples)
2F
Which two kinds of boxes have a ratio of 2:3? Justify your
answer.
☺☺ ☺ ☺
☺
☺
Just “looking” at the grid there are no
2:3 ratios. Keep in mind however,
that 2:3 is equivalent to 4:6 if we
scale the ratio up by 2. So, the
following boxes are in a ratio of 2:3.
to
4:6
2:3
☺
to
4:6
2:3
☺
3B
Luisa wants to change the ratio to 2 face-up to 3 face-down
cards. How many cards does she need to add to the original
12 cards? Draw the solution.
original drawing
2:1
If we are to change the ratio to 2:3, the second term of the original ratio must
change. Meaning for every 2 face-up cards there should now be 3 face-down cards,
therefore, you are adding a total of 8 face-down cards.
3A
Luisa has 12 playing cards. She places 2 out of every 3 cards
face-up on the table. Draw Luisa's cards, showing how
many cards are face-up and how many are face-down.
The ratio of
face-up to
face-down
cards is 8:4
or 2:1.
4B
Dr. Jin has 6 scallops and 3 sea stars in his aquarium.
Each sea star eats 4 scallops per week. How many scallops does Dr.
Jin need to add to his tank to feed the sea stars for a week?
If each sea star eats 4 scallops per week and there are 3 sea stars,
then they need a total of 12 scallops. There are already 6 so, 6
more scallops need to be added to the aquarium.
4C
Dr. Jin has 6 scallops and 3 sea stars in his aquarium.
One of Dr. Jin’s fellow scientists brings him two more sea stars. What will
the ratio of sea stars to scallops need to be in order to feed the sea stars for
a week?
If two sea stars are added, that is a total of 5 sea stars.
They need a total of 20 (5 × 4 = 20) scallops. So the
ratio is 5:20.