ACT algebra content

ACT algebra content

ratio

Objectives:

• Review concepts covered on algebra portion of ACT

• Review example questions by using the common ACT formulas

The topic we will focus on is based on ACT Algebra questions

• Ratios

Poll

Do you feel confident about this topic?

• yes

• no

• kind of

Multiple Choice

Which statement best describes what a ratio is.

• A number

• A comparison of two quantities using division.

• A comparison

• A comparison of many things.

Multiple Choice

If I have the following ratio, do I need to scale up or down?
1                 2
---  =         ----
3               ?

• up (multiply)
• down (divide)

Multiple Choice

Which of the following is not equivalent to 3 : 4

• 12 : 16

• 20 : 15

• 3/4 : 1

• 6 : 8

Multiple Choice

Are the following ratios similar?

• Yes

• No

Multiple Choice

Luz earns $400 for 40 hours of work. Use a ratio table to determine how much she earns for 6 hours of work.

• $60.00

• $20.00

• $40.00

• $10.00

Multiple Choice

_{Simplify the following ratio
8 :  12}

• 1 : 3
• 2 : 3
• 3 : 4
• 4 : 5

“Part-to-Part” and “Part-to-Whole” Ratios

• The examples so far have been “part-to-part” (comparing one part to another). But a ratio can also show a part compare to the whole. Example: There are 5 puppies, 2 are boys, and 3 are girls

• Part-to-Part:

  The ratio of boys to girls is 2:3

  The ratio of girls to boys is 3:2

• Part-to-Whole:

  The ratio of boys to all pups is 2:5

  The ration of girls to all pups is 3:5

Multiple Choice

Is this a part to whole or part to part?
 $\frac{12\ students\ prefer\ pet\ cats}{48\ total\ students\ voted}$  

• Part to whole

• Part to part

Multiple Choice

Is this a part to part or part to whole ratio?

 $\frac{43\ students\ prefer\ basketball}{28\ students\ prefer\ football}$  

• Part to Whole

• Part to Part

Multiple Choice

Serena’s book collection contains 23 fiction books and 4 non-fiction books.

• Part to whole

• Part to part

Multiple Choice

Of the 200 students surveyed, 120 prefer bananas

• Part to Whole

• Part to Part

Scaling

• We can use ratios to scale drawing up or down (using multiplication or division).

Example:

The height to width ratio of the Indian Flag is 2:3

So for every 2 (inches, feet, etc.) of height there should be 3 of width. 

If we made the flag 20 inches high, it should be 30 inches wide. 

If we made the flag 40 cm high, it should be 60 cm wide (which is still in the ratio 2:3).

Scaling Example

Allie measured her foot and it was 21cm long, and then she measured her Mother’s foot, and it was 24cm long. Then she thought to measure heights, and found she is 133cm tall and her mon is 152cm tall. 

Is the "foot-to-height” ratio the same?

Multiple Choice

• 8

• 2

• 128

• 4

Multiple Choice

• 12 yds

• 6 yds

• 16 yds

• 9 yds

Multiple Choice

• 10

• 7

• 4

• 21

Multiple Choice

• 2

• 5

• 4

• 1