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What does the Ratios, Rates and Proportions revision sheet cover?

What makes a relationship proportional, Three ways to write the same thing, the equation form, k constant, the constant read off any one pair, the proportion form, then cross multiply, Worked: a constant rate, The three shapes this topic comes in, Rate, Proportion, Scale, Sharing, Part to part against part to whole.

Is this for Digital SAT SAT Math?

Yes, it is written for the Digital SAT SAT Math syllabus.

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Ratios, Rates and Proportions — Digital SAT SAT Math revision notes

A 3-page visual revision sheet for Ratios, Rates and Proportions, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Ratios, Rates and Proportions revision notes, page 1 of 3 — A preview of page 1 — all 3 pages open full size in the app.

Ratios, Rates and Proportions in one look

one relationship held constant while the numbers are scaled up and down

What makes a relationship proportional

two quantities are proportional when their ratio never changes. Triple one and the other triples too
every proportional relationship can be written y=kx, where k is the constant of proportionality, the amount of y that goes with one unit of x
a RATE is a ratio with different units on top and bottom: pages per minute, rupees per litre, people per square kilometre
a UNIT rate is that ratio rewritten with 1 in the denominator, which is what makes it easy to scale to any other amount

Three ways to write the same thing

the equation form, k constant y=kx
the constant read off any one pair k=y/x
the proportion form, then cross multiply a/b=c/d⇒ ad=bc

Worked: a constant rate

Q. a machine fills 84 bottles in 6 minutes. At the same rate, how many bottles does it fill in 15 minutes?

unit rate first: 84/6=14 bottles per minute
scale to the time asked for: 14×15=210
or scale the whole block instead: 15 minutes is 2.5 times 6 minutes, so 2.5×84=210

Answer: 210 bottles

The three shapes this topic comes in

Rate: an amount per one unit of something else. Find the unit rate, then multiply
Proportion: two ratios set equal with one unknown. Cross multiply and divide
Scale: a drawing, map or similar figure. Every matching length shares one scale factor
Sharing: a total split in a given ratio. Add the parts, divide the total by that

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What this Ratios, Rates and Proportions sheet covers

What makes a relationship proportional
Three ways to write the same thing
the equation form, k constant
the constant read off any one pair
the proportion form, then cross multiply
Worked: a constant rate
The three shapes this topic comes in
Rate
Proportion
Scale
Sharing
Part to part against part to whole
Worked: splitting a total in a ratio
Similar figures share one scale factor
Worked: scale factor
Which setup does the question want
Pacing and the calculator
Symbols and terms
Traps that cost points
Tricks that save time

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