Mathematics 1: Ratio, Proportion & Rate of Change

What does it mean for two quantities to be in direct proportion?

One quantity is equal to a constant multiplied by the other.

What is the equation for direct proportion?

y = kx

How do you find the constant of proportionality?

Substitute a known pair of values into the equation and solve for k.

What does it mean for two quantities to be in inverse proportion?

As one quantity increases, the other decreases so that their product is constant.

What is the equation for inverse proportion?

y = k/x

How do you solve a direct proportion problem?

Find k using known values, then use the equation to find the unknown.

How do you solve an inverse proportion problem?

Find k using known values, then substitute to find the unknown.

What is a ratio?

A comparison of two or more quantities.

How do you simplify a ratio?

Divide every part by the highest common factor.

How do you divide a quantity in a given ratio?

Add the ratio parts, find the value of one part, then multiply.

What is a unit rate?

A rate expressed per one unit.

What is the difference between a ratio and a fraction?

A ratio compares quantities; a fraction represents part of a whole.

How do you convert between fractions, decimals and percentages?

Use multiplication or division by 100 as appropriate.

How do you increase a quantity by a percentage?

Multiply by (1 + percentage/100).

How do you decrease a quantity by a percentage?

Multiply by (1 − percentage/100).

What is compound percentage change?

Applying a percentage multiplier repeatedly.

What multiplier represents a 12% increase?

1.12

What multiplier represents a 12% decrease?

0.88

How do you solve reverse percentage problems?

Divide by the percentage multiplier.

What is the formula for speed?

Speed = Distance ÷ Time

What is the formula for density?

Density = Mass ÷ Volume

What is the formula for pressure?

Pressure = Force ÷ Area