7.1 Group Work (Ratio and Proportion)

Front

What is a ratio?

Back

A ratio is a comparison of two quantities by division, expressed as 'a:b' or 'a/b'.

Front

How do you simplify a ratio?

Back

To simplify a ratio, divide both terms by their greatest common divisor (GCD).

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal, expressed as 'a/b = c/d'.

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply and then solve for the unknown variable.

Front

What is the formula for finding the perimeter of a rectangle?

Back

The perimeter P of a rectangle is given by the formula P = 2(length + width).

Front

If FG : GH = 4 : 3 and FH = 56, how do you find FG and GH?

Back

Set FG = 4x and GH = 3x. Then, 4x + 3x = 56. Solve for x to find FG and GH.

Front

What is the relationship between the sides of a rectangle and its perimeter?

Back

The perimeter is directly related to the lengths of the sides; increasing the length or width increases the perimeter.

Front

How do you express a ratio in simplest form?

Back

Divide both terms of the ratio by their GCD until no further simplification is possible.

Front

What is the ratio of the length to the width of a rectangle with dimensions 20 ft and 16 ft?

Back

The ratio is 20:16, which simplifies to 5:4.

Front

How do you find the dimensions of a rectangle given its perimeter and the ratio of its sides?

Back

Use the perimeter formula and the ratio to set up equations, then solve for the dimensions.