29 Understanding Ratios

A ratio is the comparison of two or more objects.

A ratio of two numbers a and b can be written as

$a:b$ or $\frac{a}{b}$

A ratio of three objects a, b, and c, is usually written as

$a:b:c$

A proportion is the comparison of two or more ratios:

$\frac{a}{b}=\frac{c}{d}=\frac{e}{f}$

For example, if there is 1 boy and 3 girls you could write the ratio as:

$1:3$ (for every one boy there are 3 girls)

A Ratio Compares Values

A ratio says how much of one thing there is compared to another thing.

There are 2 green squares to 5 yellow squares.

The three ways to write this are $2:5$, 2 to 5, or $\frac{2}{5}$

You can “scale up” your ratio like this:

$4:10$

The trick with ratios is to always multiply or divide the numbers by the same value.

$4:10$ is the same as $4\times 2:10\times 2=8:20$

Everything you have read so far is part-to-part ratios. Ratios can also be a part compared to the whole number.

There are 7 fish, 5 are black and 2 are purple.

• Part to part:
  • The ratio of black to purple is $5:2$ or $\frac{5}{2}$
  • The ratio of purple to black is $2:5$ or $\frac{2}{5}$
• Part to whole:
  • The ratio of black to all fish is $5:7$ or $\frac{5}{7}$
  • The ratio of purple to all fish is $2:7$ or $\frac{2}{7}$

Blueprints

When we read blueprints in the trades, it is not often that the picture is the actual size of the object. Therefore, a ratio needs to be given to understand the scale at which the dimensions are shown in the picture compared to the real-life-sized object being built.

A scale is shown as a ratio, for example $1:100$. A drawing at a scale of $1:100$ means that the object is 100 times smaller than in real-life scale $1:1$. You could also say, 1 unit in the drawing is equal to 100 units in real life.

A machine part, for example, may be half the size ($\frac{1}{2}$″ = $1$″); a building may be drawn $\frac{1}{48}$ ($\frac{1}{4}$″=1’-0”); a map may be drawn $\frac{1}{200}$ size (1”=100’-0”); and a gear in that wristwatch may be ten times size (10″ = 1″).

Blueprint drawings are typically drawn in

• $1:20$, $1:50$ or $1:100$ (Metric units) or
• $\frac{1}{4}$″ or $\frac{1}{8}$″ (Imperial units) scales

To scale a Metric drawing

Multiply the measurement on the drawing with the denominator where the denominator is the number after the colon.

Example – Blueprint Drawing Scale $1:50$

An actual length of 1 cm is measured on a $1:50$ blueprint floor plan. The physical length can be calculated as

(1 cm) 50 = 50 cm

Imperial units – US

A $\frac{1}{4}$″ scale means that each $\frac{1}{4}$″ (inch) on the plan counts for 1′ (feet) of actual physical length.

To scale a blueprint in imperial units to actual feet, multiply the measurement on the drawing (in inches decimal equivalent) with the denominator where the denominator is the bottom number.

Example – Blueprint Drawing Scale $\frac{1}{4}$

An actual length is measured to 1-3/8” on a $\frac{1}{4}$ blueprint floor plan. The physical length can be calculated as

(1-3/8 inch) 4 = (1.375 inch) 4

= 5.5 feet

= 5′ 6″

If you know the measurement of the actual object, and have the ratio scale, you would divide the number of the real life measurements by the denominator of the ratio.

Commonly Used Drawing Scales

Details

• $1:1$
• $1:5$
• $1:10$
• $1:20$

Component drawings, assembly

• $1:20$
• $1:10$
• $1:5$

Floor plans, general arrangement (GA)

• $1:40$
• $1:50$

Location plot plans

• $1:80$
• $1:100$
• $1:200$
• $1:500$

Block plan, city maps, and larger

• $1:1000$
• $1:1250$
• $1:2500$

Ordnance survey maps

• $1:100000$
• $1:50000$
• $1:25000$
• $1:10000$