## 9.1: Number Talk: Which is Greater?

Without calculating, decide which quotient is larger.

$11 \div 23$ or $7 \div 13$

$0.63 \div 2$ or $0.55 \div 3$

$15 \div \frac{1}{3}$ or $15 \div \frac{1}{4}$

Let’s create our own scale drawings.

Without calculating, decide which quotient is larger.

$11 \div 23$ or $7 \div 13$

$0.63 \div 2$ or $0.55 \div 3$

$15 \div \frac{1}{3}$ or $15 \div \frac{1}{4}$

Noah made a *rough sketch* of the layout of his room (not a scale drawing).

- Noah wants to create a floor plan that is a scale drawing. The actual length of Wall C is 4 m. Noah draws a segment 16 cm long to represent Wall C. What scale is he using? Explain or show your reasoning.
- Find another way to express the scale.
- Pause and discuss your responses with a partner. How do your scales compare?
- The actual lengths of Wall A, Wall B, and Wall D are 2.5 m, 2.75 m, and 3.75 m. Determine how long these walls will be on Noah’s scale floor plan.
- Use the Point tool and the Segment tool to draw the walls of Noah's scale floor plan in the applet.

A rectangle around Utah is about 270 miles wide and about 350 miles tall. The upper right corner that is missing is about 110 miles wide and about 70 miles tall.

Make a scale drawing of Utah where 1 centimeter represents 50 miles.

Make a scale drawing of Utah where 1 centimeter represents 75 miles.

How** **do the two drawings compare? How does the choice of scale influence the drawing?

A rectangular swimming pool measures 50 meters in length and 25 meters in width.

- Make a scale drawing of the swimming pool where 1 centimeter represents 5 meters.
- What are the length and width of your scale drawing?

If we want to create a scale drawing of a room's floor plan that has the scale “1 inch to 4 feet,” we can divide the actual lengths in the room (in feet) by 4 to find the corresponding lengths (in inches) for our drawing.

There is more than one way to express this scale.

These three scales are all equivalent, since they represent the same relationship between lengths on a drawing and actual lengths:

- 1 inch to 4 feet
- $\frac12$ inch to 2 feet
- $\frac14$ inch to 1 foot

Any of these scales can be used to find actual lengths and scaled lengths (lengths on a drawing). For instance, we can tell that, at this scale, an 8-foot long wall should be 2 inches long on the drawing because $\frac14 \boldcdot 8 = 2$.

The size of a scale drawing is influenced by the choice of scale. For example, here is another scale drawing of the same room using the scale 1 inch to 8 feet.