**Q1. If on a scale drawing 1 inch equals 32 inches, what scale distance equals 12 inches (1 foot)?**

**A1. Here's how we find the answer:**

**1.5 inches on the paper equals 48 inches in real life, so 1.0 inches equals 32 inches (48 ÷ 1.5 = 32)**

**We want to know what fraction of 1 inch equals 12 inches in real life.**

**That is an unknown value which I will call X.**

**X is to 1 what 12 is to 32, or to say it another way, X÷1 = 12÷32**

**First we simplify the right side - the largest common denominator of 12 and 32 is 4.**

**We find 4 goes into 12 three times and 4 goes into 32 eight times.**

**To simplify the left side we just throw away the 1, because X÷1 = X**

**Now we have X = 3/8**

**The answer is 3/8" on paper is equal to 12" in real life**

**To check our answer we could ask how many of those 3/8s are there in 12 inches?**

**One way to do this is to convert 3/8 to a decimal number.**

**Divide 8 into 1.00 and you get .125 then multiply by 3 and you have .375**

**Now we do the division 12 ÷ .375 = 32 which is where we started (**

**1 inch equals 32 inches)**

Whew! Why go through such complications? Why not scale 1:10 or something simple? Well, we use this scale because you can show a typical room or two of a house on one piece of paper.

**Q2. Assume an inch of margin on all sides of a sheet of 8 1/2" x 11" paper. What is the largest room that can be drawn on this paper at 1:32 scale?**

**Round the answer to the nearest foot.**

**A2. Subtract the margins to find remaining space, and calculate the largest scaled room that will fit.**

**(8.5 - 2 = 6.5) and (11-2 = 9) so 6.5 inches x 9 inches is the free space for drawing a room.**

6.5 x 32 (our scale) = 208 inches Divide 208 ÷ 12 = 17 feet 4 inches which we round to 17

9 x 32 = 288 inches Divide 288 ÷ 12 = 24 feet 0 inches

**The largest room that will fit on this paper is 17 x 24 feet.**

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