$Sq ft of bldg provided, feet of bldg burnt given, questions ask to represent the burnt structure in a fraction please help$

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$Sq ft of bldg provided, feet of bldg burnt given, questions ask to represent the burnt structure in a fraction please help$

Hey guys i take a fire dept exam here in a few days and there are a few math questions i cannot figure out how to compute, well i figured out a few but my method doesnt work for some of the other questions leaving me stuck finding a formula or something that works for them all...thank you and here we go

Instructions: all calculations must be done in head no scratch paper, i have 10 seconds to answer each question, speed is paramount, "some of your answers will not be exact and may be rounded, ex- if the answer is close to 1/3 but not exaclty 1/3 choose the closest choice in the answer key"

i will provide 4-5 questions now
questions- "if a building is 4085 square feet and 1600 feet of the bulding burns what fraction of the bldg is left?" answer-3/5

if a building is 2825 square feet and 2100 feet of the bulding burns what fraction of the bldg is left?--ans--1/4
if a building is 1600 square feet and 700 feet of the bulding burns what fraction of the bldg is left?--ans--1/2
if a building is 1010 square feet and 650 feet of the bulding burns what fraction of the bldg is left?----ans----4/10
if a building is 2425 square feet and 300bfeet of the bulding burns what fraction of the bldg is left?-----answer--7/8

please help me figure out a way to successfully complete this math in my head within the time frame, i dont need EXACT I just need to be close enough to the right fraction to choose the right answer on the multiple choice.... my exam in sunday im overall prepared however this portion is what is snagging--keep in mind this must be done in my head within 10 seconds with no paper so the simplier the better, and as long as i am close enough to choose the right fraction from mltpl choice.. thank you!

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Chris H

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Hi Chris, firstly major thank you for your future service as a fireman; I wish you the best of luck! Now onto the math...

The name of the game here is rounding; if the simplifications don't seem straightforward it's because you either rounded incorrectly or not enough.

In the questions you attached, it seems like all the fractions involve 4-digit numbers in the top and bottom. You only really need the first two; let's see how that works in practice.

**Forgot to answer the first example question that's at end**

1) We want to simplify 2100/2825. This is pretty close to 2100/2800. (Notice we only kept the first two digits.)

So now, we can cancel out the two zeros on the top with the two zeros on the bottom. (Mathematically, we just divided both the numerator and denominator by .01, but that detail is unnecessary.) So canceling out the zeros, we are left with 21/28.

If you know your multiplications, it is easy to see this is 1/4 if you divide both the numerator and denominator by 7. (NOW NOTE THIS IS THE FRACTION THAT BURNT SO THE FRACTION THAT DID NOT BURN IS 3/4 ) -- answer key might be incorrect on this one; I'm very confident in this answer

2) Likewise we want to simplify 700/1600. Now the top number only has 1 non-zero digit so rounding won't be much help. But, we can cancel out the two zeros from the numerator and denominator like we did before. We are left with 7/16. We know 8/16 is 1/2 so 7/16 is probably just a bit less than 1/2. Thus, we can say our answer is approximately 1/2. SO 1/2 OF THE BUILDING BURNT; THUS 1/2 OF THE BUILDING WAS NOT BURNT

3) Simplify 650/1010. Let us cancel one zero from the top and bottom; we are left with 65/101. That's basically 65/100 which is 65% or .65. So approximately 35% of the building did not burn which is approximately 40%.

4) 300/2425 is basically 300/2400. Which is basically 3/24 which is basically 1/8. So 1/8 of the building is burnt so 7/8 of the building is left.

FIRST QUESTION
So, 1600/4085 was burnt. That's basically 1600/4000 which is just 16/40 which is just 8/20 which is just 4/10 or 2/5. So the fraction not burnt is 3/5 (1- 2/5).

If you have any questions feel free to comment. :)

Monke

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$Sq ft of bldg provided, feet of bldg burnt given, questions ask to represent the burnt structure in a fraction please help$

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