how do I estimate fractions?

Question

Here are the problems

(1) 14 1/7 - 5/6

(2) 5 5/6 then divide by 3.

(3) About how many 3 1/2 foot shelfs can a carpenter cut from a 12foot board for a bookcase.

Well that's what it says in my text book.

Answer 1

Kudos to answer 1 for even bothering.

Beyond that; last time I checked, there were no 7ths dictated in any means or tool of measuring. Nor can I find any 1/6 measurements??? Perhaps I shoulkd scribe some in to all my tapes?

Beyond, beyond that; your asking a question regarding MATH, which was; last time I checked; and Exact Science.

To "ESTIMATE" your Q you can say 3.4285714 boards; however that doesn't take into account; blade width cuts.

Steven Wolf

Answer 2

You cannot' estimate fractions anymore than you can estimate whole numbers,they have an exact value.
1) In order to subtract these fractions you have to even the playing field ei. find the least common denominator,you do that by breaking the denominator in prime numbers,discarding the duplicates and multiply the rest.
In this problem you have to do it twice,14 is really 14/1 +1/7 the prime numbers are 1,7 wicth give you a least common denominator of 7.
Divide 7 by 1= 7
Multiply 7 by 14 = 98
Divide 7 by 7 = 1
The new fraction is (98+1)/7 = 99/7.
Now you have to find the least common denominator between 7 and 6,7 is a prime number,6 is 2 and 3.
The least common denominator is 7x2x3 = 42.
Now you have 42 : 7 x 99 = 594
42 : 6 x 5 = 35
or (594 + 35)/42 = 629/42

2) same as 1).after you change the fraction multiply the denominator by 3.When you divide a fraction ,just reverse one fraction and multiply. 35/6 divided by 3/1=35/6 x 1/3 = 35/18

3) 3 1/2 = 7/2, 12 divided by 7/2 = 12 x 2/7 = 24/7 = 3 with 3/7 of a foot left over.

Answer 3

1.....14 1/7 - 5/6 =13 13/42

2......5 5/6 divided 3=17 1/3

3......3 w/1 1/2 foot waste

Answer 4

There is no such thing on an American tape measure as 1/7 or 5/6.
So (1) & (2) are not answerable.
To answer (3) however.......divide 12' by 3.5' = 3 with 1.5' leftover.