How do you add and subtract measurements?

[clhrhrklsr]

How would you figure a problem like this-

9' - 6 11/16
+17' - 9 3/4

I'm trying to reteach my self this math, and I can't remember how this is done. Please help asap!

 

[MarkFL]

Hello and welcome to MHB! :D

Just to be clear, are you trying to add 9 ft. 6 and 11/16 in. to 17 ft. 9 and 3/4 in.?

 

[clhrhrklsr]

Hello and welcome to MHB! :D

Just to be clear, are you trying to add 9 ft. 6 and 11/16 in. to 17 ft. 9 and 3/4 in.?

Yes I am. I'm not sure how you can figure those kind of problems out. I can do in correct in my scientific calculator (only have to input the measurements and wa-lah I have my answer) but I want to know how to figure this out by hand. Thanks in advance for any help.

 

[MarkFL]

Okay, what I would do is begin by adding the fractions of inches:

\(\displaystyle \frac{11}{16}+\frac{3}{4}\)

We need to get a common denominator, which the lowest possible is 16:

\(\displaystyle \frac{11}{16}+\frac{3}{4}\cdot\frac{4}{4}\)

\(\displaystyle \frac{11}{16}+\frac{12}{16}=\frac{11+12}{16}=\frac{16+7}{16}=1+\frac{7}{16}\)

So we know the end result will have 7/16 in. at the end. We take the 1 in. and add it to the other two values for inches:

\(\displaystyle 6+9+1=12+4=1\text{ ft}+4\text{in}\)

So we now know that 4 and 7/16 in. is at the end. We take the 1 ft. and add it to the other two values for feet:

\(\displaystyle 9+17+1=27\)

Thus, we know the sum is:

27 ft. 4 and 7/16 in.

 

[clhrhrklsr]

\(\displaystyle \frac{11}{16}+\frac{12}{16}=\frac{11+12}{16}=\frac{16+7}{16}=1+\frac{7}{16}\)

So we know the end result will have 7/16 in. at the end. We take the 1 in. and add it to the other two values for inches:

How do you figure \(\displaystyle \frac{11}{16}+\frac{12}{16}=\frac{11+12}{16}=\frac{16+7}{16}=1+\frac{7}{16}\)

how does frac{11+12}{16}=\frac{16+7}{16}=1+\frac{7}{16}[/MATH]

I do not follow.

 

[ineedhelpnow]

He's showing off his adding fractions moves. :D i believe what Mark did is this:

So $16+7=23$
and so does $11+12$
you follow?

so then in order to be able to simplify to $1+ \frac{7}{16}$ he just made it simple and added a little onto 11 and took some of 12 so he gets 16 on the numerator and 16/16 can easily be simplified to 1. and then there's still a 7/16 which gives $1+ \frac{7}{16}$.
It would have been the same if you did $\frac{11+12}{16}=\frac{23}{16}=1\frac{7}{16}$ which is the same as $1+\frac{7}{16}$

make sense?

 

[clhrhrklsr]

He's showing off his adding fractions moves. :D i believe what Mark did is this:

So $16+7=23$
and so does $11+12$
you follow?

so then in order to be able to simplify to $1+ \frac{7}{16}$ he just made it simple and added a little onto 11 and took some of 12 so he gets 16 on the numerator and 16/16 can easily be simplified to 1. and then there's still a 7/16 which gives $1+ \frac{7}{16}$.
It would have been the same if you did $\frac{11+12}{16}=\frac{23}{16}=1\frac{7}{16}$ which is the same as $1+\frac{7}{16}$

make sense?

I'm getting a solid ground with this now. Thanks for the help so far. The only part I'm confused with now is this-

$\frac{11+12}{16}=\frac{23}{16}=1\frac{7}{16}$

how do you get this?

 

[MarkFL]

Suppose you wanted to compute the sum:

\(\displaystyle 1+\frac{7}{16}\)

In order to proceed, you would want to rewrite 1 as 16/16 so that we have a common denominator:

\(\displaystyle \frac{16}{16}+\frac{7}{16}\)

Now, a property of fractions is:

\(\displaystyle \frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}\)

and so using this, the sum becomes:

\(\displaystyle \frac{16+7}{16}=\frac{23}{16}\)

So, just look at this in reverse, and you see how:

\(\displaystyle \frac{23}{16}=1+\frac{7}{16}\)

 

[clhrhrklsr]

Suppose you wanted to compute the sum:

\(\displaystyle 1+\frac{7}{16}\)

In order to proceed, you would want to rewrite 1 as 16/16 so that we have a common denominator:

\(\displaystyle \frac{16}{16}+\frac{7}{16}\)

Now, a property of fractions is:

\(\displaystyle \frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}\)

and so using this, the sum becomes:

\(\displaystyle \frac{16+7}{16}=\frac{23}{16}\)

So, just look at this in reverse, and you see how:

\(\displaystyle \frac{23}{16}=1+\frac{7}{16}\)

I understand this way.

How do you get $\frac{23}{16}=1+\frac{7}{16}$?

I understand you have this- $\frac{11}{16}+\frac{12}{16}=\frac{23}{16}$
but what i don't understand is how you get $1+\frac{7}{16}$ from the $\frac{23}{16}$.

 

[ineedhelpnow]

it's a mixed fraction. you see how many times the denominator goes into the numerator and that number goes in the front (in this case 1) and then there is 7 out of that 16 remaining so $1\frac{7}{16}$ or $1+\frac{7}{16}$

- - - Updated - - -

so:
23/16
16 goes into 23 one time but there's a remainder. 23-16=7 and so you still have 7 out of that 16 left therefore you have 1 and 7/16

i hope you can make sense of this. i know my explanations might be very confusing.

 

[MarkFL]

I understand this way.

How do you get $\frac{23}{16}=1+\frac{7}{16}$?

I understand you have this- $\frac{11}{16}+\frac{12}{16}=\frac{23}{16}$
but what i don't understand is how you get $1+\frac{7}{16}$ from the $\frac{23}{16}$.

Suppose we have the fraction:

\(\displaystyle \frac{p}{q}\) where $p$ and $q$ are both positive integers and $p>q$.

Now, since $p$ is greater than $q$, we could rewrite $p$ as:

\(\displaystyle p=mq+n\) where $m$ and $n$ are both positive integers and $n<q$. Like ineedhelpnow points out, you want to find the greatest number of times $q$ will go into $p$ (we call this $m$ here), where $n$ is the remainder. In our case 16 goes into 23 1 time with a remainder of 7.

And so back to the general problem, the fraction becomes:

\(\displaystyle \frac{mq+n}{q}=m\frac{q}{q}+\frac{n}{q}=m+\frac{n}{q}\)

Does this make sense?

 

[ineedhelpnow]

or for example when you say one and a half which is $1\frac{1}{2}$ it is equivalent to $\frac{3}{2}$ because you multiply the denominator (2) by the number in front (1) which is 2 and then you add the the numerator (1) to it which is 3. so 3 over the denominator 2. $\frac{3}{2}$

$1\frac{7}{16}$ it is equivalent to $\frac{23}{16}$ because you multiply the denominator (16) by the number in front (1) which is 16 and then you add the the numerator (7) to it which is 23. so 23 over the denominator 16. $\frac{23}{16}$

 

[clhrhrklsr]

or for example when you say one and a half which is $1\frac{1}{2}$ it is equivalent to $\frac{3}{2}$ because you multiply the denominator (2) by the number in front (1) which is 2 and then you add the the numerator (1) to it which is 3. so 3 over the denominator 2. $\frac{3}{2}$

$1\frac{7}{16}$ it is equivalent to $\frac{23}{16}$ because you multiply the denominator (16) by the number in front (1) which is 16 and then you add the the numerator (7) to it which is 23. so 23 over the denominator 16. $\frac{23}{16}$

Ok. I have figured it all out I believe now.

Now if you all have time, could you tell me how this would be figured?

43 ft. 5 \frac{3}{4} + 12 ft. 1 \frac{3}{16}

I'm studying practice questions for a draftsman test and I can work better if I see examples worked out and see how they are worked, instead of spending hours and hours figuring out one problem. I'm trying to get this stuff down pat for when I do take the actual test, I have to take it once with calculator and once without.

 

[ineedhelpnow]

put a dollar sign in front of your latex command and after. its best to preview your post first so you notice any mistakes. :)

 

[MarkFL]

You'll get more out of this if you are an active participant in the process of getting the solution. :D

Begin by adding the fractions of inches in the two measurements. What it the lowest common denominator?

 

[clhrhrklsr]

You'll get more out of this if you are an active participant in the process of getting the solution. :D

Begin by adding the fractions of inches in the two measurements. What it the lowest common denominator?

The LCD would be 16, right?

 

[Deveno]

I used to have to add measurements like this all the time, first as a carpenter, then as a truss designer.

First, the fractions.

We have 11/16 and 3/4, and to add these, we need to convert quarter-inches to sixteenths.

Since there are 4 sixteenths in a quarter-inch, we have:

1/4 = 4/16, so 3/4 = 3*(4/16) = 4/16 + 4/16 + 4/16 = 12/16. Now, we can add the sixteenths together, to get:

11/16 + 12/16 = 23/16 (we're adding sixteenths, we have 11 and 12 of them, and 11 + 12 = 23).

Now 23 is more than 16, and 16/16 = 1 whole inch. So we subtract 16 from 23 to find out how many sixteenths we have "left over" (how many sixteenths we go PAST one inch).

23 - 16 = 7, so 23/16 = 16/16 + 7/16 = 1"-7/16.

So 7/16 is going to be our "fraction of an inch", and the two fractions in our original measurements contribute "one to the inches".

Now we add the inches. 6" + 9" + 1" (the 1 is "carried over from the fractions") is 16". We have another conversion to do here, since 12" = 1', and we have more than 12" in our sum.

So we have to subtract 12 from 16, to find out "how many inches" are left over.

16" = 12" + 4" = 1' 4". The 4" will stay-the 1' will be added to the other foot-measurements.

So, so far, we have 4"-7/16 as "fractional feet", and our sum of the "fractional feet" contributes 1' to the total.

Now, we can finally "add up the feet" (no more converting to worry about).

****************

You can, if you like, work from "big to small". Add the feet first:

9 + 17 = 26'.

Add the inches next: 6" + 9" = 15" = 12" + 3" = 1' 3".

Add this to our feet: 26' + 1' 3" = 27' 3".

Add the fractions next (Remember to convert fractions larger than 16/16 to inches and and a fraction).

Either way works just fine, and should give you the same answer.

One thing to be careful of when going "big to small" if you have a measurement very close to "an even foot", like:

2' 11" -15/16, you may wind up having to "go bacK" and change not only the "inches" part, but also the "feet" part.

 

[MarkFL]

The LCD would be 16, right?

Yes, so what do you get when you add the two fractions, using the common denominator?