Question from a reader:

I’m currently studying and writing down problems and math just to pass a test at a local union to train for a journeyman position. But here’s the problem, I’ve been out of school for sometime now and forgot most of the stuff. Here’s what is really getting to me and I can’t find any information on the web yet. So I’m going to let it rip and see if u can figure out the problems and explain how you got them so that I can get them.

Here’s the first one…

9 ft 7 5/8 in + 22 ft 6 3/4 in + 15 ft 11 3/16 in

My answer was: 48 ft 1 5/16 in. I feel like I missed up somewhere though

Here’s the second….

17 ft 7 1/2 in – 14 ft 9 7/8 in…

This one I don’t understand at all. This would be a big help from u. Thank you

Answer:

Starting with the first problem – addition.

Will use some rules of arithmetic to rewrite the problem to make it easier to work.

9 ft 7 5/8 in + 22 ft 6 3/4 in + 15 ft 11 3/16 in =

(9 ft + 7 in + 5/8 in ) + (22 ft + 6 in +3/4 in) + (15 ft + 11 in + 3/16 in)

Can now rearrange.

Since we have different units of measure will be easier collect same units of measure together.

Also will group the fractions together.

9 ft + 7 in + 5/8 in + 22 ft + 6 in +3/4 in + 15 ft + 11 in + 3/16 in =

(9 ft + 22 ft + 15 ft) + (7 in + 6 in + 11 in) + (5/8 in + 3/4 in + 3/16 in)

9 ft + 22 ft + 15 ft = 46 ft

7 in + 6 in + 11 in = 24 in

Now look at just the fraction part.

5/8 in + 3/4 in + 3/16 in -> to add or subtract fractions you need to change them to a common denominator.

For 8, 4, 16 the common denominator is 16 -> the number all of the denominators will all divide into evenly; or can look at it as the number for which all are a multiple. In this case 8*2 = 16; 4*4 = 16; 16*1 = 16.

To get a common denominator for each on we multiply numerator (top) and denominator (bottom) by the multiple. Thus in this case we get:

10/16 + 12/16 + 3/16 -> and now since they are all the same denominator we can add the numerators.

(10 +12 +3)/16 = 25/16 since 25 > 16 then we can write this as a mixed number

25 = 1*16 + 9 thus 25/16 = 16/16 + 9/16 thus 25/16 = 1 9/16 as a mixed number.

1 9/16 in = 1 in + 9/16 in

So:

From before:

9 ft + 22 ft + 15 ft = 46 ft

7 in + 6 in + 11 in = 24 in

5/8 in + 3/4 in + 3/16 in = 1 9/16 in

Since 24 in = 2 ft

46 ft + 24 in + 1 in + 9/16 in = 46 ft + 2 ft + 1 in 9/16 in = 48 ft + 1 in + 9/16 in

And finally we get:

48 ft + 1 in + 9/16 in = 48 ft 1 9/16 in

Second problem, subtraction, using the same strategy.

17 ft 7 1/2 in – 14 ft 9 7/8 in

Since it is subtraction we need to make sure we keep that in mind when we regroup the numbers.

As before we can break the problem down using arithmetic rules.

17 ft 7 1/2 in – 14 ft 9 7/8 in = (17 ft + 7 in + 1/2 in) – (14 ft + 9 in + 7/8 in)

= 17 ft + 7 in + 1/2 in – 14 ft – 9 in – 7/8 in

We can rearrange to get like units together as well as integer and fractions together

(17 ft + 7 in + 1/2 in) – (14 ft + 9 in + 7/8 in) =

(17 ft – 14 ft) + (7 in – 9 in) + (1/2 in – 7/8 in) = (3 ft) + (-2 in) + (1/2 in – 7/8 in)

Thus we have:

3 ft + (- 2 in) = 36 in – 2 in = 34 in

34 in = 2(12) in + 10 in = 2 ft + 10 in

Now for the fraction:

1/2 in – 7/8 in -> the common denominator is 8 since 4*2 = 8 and 1*8 = 8

4/8 in – 7/8 in = (4 – 7)/8 in = -3/8 in

Combining both parts:

2ft + 10 in + (-3/8 in) = 2 ft + 10 in – 3/8 in

To make working the subtraction of the fraction a little easier can look at the problem this way

(10 in = 9 in + 1 in):

2 ft + 10 in – 3/8 in = 2 ft + 9 in + 1 in – 3/8 in

1 in – 3/8 in = 8/8 in – 3/8 in = ( 8 – 3)/8 in = 5/8 in -> so

2 ft + 10 in + (-3/8 in) = 2 ft + 9 in + (1 in – 3/8 in) = 2 ft + 9 in + 5/8 in

2 ft + 9 in + 5/8 in = 2 ft 9 5/8 in

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