Fractions Question

[dave1014]

Dear Colleagues,

Please click on the thumbnail / full image and look at Page 97 and the second grey box titled 'Example', where it says "Duncan's maintenance calculation will be reduced by
13/28 ( [7/14+ 6/14 ]) / 2 ) etc.

My question is : How did the calculation arrive at the fractions 7/14 + 6 / 14 ?.

Thank you

 

[Steven G]

Just look at the table!
175 or more, which includes 180, is 1/2
156-174, which includes 156, is 3/7

How would you add 1/2 and 3/7?

 

[ksdhart2]

Hint: "One half" = \(\displaystyle \frac{1}{2} = \frac{??}{14}\)

Another hint: "Three sevenths" = \(\displaystyle \frac{3}{7} = \frac{??}{14}\)

 

[dave1014]

Thank you for the replies.

Apologies, if I add 1/2 + 3/7 = 13/14 ( how do I get from this to 7/14 + 6/14 ) ?

 

[Steven G]

If you want to change the way a number looks you can multiply by 1. But understand that there are numerous way of writing 1. For example 7/7=1, 19/19 = 1, .56/.56 = 1, ...
Now before you can add fractions you MUST first have a common denominator.
Now think of numbers on the 2 times table (2, 4, 6, 8, ...) and numbers on the 7 table (7, 14, 21, 28, ...). I got these two numbers from the denominators of the fractions we want to add. Now find the smallest common multiple on both those times tables. The answer is 14

Now (1/2) = (1/2)*(1) = (1/2)*(7/7) = 7/ 14
While (3/7) = (3/7)*(1) = (3/7)*(2/2) =6/14

So 1/2 + 3/7 =7/14 +6/14 = (7+6)/14 = 13/14