How do you evaluate #16\frac { 2} { 7} - 2\frac { 1} { 2} \cdot 1\frac { 1} { 7} + \frac { 9} { 14}#?

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Feb 11, 2017

Answer:

#16 2/7 - 2 1/2*1 1/7 + 9/14 = 14 1/14#

Explanation:

Given:

#16 2/7 - 2 1/2*1 1/7 + 9/14#

First let us convert all of the mixed numbers to improper fractions:

#16 2/7 = 16 + 2/7 = (16*7)/7+2/7 = 112/7+2/7 = 114/7#

#2 1/2 = 2 + 1/2 = (2*2)/2 + 1/2 = 4/2+1/2 = 5/2#

#1 1/7 = 1 + 1/7 = 7/7+1/7 = 8/7#

So our original expression can be rewritten as:

#114/7 - 5/2*8/7 + 9/14#

Next note that multiplication has higher precedence than addition or multiplication, so we need to perform the multiplication #5/2*8/7# first:

#114/7 - color(blue)(5/2*8/7)+9/14 = 114/7 - (5*8)/(2*7)+9/14 = 114/7-40/14+9/14#

In order to add or subtract these fractions, they need to have the same denominators, so we multiply #114/7# by #2/2# to give it a denominator #14# like the other fractions:

#114/7 = (114*2)/(7*2) = 228/14#

So our express can be rewritten:

#228/14-40/14+9/14 = (228-40+9)/14#

Then note that addition and subtraction have the same priority, so we need to evaluate them from left to right:

#(color(blue)(228-40)+9)/14 = (188+9)/14 = 197/14#

To express this as a mixed number, we divide #197# by #14# to give a quotient #14# and remainder #1#, so:

#197/14 = 14+1/14 = 14 1/14#

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Feb 12, 2017

Answer:

#=14 1/14#

Explanation:

It is possible to work with the whole numbers separately when adding or subtracting.

Only for multiplication do we have to use improper fractions.

There are 3 terms, do the multiplication first.

#16 2/7 color(blue)(-2 1/2 xx 1 1/7) +9/14#

#=16 2/7color(blue)(-5/2 xx8/7) +9/14#

We would usually cancel in the middle term. However we will need a common denominator in the next step so leave as it is. Simplify by multiplying straight across.

#16 4/14 color(blue)(-40/14) +9/14" "# all have the same denominator

#=16 4/14 color(blue)(-2 12/14) +9/14" "# change to a mixed number

#= 14 (4-12+9)/14#

#=14 1/14#

Working with mixed numbers gives us smaller numbers to work with. The numbers in improper fractions are often uncomfortably big.

(Answer in the same form as the numbers were given.)

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Feb 11, 2017

Answer:

#14 1/14#

Explanation:

#16 2/7-2 1/2*1 1/7+9/14#

#:.=114/7-(5/2 xx 8/7)+9/14#

#:.=114/7-(40/14)+9/14#

#:.=(228-40+9)/14#

#:.=197/14#

#:.=14 1/14#

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