Sherry has two rectangular garden plots at the community garden. one plot measures 5 1/2 feet by 9 1/2 feet. the other plot measures 4 1/4 feet by 6 1/2 feet. how many total square feet does sherry have.

  79 7/8 ft²

Step-by-step explanation:

A calculator can take the tedium out of math with mixed numbers or fractions. (See below.)

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If you like the tedium or just need to practice your arithmetic with fractions, you can do it as follows.

First of all, you need to know that the area of a rectangular plot is the product of its length and width. So, we need to compute ...

  (5 1/2)×(9 1/2) + (4 1/4)×(6 1/2)

You can do it as mixed numbers:

  (45 +5/2 + 9/2 + 1/4) + (24 + 4/2 + 6/4 + 1/8) = 69 + 18/2 + 7/4 + 1/8

  = 69 + 9 + 1 3/4 + 1/8 = 79 + 6/8 + 1/8 = 79 7/8

Or, you can do it by converting to improper fractions:

  11/2×19/2 + 17/4×13/2 = 209/4 + 221/8 = (418 +221)/8 = 639/8 = 79 7/8

You can also do it using decimal numbers:

  5.5×9.5 + 4.25×6.5 = 52.25 +27.625 = 79.875 = 79 7/8

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Dimensions are in feet, so the area is in square feet.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

so, converting firstly the mixed fractions to improper fractions and then "adding".