In general to be able to add or subtract fractions you need to have the same denominator so that you can add the numerators.
The easiest way to find the same denominator is to identify the lowest common denominator (LCD).
You can find the LCD by finding the prime factors of the denominators in question and multiplying them all together. If the denominators share a prime factor, only multiply it once.
Sometimes you can just eyeball the numbers to find the LCD, which might be faster.
For #W we need to find the LCD of 10 and 6, so prime factorize:
10 = 2 x 5
6 = 2 x 3
LCD = 2 x 5 x 3 = 30
The LCD is 30, so we need to change the fraction to reflect that. Remember, what you do to the denominator you need to do to the numerator as well. So:
-9/10 becomes -27/30 (both multiplied by 3)
-1/6 becomes -5/30 (both multiples by 5)
Now you can easily add:
-27/30 + (-5/30) = -32/30
In summary:
Step #1: find LCD (prime factor or eyeball)
Step #2: multiply the numerator of each fraction by the factor needed to obtain the LCD in that denominator
Step #3: add the fractions now that they have the LCD
Here’s the solution to #G:
-¾ + (-7/12)
Step #1:
4 = 2 x 2
12 = 2 x 2 x 3
LCD = 2 x 2 x 3 (count each unique prime factor once)
Step #2:
-¾ becomes -9/12 (both multiplied by 3)
-7/12 stays the same (it already has the LCD)
Step #3:
-9/12 + (-7/12) = -16/12
Let me know if you have any questions. Try to work though the others!
In this problem, the reference of the scale is referring to feet. Firstly, convert 72 inches to feet so that you can properly make the proportion.
72 inches = 6 feet
With the scale of 2 inches per 3 feet, we can set up an easy proportion to see how wide the door will be on the drawing.
3 feet 6 feet
——— = ————
2 inc. ‘x’ inc.
3x=12
X=4 inches
Solving the proportion by cross-multiplication reveals that the scale drawing of the patio door would be 4 inches wide.
Answer:
32 feet
Step-by-step explanation:
area of square is given by side^2
Perimeter of square is given by 4*side
_______________________________
Given
area of square = 64 sq feet
side^2 = 64
side^2 = 8^2
side = 8
thus side = 8 feet
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The dog pen is fenced with chain, hence chain will be fence at the edge of square and at the perimeter.
Thus, length of chain required will be same as the Perimeter of square.
Perimeter of given dog pen with side length 8 feet = 4*8 = 32 feet.
Thus, 32 feet of chain fence is required.
