<span>Least Common Denominator (LCD) is the least number which all the denominators can divide without remainder. The given denominators are 2, 16 and 8. The least number 2, 16 and 8 will divide without remainder is 16. Therefore, to express the fractions 1/2, 3/12, and 7/8 with an LCD, we multiply both the numerator and the denominator of each of the fractions with a common factor that makes the denominator to be 16. Therefore, 1/2, 3/16 and 7/8 expressed with an LCD are (1 x 8) / (2 x 8), 3/16, (7 x 2) / (8 x 2) = 8/16, 3/16, and 14/16.</span>
I’ve attached my work below
Hope it helps!!
Answer:
Hence the number of pages read by Lonnie is 16 pages when they read a combined of 36 pages.
Step-by-step explanation:
The table that can be formed by the rate at which they study the number of pages of a book is:
Fred Lonnie total
5 4 9
10 8 18
15 12 27
20 16 36
That means when they read a combined of 36 pages.
Then the number of pages read by Fred is 20 pages.
and the number of pages read by Lonnie is 16 pages.
(
Also it could be done as :
Let Fred reads 'x' pages.
so, the number of pages read by Lonnie is: (4/5)x
Hence,
x+(4/5)x=36
on solving this linear equation we have:
x=20
and (4/5)x=16
)
Hence the number of pages read by Lonnie is 16 pages when they read a combined of 36 pages.
This is a classic example of a 45-45-90 triangle: it's a right triangle (one angle of 90) & two other sides of the same length, which means two angles of the same length (and 45 is the only number that will work). With a 45-45-90 triangle, the lengths of the legs are easy to determine:
45-45-90
1-1-sqrt2
Where the hypotenuse corresponds to sqrt2.
Now, your hypotenuse is 10.
To figure out what each leg is, divide 10/sqrt2 (because sqrt2/sqrt2 = 1, which is a leg length in the explanation above).
Problem: you can't divide by radicals. So, we'll have to rationalize the denominator:
(10•sqrt2)/(sqrt2•sqrt2)
This can be rewritten:
10sqrt2/sqrt(2•2)
=10sqrt2/sqrt4
=10sqrt2/2
=5sqrt2
Hope this helps!!
