Each of the problems asks you to a similar idea: get a common denominator with the fractions and then subtract.
Problem 1: 28 3/8 - 19 5/6
The factors of 8 are 2, 2, and 2. The factors of 6 are 2 and 3. We take one two that's repeated, two more twos from 8, and a 3 for the common denominator. So, 2 * 2 * 2 * 3 = 24 is the lowest common denominator (LCD).
Now change the fractions to the common denominators
3/8 = ? / 24 We go from 8 to 24 multiplying by 3, so 3 multiplied by 3 is 9.
5/6 = ? / 24 We go from 6 to 24 multipling by 4, so 5 multiplied by 4 is 20.
Then,
28 3/8 - 19 5/6
= 28 9/24 - 19 20/24 <----use common denominators
= 27 33/24 - 19 20/24 <--- borrow from the whole number
= 8 13/24 <---- subtract whole numbers and fraction numerators
Problem 2 works similarly to problem 1, with an LCD of 15.
18 2/5 - 9 13/15
= 18 6/15 - 9 13/15
= 17 21/15 - 9 13/15
= 8 8/15
Thus the differences are 8 13/24 (1st) and 8 8/15 (2nd).
Answer: 17, 19, 21
Step-by-step explanation:
Three consecutive odd numbers: x, x+2, x+4 (since odd numbers occur every other number)
Just to show you that the numbers are x, x+2, and x+4, just say x is 13 then x+2 is 15 and x+4 is 17 (3 consecutive odd numbers)
Now the second equation:
3x = 2(x+4) + 9
three times smallest number (which is x) is equal to 2 times the largest number (x+4) plus 9
Now solve
3x = 2(x+4) +9
3x = 2x + 8 + 9
3x = 2x + 17
x = 17
x+2 = 19
x+3 = 21
Answer:
uhm with what? there isn't anything here?
Step-by-step explanation:
Find angle a2 which is 40 degrees because it is parallel to angle c.
Find the total of d1 and d2.
total of d1 and d2: 180 - 40 - 40 = 100 degrees
Find d1 and d2 separately.
100 divided by 2 = 50 degrees
Use d1 to find b1 to find total of a1 and a2.
b1 is parallel to d1 so b1 = 50 degrees
a1 and a2 = 180 - 50 - 50 = 80 degrees
a1 = 80 divided by 2 = 40
Since a1 and c1 are parallel due to alternate angles, c1 is 40 degrees
Find b2 now which requires you to do total - minus all angles in the triangle with angle b2.
180 - 40 - 50 - 40 = 50 degrees (angle b2)
AOB has b1 and a1.
40 + 50 = 90 degrees (a1 + b1 = AOB)
The answer is 90 degrees
