Multiply what’s on the outside to the inside, the variable is always a lower case letter such as x,
Answer:
Kindly check explanation
Step-by-step explanation:
When performing addition and subtraction of decimals, it is important to arrange the numbers being added or subtracted such that the decimal points are in line. This is particularly important so that the place value of the numbers are in accord.
To simplify, when then decimals are in line, then the tenth value of the first number will be added to the tenth value of the second. Without this arrangement, one might be adding the hundredth placed value to the tenth or unit value which is mathematically incorrect and will yield a wrong result.
For instance :
6.32 - 0.5
Here, when the decimal point of each number is in line, the tenth placed value of the first number (3) matches the tenth placed number of the second number (5) and all others also fall in place automatically.
____6.32
- ___0.5
________
___ 5.82
________
<h2><u>
ABSOLUTE VALUE</u></h2>
The absolute value of a number is the distance from 0 to that number. The distance is positive, hence, the absolute value is always a positive number.
<h3>Exercise</h3>
Replace the value of x:
The absolute value of a number is the numerical value of the number, without regard to its sign.
<h3><u>Answer.</u> 12</h3>
Answer:
Step-by-step explanation:
2005 AMC 8 Problems/Problem 20
Problem
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 24$
Solution
Alice moves $5k$ steps and Bob moves $9k$ steps, where $k$ is the turn they are on. Alice and Bob coincide when the number of steps they move collectively, $14k$, is a multiple of $12$. Since this number must be a multiple of $12$, as stated in the previous sentence, $14$ has a factor $2$, $k$ must have a factor of $6$. The smallest number of turns that is a multiple of $6$ is $\boxed{\textbf{(A)}\ 6}$.
See Also
2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 19 Followed by
Problem 21
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
