Calculate the distance between the points -2/3 and 3/4 on the number line. Please show how you come to the answer.
The point -2/3 is to the left of the y-axis, and 3/4 is the right of the y-axis. The distance between the two points would be the sum of the respective distances from the y-axis, namely 2/3 and 3/4.
D=2/3+3/4=?
1 5/12?
You're close.
2/3+3/4=8/12+9/12=?
To calculate the distance between two points on the number line, we need to find the absolute difference between the coordinates of the two points.
Given the points -2/3 and 3/4 on the number line, let's find the absolute difference between their coordinates:
Absolute difference = |3/4 - (-2/3)|
To subtract the fractions, we need a common denominator:
3/4 = (3/4) * (3/3) = 9/12
-2/3 = (-2/3) * (4/4) = -8/12
Now we can find the absolute difference:
|9/12 - (-8/12)| = |9/12 + 8/12|
Adding the fractions:
9/12 + 8/12 = 17/12
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 1 in this case:
17/12 ÷ 1/1 = 17/12
The distance between -2/3 and 3/4 on the number line is 17/12.
Not really, when you measure distances, they are positive. It's like an absolute value. You measure from -2/3 to 0 (y-axis), and then from 0 (y-axis) to 3/4.
Give it another try, and I am sure you'll get it this time.
how do you get 8/12 + 9/12? it's the samething isn't is? 17/12 = 1 5/12 yes?
Sorry, I just realized your previous answer was correct. I have just misread it as 15/12. Sorry.
Sometimes by writing it as 1-5/12 will reduce the errors. But it was my oversight.
Back to how we can get the answer:
From
2/3 + 3/4,
we look for the lowest common multiple (LCM) of the denominators, 3 and 4.
The LCM is the product of the two numbers if there are no common factors, as in our case.
The LCM will become the common denominator of the two fractions. So we look for
2/3 = ? / 12
You can get that by proportions, i.e. cross multiplying 2*12/3=8, or
3*4=12, so 2*4=8
Whichever way you do it, you get
2/3+3/4=8/12+9/12=17/12
Even here, you have to check out if you have common factors between the numerator and the denominator in case a reduction is required.
Finally, since it is an improper fraction (numerator is greater than the denominator), it must be reduced to a mixed number, i.e. a number accompanied by a proper fraction.
So
17/12=1 5/12, as you have done.