Two rulers are the same length. Ruler A is divided into 357 units while ruler B is divided into 255 units The rulers are placed side by side with the 0 marks lined up and the 375th mark of ruler A aligned with the 255th mark of ruler B. How many total places will the marks on the rulers be aligned?
357A = 255B
A/B = 255/357 = 5/7
A - B
5 7
10 14
15 21
...
255 357
there will be 52 of those line-ups , obtained by 255/5 = 51, or 357/6 = 51, plus the line-up at the zeros
A ruler measures length to the nearest 0.25 inches. Which is the most appropriate way to report length using this ruler?
To find the number of total places where the marks on the rulers are aligned, we need to determine the least common multiple (LCM) of the two numbers - 357 and 255.
To do this, we can use the formula:
LCM(a, b) = (a * b) / GCD(a, b)
Where a and b are the given numbers, and GCD denotes the greatest common divisor.
To find the GCD of 357 and 255, we can use the Euclidean algorithm:
1. Divide 357 by 255:
357 ÷ 255 = 1 remainder 102
2. Divide 255 by the remainder obtained (102):
255 ÷ 102 = 2 remainder 51
3. Divide 102 by the new remainder (51):
102 ÷ 51 = 2 remainder 0
4. Since the remainder is now 0, the GCD of 357 and 255 is 51.
Now we can find the LCM using the formula:
LCM(357, 255) = (357 * 255) / 51
LCM(357, 255) = 90855 / 51
LCM(357, 255) = 1785
Therefore, the total number of places where the marks on the rulers will align is 1785.