In a game there are black counters and white counters. One third of the counters are black. What is the ratio of black counters to white counters?
black counters ---- 1/3
white counters ----- 2/3
ratio of black : white = 1/3 : 2/3
= 1 : 2
To find the ratio of black counters to white counters, we first need to determine the number of black and white counters in the game.
Let's assume there are a total of "x" counters in the game.
Given that one-third of the counters are black, it means that (1/3) * x counters are black.
To find the number of white counters, we can subtract the number of black counters from the total number of counters:
x - (1/3) * x = (2/3) * x
Thus, there are (2/3) * x white counters.
Now, to find the ratio of black counters to white counters, we can divide the number of black counters by the number of white counters:
[(1/3) * x] / [(2/3) * x] = (1/3) / (2/3)
To simplify this ratio, we can multiply both the numerator and denominator by the reciprocal of 2/3, which is 3/2:
(1/3) / (2/3) * (3/2) / (3/2) = 1/2
Therefore, the ratio of black counters to white counters is 1:2.
To find the ratio of black counters to white counters, you need to know the total number of counters first. Since one third of the counters are black, this means that there are two thirds of the counters that are white.
To calculate the ratio, you can set up a fraction with the number of black counters as the numerator and the number of white counters as the denominator. In this case, since we don't know the specific total number of counters, we can assign a variable like "x" to represent the total.
Let's write the fraction: black counters / white counters = (1/3)x / (2/3)x
Now you can simplify this fraction. You can do this by multiplying both the numerator and the denominator by 3 to get rid of the fractions.
black counters / white counters = (1/3)x / (2/3)x * 3/3
Simplifying further, you get:
black counters / white counters = (1/3)x * 3 / (2/3)x * 3
black counters / white counters = (1*x)/3 / (2*x)/3
black counters / white counters = x / 2x
Finally, you can simplify the fraction by dividing both the numerator and the denominator by "x". This will cancel out the "x" terms in the ratio:
black counters / white counters = 1 / 2
Therefore, the ratio of black counters to white counters is 1:2.