Write the ratio that compares 24 apples to 14 oranges using fractional notation. Simplify the improper fraction in lowest terms
The ratio comparing 24 apples to 14 oranges can be written as:
24 apples / 14 oranges
To simplify the ratio in fractional notation, we divide both numbers by their greatest common factor, which is 2 in this case:
24 ÷ 2 = 12
14 ÷ 2 = 7
So the simplified ratio in fractional notation is:
12/7
Which of the following, Option 1 or Option 2, is a proportion?
1) 4/5 = 20/25
2) 4/5 = 16/30
A proportion is an equation that states that two ratios are equal. So, in order to determine if the given options are proportions, we need to check if the ratios are equal.
1) 4/5 = 20/25
To check if this is a proportion, we can cross multiply:
4 x 25 = 5 x 20
100 = 100
Since the cross products are equal, the given ratios are equal, making Option 1 a proportion.
2) 4/5 = 16/30
Again, to check if this is a proportion, we cross multiply:
4 x 30 = 5 x 16
120 ≠ 80
Since the cross products are not equal, the given ratios are not equal, making Option 2 not a proportion.
Therefore, Option 1 is a proportion.
The number of points that Yuki scored in a basketball game is represented by the equation 5y = 110x. In this equation, y represents the total number of points and x represents number of games. How many points did Yuki average per game?
To find the average number of points Yuki scored per game, we need to divide the total number of points by the number of games played.
Given that the equation is 5y = 110x, we can rearrange it to solve for y, the total number of points scored in terms of x, the number of games:
y = 110x / 5
y = 22x
This equation tells us that the total number of points Yuki scored (y) is 22 times the number of games played (x).
Therefore, Yuki averaged 22 points per game.