a pizza has 3/4 slices of pepperoni, 5/8 slices of bell peppers, and 4/16 mushrooms each slice has at least one topping. How many slices have all 3 toppings?
To find out how many slices have all three toppings (pepperoni, bell peppers, and mushrooms), we need to determine the common fraction between the three toppings.
First, let's find the least common denominator (LCD) among the fractions 3/4, 5/8, and 4/16:
- The LCD of 4 and 8 is 8.
- The LCD of 4 and 16 is 16.
- The LCD of 8 and 16 is 16.
So, the LCD of all three fractions is 16.
Now, let's convert the fractions to have a denominator of 16:
- For 3/4, we multiply the numerator and denominator by 4: (3/4) * (4/4) = 12/16.
- For 5/8, we multiply the numerator and denominator by 2: (5/8) * (2/2) = 10/16.
- For 4/16, no conversion is needed.
Now, we can compare the numerators of the converted fractions to find the number of slices with all three toppings:
- The numerator of the pepperoni fraction is 12.
- The numerator of the bell peppers fraction is 10.
- The numerator of the mushrooms fraction is 4.
To find the number of slices with all three toppings, we take the minimum value among the three numerators, which is 4.
Therefore, there are 4 slices with all three toppings on the pizza.