i need help with this homework question: it takes 1and1/3 ounces of cocoa to make a cup of hot cocoa. how many cups can be made from 32 ounces of cocoa?
You will need to divide 32 by 1 and 1/3. 1 1/3 = 4/3. 32 divided by 4/3 is the same as 32 x 3/4 because dividing is the same as multiplying by the reciprocal of the second number. The answer is 24.
To solve this problem, you need to divide the total amount of cocoa (32 ounces) by the amount of cocoa needed to make one cup of hot cocoa (1 and 1/3 ounces). Here is a step-by-step explanation of how to calculate it:
Step 1: Convert the mixed number 1 and 1/3 into an improper fraction. To do this, multiply the whole number (1) by the denominator (3) and add the result to the numerator (1). This gives you 4/3.
Step 2: Divide the total amount of cocoa (32 ounces) by the amount of cocoa needed for one cup (4/3 ounces). Remember, dividing by a fraction is the same as multiplying by its reciprocal. So, you can rewrite the division as a multiplication by flipping the numerator and denominator of the fraction you are dividing by. Thus, 32 divided by 4/3 is the same as 32 multiplied by 3/4.
Step 3: Multiply the numerators (32 x 3 = 96) and multiply the denominators (1 x 4 = 4) to get the product 96/4.
Step 4: Simplify the fraction. Both the numerator and denominator are divisible by 4, so divide them both by 4. This will give you 24/1, which can be simplified to just 24.
Therefore, there are 24 cups of hot cocoa that can be made from 32 ounces of cocoa.