Can you check the following?

1. A recipe for muffins needs 1/2 cup of milk. You are making 3/4 of the recipe. How much milk do you need?

Ans: (1/2) / (3/4)
= (1/2) x (4/3)
= 2/3 cups

2. Betty is running on a track that is 2/3 of a mile long. So far she has run 1/2 of the way around the whole track. How far has she run so far?

Ans: (2/3) / (1/2)
= (2/3) x (2/1)
= 4/3 = 1 1/3 miles

Why did you increase the amount of milk when you're making less than a whole recipe?

Does your answer for 2 make sense to you?

You should do 1/2 * 3/4, not the other way around.

To solve the first problem, you need to find out how much milk is needed when making 3/4 of the recipe.

1. Start by writing the given information: 1/2 cup of milk.

2. Next, determine the amount of milk needed for 3/4 of the recipe. To do this, divide 1/2 by 3/4.

3. When dividing fractions, you can multiply the numerator of the first fraction by the denominator of the second fraction, and the denominator of the first fraction by the numerator of the second fraction.

(1/2) / (3/4) = (1/2) x (4/3)

4. Simplify the resulting fraction. In this case, multiplying the numerators gives you 4, and multiplying the denominators gives you 2. So the answer is 4/2.

5. Finally, reduce the fraction to its simplest form. The numerator and denominator, both of which are divisible by 2, can be divided by 2. The resulting fraction is 2/1, which equals 2.

Therefore, when making 3/4 of the recipe, you would need 2/3 cups of milk.

To solve the second problem, you need to determine how far Betty has run so far, given that she has completed 1/2 of the track, which is 2/3 of a mile long.

1. Start by writing the given information: The track length is 2/3 mile and Betty has run 1/2 of the track.

2. To find out how far she has run, you need to determine 1/2 of 2/3.

3. Multiply the numerators and denominators of the fractions.

(2/3) / (1/2) = (2/3) x (2/1)

4. Multiply the numerators (2 x 2) to get 4, and multiply the denominators (3 x 1) to get 3.

5. The resulting fraction is 4/3, which is equal to 1 1/3 in mixed number form.

Therefore, Betty has run 1 1/3 miles so far.