Question

You are helping to prepare baked goods for a school bake sale. You need to adjust recipes, combine ingredients, and solve problems involving fractions. Complete all four parts of the task, showing your work and answering each question. You are making two types of batter for the bake sale: cake batter and muffin batter. The recipes call for the following amounts of flour: • Cake batter: 3/4 cup of flour Muffin batter: 2/3 cup of flour When showing your work in the space provided, be sure to use the/to show fractions. Example: 1/2 + 1/2 = 2/2 = 1 P 1 5 points How much flour do you need in total to make both the cake and muffin batter?

Answer 1

To find the total amount of flour needed for both the cake batter and muffin batter, we need to add the amounts of flour for each type of batter.

The amounts of flour are:

• Cake batter: \( \frac{3}{4} \) cup of flour
• Muffin batter: \( \frac{2}{3} \) cup of flour

To add these two fractions, we need a common denominator. The denominators are 4 and 3. The least common multiple (LCM) of 4 and 3 is 12.

Now we convert each fraction to have a denominator of 12:

1. For \( \frac{3}{4} \): \[ \frac{3}{4} \times \frac{3}{3} = \frac{9}{12} \]

2. For \( \frac{2}{3} \): \[ \frac{2}{3} \times \frac{4}{4} = \frac{8}{12} \]

Now, we can add the two fractions: \[ \frac{9}{12} + \frac{8}{12} = \frac{17}{12} \]

So the total flour needed is \( \frac{17}{12} \) cups. To express this in a mixed number form: \[ \frac{17}{12} = 1 \frac{5}{12} \]

Thus, the total amount of flour needed in total to make both the cake and muffin batter is \( \frac{17}{12} \) cups or \( 1 \frac{5}{12} \) cups.

Answer 2

Show your work and simpler pls

Answer 3

Sure! Let’s break it down step by step in a simpler way.

Step 1: Write down the amounts of flour needed

• Cake batter: \( \frac{3}{4} \) cup
• Muffin batter: \( \frac{2}{3} \) cup

Step 2: Find a common denominator

The denominators are 4 and 3. The least common multiple (LCM) of 4 and 3 is 12.

Step 3: Convert each fraction to have the same denominator

1. Convert \( \frac{3}{4} \): \[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]

2. Convert \( \frac{2}{3} \): \[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]

Step 4: Add the two fractions

Now, we can add \( \frac{9}{12} \) and \( \frac{8}{12} \): \[ \frac{9}{12} + \frac{8}{12} = \frac{17}{12} \]

Step 5: Result

So, the total amount of flour needed: \[ \frac{17}{12} \text{ cups} \]

Step 6: Optional - Convert to a mixed number

\( \frac{17}{12} \) can also be expressed as a mixed number:

• \( 12 \) goes into \( 17 \) once (1), with a remainder of \( 5 \). So, \[ \frac{17}{12} = 1 \frac{5}{12} \]

Final Answer

You need \( \frac{17}{12} \) cups of flour, or \( 1 \frac{5}{12} \) cups of flour in total to make both the cake and muffin batter.

Answer 4

How much flour will you need after tripling both recipes

Answer 5

To find out how much flour you will need after tripling both recipes, we first need to calculate the amount of flour for each recipe when tripled, and then add the two amounts together.

Step 1: Original amounts of flour

• Cake batter: \( \frac{3}{4} \) cup
• Muffin batter: \( \frac{2}{3} \) cup

Step 2: Triple each amount

1. For the cake batter: \[ \text{Cake batter} = 3 \times \frac{3}{4} = \frac{9}{4} \text{ cups} \]

2. For the muffin batter: \[ \text{Muffin batter} = 3 \times \frac{2}{3} = \frac{6}{3} = 2 \text{ cups} \]

Step 3: Add the two amounts together

Now, we need to add \( \frac{9}{4} \) cups and \( 2 \) cups (which can be converted to a fraction).

Convert \( 2 \) cups to a fraction with a denominator of 4: \[ 2 = \frac{2 \times 4}{1 \times 4} = \frac{8}{4} \]

Now, add the two fractions: \[ \frac{9}{4} + \frac{8}{4} = \frac{17}{4} \]

Step 4: Final Result

The total amount of flour needed after tripling both recipes is: \[ \frac{17}{4} \text{ cups} \]

Step 5: Convert to a mixed number (if desired)

To convert \( \frac{17}{4} \) into a mixed number:

• \( 4 \) goes into \( 17 \) four times (4), with a remainder of \( 1 \). So, \[ \frac{17}{4} = 4 \frac{1}{4} \]

Final Answer

You will need \( \frac{17}{4} \) cups of flour, which is also \( 4 \frac{1}{4} \) cups of flour, after tripling both recipes.

Answer 6

You check your supplies and realize that you only have 3 1/2 cups of flour on hand. How much more flour do you need to meet the requirements of the triples recipe? Subtract the flour you have from the flour you need.

Answer 7

To determine how much more flour you need, we will subtract the amount of flour you have from the total amount of flour required for the tripled recipes.

Step 1: Total flour needed for tripled recipes

From the previous calculation, the total amount of flour needed after tripling both recipes is: \[ \frac{17}{4} \text{ cups} \]

Step 2: Convert \( \frac{17}{4} \) to a mixed number

As calculated earlier: \[ \frac{17}{4} = 4 \frac{1}{4} \text{ cups} \]

Step 3: Flour you have on hand

You have: \[ 3 \frac{1}{2} \text{ cups} \]

Step 4: Convert \( 3 \frac{1}{2} \) to an improper fraction

To convert \( 3 \frac{1}{2} \) to an improper fraction: \[ 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \text{ cups} \]

Step 5: Subtract the flour you have from the flour needed

To subtract \( \frac{7}{2} \) from \( \frac{17}{4} \), we first need a common denominator. The least common denominator of 2 and 4 is 4.

Convert \( \frac{7}{2} \) to have a denominator of 4: \[ \frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4} \]

Now, subtract: \[ \frac{17}{4} - \frac{14}{4} = \frac{3}{4} \]

Final Answer

You need an additional \( \frac{3}{4} \) cup of flour to meet the requirements of the tripled recipe.

Answer 8

After buying the additional flour, you decide to use part of it for other bake sale recipes. You plan to use 3/4 cup of flour to make mini pies. Each pie requires 1/6 cup of flour. How many pies can you make with the 3/4 cup of flour you have?

Answer 9

To determine how many mini pies you can make with \( \frac{3}{4} \) cup of flour, we need to divide the total amount of flour available by the amount of flour needed for each pie.

Step 1: Write down the amounts

• Flour available: \( \frac{3}{4} \) cup
• Flour per pie: \( \frac{1}{6} \) cup

Step 2: Divide \( \frac{3}{4} \) by \( \frac{1}{6} \)

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \( \frac{1}{6} \) is \( 6 \).

So we can perform the calculation as follows: \[ \frac{3}{4} \div \frac{1}{6} = \frac{3}{4} \times 6 \]

Step 3: Convert \( 6 \) to a fraction

To multiply, we can write \( 6 \) as \( \frac{6}{1} \): \[ \frac{3}{4} \times \frac{6}{1} = \frac{3 \times 6}{4 \times 1} = \frac{18}{4} \]

Step 4: Simplify \( \frac{18}{4} \)

Now, we simplify \( \frac{18}{4} \):

• Divide both the numerator and the denominator by 2: \[ \frac{18 \div 2}{4 \div 2} = \frac{9}{2} \]

Step 5: Convert to a mixed number (if needed)

To express \( \frac{9}{2} \) as a mixed number:

• \( 2 \) goes into \( 9 \) four times (4) with a remainder of \( 1 \): \[ \frac{9}{2} = 4 \frac{1}{2} \]

Final Answer

You can make 4 and a half pies with \( \frac{3}{4} \) cup of flour. Since you cannot make half a pie in a real situation, you can say you can make 4 complete mini pies.