Christine(C) and Ty(T) save quarters in a jar together. The jar had $28 in it, then Christine put in C quarters and Ty put in T quarters. Which expression can be used to represent the amount of money in the bank now?(1 point)

Question

Responses

CT + 28
CT + 28

0.50(C + T) + 28
0.50(C + T) + 28

0.25C + 0.25T + 28
0.25C + 0.25T + 28

0.25FJ + 28

Answer 1

To represent the amount of money in the bank after Christine and Ty both add their quarters, we first need to understand that each quarter is worth $0.25.

1. Christine adds C quarters: This is equivalent to adding \(0.25C\) dollars.
2. Ty adds T quarters: This is equivalent to adding \(0.25T\) dollars.
3. The initial amount in the jar: This is $28.

Therefore, the total amount of money in the bank after both of them have added their quarters can be expressed as:

\[ 0.25C + 0.25T + 28 \]

So the correct response is:

0.25C + 0.25T + 28

Answer 2

A ribbon 6 1/8
feet in length is shortened by having 2 1/12
feet cut off one end. What is the length of the shortened ribbon?(1 point)
Responses

4 1/24
feet
4 and 1 over 24 feet

4 5/24
feet
4 and 5 over 24 feet

4 9/24
feet
4 and 9 over 24 feet

3 5/24
feet

Answer 3

To find the length of the shortened ribbon, we start with the original length of the ribbon and subtract the amount cut off.

1. Original length of the ribbon: \(6 \frac{1}{8}\) feet
2. Length cut off: \(2 \frac{1}{12}\) feet

Step 1: Convert Mixed Numbers to Improper Fractions

• Convert \(6 \frac{1}{8}\): \[ 6 \frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{48 + 1}{8} = \frac{49}{8} \]

• Convert \(2 \frac{1}{12}\): \[ 2 \frac{1}{12} = \frac{2 \times 12 + 1}{12} = \frac{24 + 1}{12} = \frac{25}{12} \]

Step 2: Find a Common Denominator

We need to subtract these two fractions, so we should find a common denominator. The least common multiple of 8 and 12 is 24.

• Convert \(\frac{49}{8}\) to a denominator of 24: \[ \frac{49}{8} = \frac{49 \times 3}{8 \times 3} = \frac{147}{24} \]

• Convert \(\frac{25}{12}\) to a denominator of 24: \[ \frac{25}{12} = \frac{25 \times 2}{12 \times 2} = \frac{50}{24} \]

Step 3: Subtract the Fractions

Now we subtract \(\frac{50}{24}\) from \(\frac{147}{24}\): \[ \frac{147}{24} - \frac{50}{24} = \frac{147 - 50}{24} = \frac{97}{24} \]

Step 4: Convert Back to Mixed Number

Now, we convert \(\frac{97}{24}\) back to a mixed number:

• \(97\) divided by \(24\) is \(4\) (since \(24 \times 4 = 96\)), with a remainder of \(1\). \[ \frac{97}{24} = 4 \frac{1}{24} \]

Thus, the length of the shortened ribbon is:

4 1/24 feet

Answer 4

Simplify the expression.

0.625+3/4


(1 point)
Responses

11/8
11 eighths

3/2
3 halves

11/9
11 ninths

8/11

Answer 5

To simplify the expression \(0.625 + \frac{3}{4}\), we first convert \(0.625\) to a fraction.

Step 1: Convert \(0.625\) to a Fraction

\(0.625\) can be expressed as: \[ 0.625 = \frac{625}{1000} \]

Next, we can simplify \(\frac{625}{1000}\) by dividing the numerator and denominator by their greatest common divisor, which is \(125\): \[ \frac{625 \div 125}{1000 \div 125} = \frac{5}{8} \]

So, \(0.625\) is equal to \(\frac{5}{8}\).

Step 2: Add \(\frac{5}{8}\) and \(\frac{3}{4}\)

We need a common denominator to add these two fractions. The denominator of \(\frac{3}{4}\) can be converted to eighths: \[ \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \]

Step 3: Add the Two Fractions

Now we can add: \[ \frac{5}{8} + \frac{6}{8} = \frac{5 + 6}{8} = \frac{11}{8} \]

Conclusion

The simplified expression \(0.625 + \frac{3}{4}\) is:

11/8 (or "11 eighths")

Answer 6

Divide.

−4/17÷−3/4


(1 point)
Responses

−3/17
negative 3 over 17

3/17
3 over 17

−16/51
negative 16 over 51

16/51

Answer 7

To divide the fractions \(-\frac{4}{17} \div -\frac{3}{4}\), we follow these steps:

Step 1: Change Division to Multiplication

When dividing by a fraction, we multiply by its reciprocal. Therefore: \[ -\frac{4}{17} \div -\frac{3}{4} = -\frac{4}{17} \times -\frac{4}{3} \]

Step 2: Multiply the Fractions

Now we multiply the numerators and the denominators: \[ \frac{(-4) \times (-4)}{17 \times 3} = \frac{16}{51} \]

Conclusion

The result of the division \(-\frac{4}{17} \div -\frac{3}{4}\) is:

16/51

Answer 8

At Georgia Connections Academy, 2/5
of the students are in a club. Of the students in a club, 1/4
participate in eSports club. What fraction of the students at GACA participate in eSports?(1 point)
Responses

1/10
1 tenth

1/5
1 fifth

2/9
2 ninths

2/3

Answer 9

To find the fraction of the students at Georgia Connections Academy (GACA) that participate in the eSports club, we can follow these steps:

Step 1: Determine the Fraction of Students in the Club

Given that \( \frac{2}{5} \) of the students are in a club.

Step 2: Determine the Fraction of Students in the eSports Club

Of the students in the club, \( \frac{1}{4} \) participate in the eSports club.

Step 3: Calculate the Fraction of Students Participating in eSports

To find the fraction of all students that participate in eSports, we multiply the fraction of students in the club by the fraction of club members who are in the eSports club:

\[ \text{Fraction of students in eSports} = \left(\frac{2}{5}\right) \times \left(\frac{1}{4}\right) = \frac{2 \times 1}{5 \times 4} = \frac{2}{20} \]

Step 4: Simplify the Fraction

Now simplify \( \frac{2}{20} \):

\[ \frac{2}{20} = \frac{1}{10} \]

Conclusion

The fraction of the students at GACA who participate in eSports is:

1/10 (or "1 tenth").

Answer 10

Mr. Brokaw's class has 60 students, 1/4
of the students needed help for an upcoming test. If Mr. Brokaw equally divides the students that need help into 5 small groups, how many students are in each group?(1 point)
Responses

15
15

12
12

3
3

5

Answer 11

To determine how many students are in each group, we will follow these steps:

Step 1: Find the Number of Students Needing Help

Given that there are 60 students in Mr. Brokaw's class and \( \frac{1}{4} \) of them needed help:

\[ \text{Number of students needing help} = \frac{1}{4} \times 60 = 15 \]

Step 2: Divide the Students Needing Help into Groups

Mr. Brokaw divides the 15 students who need help into 5 small groups:

\[ \text{Number of students in each group} = \frac{15}{5} = 3 \]

Conclusion

The number of students in each group is:

3