Divide.

Question

2 1/3÷2/5
(1 point)
Responses

14/15
14 over 15

4/5
4 fifths

9/16
9 over 16

5 5/6

Answer 1

To divide \(2 \frac{1}{3}\) by \(\frac{2}{5}\), follow these steps:

1. Convert \(2 \frac{1}{3}\) to an improper fraction: \[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]

2. Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{7}{3} \div \frac{2}{5} = \frac{7}{3} \times \frac{5}{2} \]

3. Multiply the fractions: \[ \frac{7 \times 5}{3 \times 2} = \frac{35}{6} \]

4. Now, convert \(\frac{35}{6}\) to a mixed number: \[ 35 \div 6 = 5 \quad \text{remainder } 5 \] Thus, \(\frac{35}{6} = 5 \frac{5}{6}\).

The result is: \[ 5 \frac{5}{6} \]

So the answer is 5 5/6.

Answer 2

Divide

84 by -7

(1 point)
Responses

12
12

-13
-13

-12
-12

-14

Answer 3

To divide 84 by -7:

\[ 84 \div -7 = -12 \]

So the answer is -12.

Answer 4

Find the product.

−4/7(−11/2)
(1 point)
Responses

−41/14
negative 41 over 14

41/14
41 over 14

−22/7
negative 22 sevenths

22/7

Answer 5

To find the product of \(-\frac{4}{7}\) and \(-\frac{11}{2}\), multiply the two fractions:

\[ -\frac{4}{7} \times -\frac{11}{2} \]

When you multiply two negative numbers, the result is positive:

\[ \frac{4 \times 11}{7 \times 2} = \frac{44}{14} \]

Now, simplify \(\frac{44}{14}\):

\[ \frac{44 \div 2}{14 \div 2} = \frac{22}{7} \]

Thus, the product is:

\[ \frac{22}{7} \]

So the answer is 22/7.

Answer 6

Find the product.

9(−3/7)(−1/3)
(1 point)
Responses

−3/7
negative 3 sevenths

−9/7
negative 9 sevenths

9/7
9 sevenths

3/7

Answer 7

To find the product of \(9\), \(-\frac{3}{7}\), and \(-\frac{1}{3}\), we will follow these steps:

1. First, multiply the two negative fractions together: \[ -\frac{3}{7} \times -\frac{1}{3} = \frac{3 \times 1}{7 \times 3} = \frac{3}{21} \]

2. Simplify \(\frac{3}{21}\): \[ \frac{3}{21} = \frac{3 \div 3}{21 \div 3} = \frac{1}{7} \]

3. Now, multiply this result by \(9\): \[ 9 \times \frac{1}{7} = \frac{9}{7} \]

So, the final product is:

\[ \frac{9}{7} \]

The answer is 9/7.

Answer 8

How much cake will each member of the team get if 6 members share 3/4
of a cake equally?(1 point)
Responses

1/6
1 sixth

1/3
1 third

1/4
1 fourth

1/8

Answer 9

To find out how much cake each of the 6 members will get if they share \( \frac{3}{4} \) of a cake equally, you need to divide \( \frac{3}{4} \) by 6.

This can be calculated as follows:

\[ \text{Amount of cake each member gets} = \frac{3}{4} \div 6 \]

Dividing by a whole number is equivalent to multiplying by its reciprocal:

\[ \frac{3}{4} \div 6 = \frac{3}{4} \times \frac{1}{6} = \frac{3 \times 1}{4 \times 6} = \frac{3}{24} \]

Now, simplify \( \frac{3}{24} \):

\[ \frac{3}{24} = \frac{1}{8} \]

So, each member of the team will get \( \frac{1}{8} \) of the cake.

The answer is 1/8.