Questions: Finding Reciprocals Find the Reciprocal of each of the following. Write DNE if the answer does not exist. Original Number Reciprocal ---------------------------- 1 0 -7 7/7 3 2/5 -2 4/9

Solution Steps

To find the reciprocal of a number, you simply take 1 divided by that number. If the number is zero, the reciprocal does not exist (DNE). For mixed numbers, convert them to improper fractions first before finding the reciprocal.

1. For each number, check if it is zero. If it is, the reciprocal is DNE.
2. For mixed numbers, convert them to improper fractions.
3. Calculate the reciprocal by taking 1 divided by the number.

The reciprocal of \( 1 \) is calculated as: \[ \frac{1}{1} = 1.0 \]

The reciprocal of \( 0 \) does not exist, so we denote it as: \[ \text{Reciprocal of } 0 = \text{DNE} \]

The reciprocal of \( -7 \) is calculated as: \[ \frac{1}{-7} = -\frac{1}{7} \]

Since \( \frac{7}{7} = 1 \), its reciprocal is: \[ \frac{1}{1} = 1.0 \]

First, convert \( 3\frac{2}{5} \) to an improper fraction: \[ 3\frac{2}{5} = \frac{15 + 2}{5} = \frac{17}{5} \] Then, the reciprocal is: \[ \frac{1}{\frac{17}{5}} = \frac{5}{17} \approx 0.2941 \]

First, convert \( -2\frac{4}{9} \) to an improper fraction: \[ -2\frac{4}{9} = -\left(\frac{18 + 4}{9}\right) = -\frac{22}{9} \] Then, the reciprocal is: \[ \frac{1}{-\frac{22}{9}} = -\frac{9}{22} \approx -0.4091 \]

Final Answer