Asked by NICKOLAS
2/9÷(−5/9)
Answers
Answered by
GPT-4o mini
To solve the expression \( \frac{2}{9} \div \left(-\frac{5}{9}\right) \), we can rewrite the division as multiplication by the reciprocal.
So,
\[
\frac{2}{9} \div \left(-\frac{5}{9}\right) = \frac{2}{9} \times \left(-\frac{9}{5}\right)
\]
Now, when we multiply the fractions, we multiply the numerators and the denominators:
\[
\frac{2 \times (-9)}{9 \times 5} = \frac{-18}{45}
\]
Next, we can simplify \( \frac{-18}{45} \). Both the numerator and denominator can be divided by 9:
\[
\frac{-18 \div 9}{45 \div 9} = \frac{-2}{5}
\]
Thus, the answer is:
\[
\frac{2}{9} \div \left(-\frac{5}{9}\right) = -\frac{2}{5}
\]
So,
\[
\frac{2}{9} \div \left(-\frac{5}{9}\right) = \frac{2}{9} \times \left(-\frac{9}{5}\right)
\]
Now, when we multiply the fractions, we multiply the numerators and the denominators:
\[
\frac{2 \times (-9)}{9 \times 5} = \frac{-18}{45}
\]
Next, we can simplify \( \frac{-18}{45} \). Both the numerator and denominator can be divided by 9:
\[
\frac{-18 \div 9}{45 \div 9} = \frac{-2}{5}
\]
Thus, the answer is:
\[
\frac{2}{9} \div \left(-\frac{5}{9}\right) = -\frac{2}{5}
\]
Answered by
GPT-4o mini
To solve the expression \( -4 \frac{7}{8} \div (-4 \frac{1}{3}) \), we first need to convert the mixed numbers into improper fractions.
1. **Convert \( -4 \frac{7}{8} \) to an improper fraction**:
- The whole number part is \(-4\), which is \(-\frac{4 \times 8}{8} = -\frac{32}{8}\).
- Adding the fractional part gives us:
\[
-\frac{32}{8} - \frac{7}{8} = -\frac{39}{8}
\]
2. **Convert \( -4 \frac{1}{3} \) to an improper fraction**:
- The whole number part is \(-4\), which is \(-\frac{4 \times 3}{3} = -\frac{12}{3}\).
- Adding the fractional part gives us:
\[
-\frac{12}{3} - \frac{1}{3} = -\frac{13}{3}
\]
3. **Now we can proceed with the division**:
\[
-\frac{39}{8} \div -\frac{13}{3} = -\frac{39}{8} \times -\frac{3}{13}
\]
The negatives cancel out, so we have:
\[
\frac{39 \times 3}{8 \times 13} = \frac{117}{104}
\]
4. **Simplify \( \frac{117}{104} \)**:
- Check for common factors. The greatest common divisor (GCD) of 117 and 104 is 1, so the fraction is already in its simplest form.
5. **To express it as a mixed number**:
- Divide 117 by 104, which gives 1 with a remainder of 13. This can be written as:
\[
1 \frac{13}{104}
\]
Therefore, the final answer is:
\[
-4 \frac{7}{8} \div (-4 \frac{1}{3}) = \frac{117}{104} \quad \text{or} \quad 1 \frac{13}{104}
\]
1. **Convert \( -4 \frac{7}{8} \) to an improper fraction**:
- The whole number part is \(-4\), which is \(-\frac{4 \times 8}{8} = -\frac{32}{8}\).
- Adding the fractional part gives us:
\[
-\frac{32}{8} - \frac{7}{8} = -\frac{39}{8}
\]
2. **Convert \( -4 \frac{1}{3} \) to an improper fraction**:
- The whole number part is \(-4\), which is \(-\frac{4 \times 3}{3} = -\frac{12}{3}\).
- Adding the fractional part gives us:
\[
-\frac{12}{3} - \frac{1}{3} = -\frac{13}{3}
\]
3. **Now we can proceed with the division**:
\[
-\frac{39}{8} \div -\frac{13}{3} = -\frac{39}{8} \times -\frac{3}{13}
\]
The negatives cancel out, so we have:
\[
\frac{39 \times 3}{8 \times 13} = \frac{117}{104}
\]
4. **Simplify \( \frac{117}{104} \)**:
- Check for common factors. The greatest common divisor (GCD) of 117 and 104 is 1, so the fraction is already in its simplest form.
5. **To express it as a mixed number**:
- Divide 117 by 104, which gives 1 with a remainder of 13. This can be written as:
\[
1 \frac{13}{104}
\]
Therefore, the final answer is:
\[
-4 \frac{7}{8} \div (-4 \frac{1}{3}) = \frac{117}{104} \quad \text{or} \quad 1 \frac{13}{104}
\]
Answered by
GPT-4o mini
To solve the expression \(\left(\frac{2}{3} \div \frac{3}{10}\right) \div \left(-\frac{1}{3}\right)\), we will follow the order of operations step-by-step.
### Step 1: Solve the first division
First, we address \(\frac{2}{3} \div \frac{3}{10}\).
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{2}{3} \div \frac{3}{10} = \frac{2}{3} \times \frac{10}{3}
\]
Now, multiply the numerators and the denominators:
\[
\frac{2 \times 10}{3 \times 3} = \frac{20}{9}
\]
### Step 2: Solve the second division
Next, we take the result from Step 1 and divide it by \(-\frac{1}{3}\):
\[
\frac{20}{9} \div \left(-\frac{1}{3}\right) = \frac{20}{9} \times \left(-3\right)
\]
This can be simplified further:
\[
= \frac{20 \times (-3)}{9} = \frac{-60}{9}
\]
### Step 3: Simplify \(\frac{-60}{9}\)
Next, we simplify \(\frac{-60}{9}\):
- Both 60 and 9 can be divided by 3 (the GCD):
\[
\frac{-60 \div 3}{9 \div 3} = \frac{-20}{3}
\]
### Final Answer
Thus, the result of the original expression is:
\[
\left(\frac{2}{3} \div \frac{3}{10}\right) \div \left(-\frac{1}{3}\right) = -\frac{20}{3}
\]
### Step 1: Solve the first division
First, we address \(\frac{2}{3} \div \frac{3}{10}\).
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{2}{3} \div \frac{3}{10} = \frac{2}{3} \times \frac{10}{3}
\]
Now, multiply the numerators and the denominators:
\[
\frac{2 \times 10}{3 \times 3} = \frac{20}{9}
\]
### Step 2: Solve the second division
Next, we take the result from Step 1 and divide it by \(-\frac{1}{3}\):
\[
\frac{20}{9} \div \left(-\frac{1}{3}\right) = \frac{20}{9} \times \left(-3\right)
\]
This can be simplified further:
\[
= \frac{20 \times (-3)}{9} = \frac{-60}{9}
\]
### Step 3: Simplify \(\frac{-60}{9}\)
Next, we simplify \(\frac{-60}{9}\):
- Both 60 and 9 can be divided by 3 (the GCD):
\[
\frac{-60 \div 3}{9 \div 3} = \frac{-20}{3}
\]
### Final Answer
Thus, the result of the original expression is:
\[
\left(\frac{2}{3} \div \frac{3}{10}\right) \div \left(-\frac{1}{3}\right) = -\frac{20}{3}
\]
Answered by
GPT-4o mini
To convert the improper fraction \(-\frac{20}{3}\) into a mixed number, we perform the following steps:
1. **Divide the numerator by the denominator**:
- Divide \(20\) by \(3\).
- \(20 \div 3 = 6\) (the whole number part).
- The remainder is \(20 - (3 \times 6) = 20 - 18 = 2\).
2. **Put it into mixed number form**:
- The whole number part is \(6\), and the remainder is \(2\) out of \(3\), so we write it as:
\[
6 \frac{2}{3}
\]
3. **Include the negative sign**:
- Since our initial fraction was negative, we write the mixed number as:
\[
-6 \frac{2}{3}
\]
Thus, the final answer as a mixed number in simplest form is:
\[
-\mathbf{6 \frac{2}{3}}
\]
1. **Divide the numerator by the denominator**:
- Divide \(20\) by \(3\).
- \(20 \div 3 = 6\) (the whole number part).
- The remainder is \(20 - (3 \times 6) = 20 - 18 = 2\).
2. **Put it into mixed number form**:
- The whole number part is \(6\), and the remainder is \(2\) out of \(3\), so we write it as:
\[
6 \frac{2}{3}
\]
3. **Include the negative sign**:
- Since our initial fraction was negative, we write the mixed number as:
\[
-6 \frac{2}{3}
\]
Thus, the final answer as a mixed number in simplest form is:
\[
-\mathbf{6 \frac{2}{3}}
\]
Answered by
GPT-4o mini
To evaluate \((g \div h) \div k\) with the given values \(g = 5 \frac{3}{4}\), \(h = -\frac{2}{3}\), and \(k = -0.5\), we'll proceed with the calculations step by step.
### Step 1: Convert \(g\) to an improper fraction
First, convert \(g = 5 \frac{3}{4}\) to an improper fraction:
\[
5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}
\]
### Step 2: Calculate \(g \div h\)
Now, we compute \(g \div h\):
\[
\frac{23}{4} \div \left(-\frac{2}{3}\right) = \frac{23}{4} \times \left(-\frac{3}{2}\right)
\]
Now perform the multiplication:
\[
\frac{23 \times (-3)}{4 \times 2} = \frac{-69}{8}
\]
### Step 3: Calculate \((g \div h) \div k\)
Next, we will divide our result by \(k = -0.5\). First, convert \(-0.5\) to a fraction:
\[
-0.5 = -\frac{1}{2}
\]
Now, perform the calculation:
\[
\left(-\frac{69}{8}\right) \div \left(-\frac{1}{2}\right) = \left(-\frac{69}{8}\right) \times \left(-2\right)
\]
This results in:
\[
\frac{69 \times 2}{8} = \frac{138}{8}
\]
### Step 4: Simplify \(\frac{138}{8}\)
Now, simplify \(\frac{138}{8}\):
The GCD of 138 and 8 is 2, so we divide both the numerator and denominator by 2:
\[
\frac{138 \div 2}{8 \div 2} = \frac{69}{4}
\]
### Step 5: Convert to a mixed number
To express \(\frac{69}{4}\) as a mixed number:
1. Divide \(69\) by \(4\):
- \(69 \div 4 = 17\) with a remainder of \(1\).
2. Write as a mixed number:
\[
17 \frac{1}{4}
\]
### Final Answer
Thus, the value of \((g \div h) \div k\) is:
\[
\mathbf{17 \frac{1}{4}}
\]
### Step 1: Convert \(g\) to an improper fraction
First, convert \(g = 5 \frac{3}{4}\) to an improper fraction:
\[
5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}
\]
### Step 2: Calculate \(g \div h\)
Now, we compute \(g \div h\):
\[
\frac{23}{4} \div \left(-\frac{2}{3}\right) = \frac{23}{4} \times \left(-\frac{3}{2}\right)
\]
Now perform the multiplication:
\[
\frac{23 \times (-3)}{4 \times 2} = \frac{-69}{8}
\]
### Step 3: Calculate \((g \div h) \div k\)
Next, we will divide our result by \(k = -0.5\). First, convert \(-0.5\) to a fraction:
\[
-0.5 = -\frac{1}{2}
\]
Now, perform the calculation:
\[
\left(-\frac{69}{8}\right) \div \left(-\frac{1}{2}\right) = \left(-\frac{69}{8}\right) \times \left(-2\right)
\]
This results in:
\[
\frac{69 \times 2}{8} = \frac{138}{8}
\]
### Step 4: Simplify \(\frac{138}{8}\)
Now, simplify \(\frac{138}{8}\):
The GCD of 138 and 8 is 2, so we divide both the numerator and denominator by 2:
\[
\frac{138 \div 2}{8 \div 2} = \frac{69}{4}
\]
### Step 5: Convert to a mixed number
To express \(\frac{69}{4}\) as a mixed number:
1. Divide \(69\) by \(4\):
- \(69 \div 4 = 17\) with a remainder of \(1\).
2. Write as a mixed number:
\[
17 \frac{1}{4}
\]
### Final Answer
Thus, the value of \((g \div h) \div k\) is:
\[
\mathbf{17 \frac{1}{4}}
\]