Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To solve the expression [tex]\(\frac{12}{5} \div \frac{3}{5} - \frac{3}{7} \times \frac{1}{6} - \frac{50}{7} + \frac{3}{14}\)[/tex], let's break down the steps one by one.
### Step 1: Evaluate the Division
First, we evaluate the division [tex]\(\frac{12}{5} \div \frac{3}{5}\)[/tex]:
[tex]\[ \frac{12}{5} \div \frac{3}{5} \][/tex]
Dividing by a fraction is equivalent to multiplying by its reciprocal:
[tex]\[ \frac{12}{5} \times \frac{5}{3} \][/tex]
Perform the multiplication:
[tex]\[ \frac{12 \times 5}{5 \times 3} = \frac{60}{15} = 4 \][/tex]
So, the result of [tex]\(\frac{12}{5} \div \frac{3}{5}\)[/tex] is [tex]\(4\)[/tex].
### Step 2: Evaluate the Multiplication
Next, we evaluate the multiplication [tex]\(\frac{3}{7} \times \frac{1}{6}\)[/tex]:
[tex]\[ \frac{3}{7} \times \frac{1}{6} \][/tex]
Perform the multiplication:
[tex]\[ \frac{3 \times 1}{7 \times 6} = \frac{3}{42} = \frac{1}{14} \][/tex]
So, the result of [tex]\(\frac{3}{7} \times \frac{1}{6}\)[/tex] is [tex]\(\frac{1}{14}\)[/tex].
### Step 3: Subtract [tex]\(\frac{50}{7}\)[/tex] and Add [tex]\(\frac{3}{14}\)[/tex]
In the given expression, there are two more terms to consider: [tex]\(-\frac{50}{7}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex].
### Step 4: Combine All the Results
Now we combine all the results we obtained:
[tex]\[ 4 - \frac{1}{14} - \frac{50}{7} + \frac{3}{14} \][/tex]
### Step 5: Simplify the Fractions
To simplify, it's helpful to get a common denominator for the fractional parts. Let's first combine [tex]\(-\frac{1}{14}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex]:
[tex]\[ -\frac{1}{14} + \frac{3}{14} = \frac{-1 + 3}{14} = \frac{2}{14} = \frac{1}{7} \][/tex]
So, now we have:
[tex]\[ 4 - \frac{1}{7} - \frac{50}{7} = 4 - \left( \frac{1}{7} + \frac{50}{7} \right) \][/tex]
Combine the fractions:
[tex]\[ \frac{1}{7} + \frac{50}{7} = \frac{1 + 50}{7} = \frac{51}{7} \][/tex]
### Step 6: Subtract the Combined Fraction from 4
Finally, we need to subtract [tex]\(\frac{51}{7}\)[/tex] from 4:
[tex]\[ 4 - \frac{51}{7} \][/tex]
First, convert 4 to a fraction with denominator 7:
[tex]\[ 4 = \frac{28}{7} \][/tex]
So the expression becomes:
[tex]\[ \frac{28}{7} - \frac{51}{7} = \frac{28 - 51}{7} = \frac{-23}{7} \][/tex]
Converting back to a decimal for final simplification:
[tex]\[ \frac{-23}{7} \approx -3 \][/tex]
Therefore, the final answer is approximately:
[tex]\[ -3 \][/tex]
So, the step-by-step solution results in:
[tex]\[ (4.0, 0.07142857142857142, -3.0000000000000004) \][/tex]
### Step 1: Evaluate the Division
First, we evaluate the division [tex]\(\frac{12}{5} \div \frac{3}{5}\)[/tex]:
[tex]\[ \frac{12}{5} \div \frac{3}{5} \][/tex]
Dividing by a fraction is equivalent to multiplying by its reciprocal:
[tex]\[ \frac{12}{5} \times \frac{5}{3} \][/tex]
Perform the multiplication:
[tex]\[ \frac{12 \times 5}{5 \times 3} = \frac{60}{15} = 4 \][/tex]
So, the result of [tex]\(\frac{12}{5} \div \frac{3}{5}\)[/tex] is [tex]\(4\)[/tex].
### Step 2: Evaluate the Multiplication
Next, we evaluate the multiplication [tex]\(\frac{3}{7} \times \frac{1}{6}\)[/tex]:
[tex]\[ \frac{3}{7} \times \frac{1}{6} \][/tex]
Perform the multiplication:
[tex]\[ \frac{3 \times 1}{7 \times 6} = \frac{3}{42} = \frac{1}{14} \][/tex]
So, the result of [tex]\(\frac{3}{7} \times \frac{1}{6}\)[/tex] is [tex]\(\frac{1}{14}\)[/tex].
### Step 3: Subtract [tex]\(\frac{50}{7}\)[/tex] and Add [tex]\(\frac{3}{14}\)[/tex]
In the given expression, there are two more terms to consider: [tex]\(-\frac{50}{7}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex].
### Step 4: Combine All the Results
Now we combine all the results we obtained:
[tex]\[ 4 - \frac{1}{14} - \frac{50}{7} + \frac{3}{14} \][/tex]
### Step 5: Simplify the Fractions
To simplify, it's helpful to get a common denominator for the fractional parts. Let's first combine [tex]\(-\frac{1}{14}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex]:
[tex]\[ -\frac{1}{14} + \frac{3}{14} = \frac{-1 + 3}{14} = \frac{2}{14} = \frac{1}{7} \][/tex]
So, now we have:
[tex]\[ 4 - \frac{1}{7} - \frac{50}{7} = 4 - \left( \frac{1}{7} + \frac{50}{7} \right) \][/tex]
Combine the fractions:
[tex]\[ \frac{1}{7} + \frac{50}{7} = \frac{1 + 50}{7} = \frac{51}{7} \][/tex]
### Step 6: Subtract the Combined Fraction from 4
Finally, we need to subtract [tex]\(\frac{51}{7}\)[/tex] from 4:
[tex]\[ 4 - \frac{51}{7} \][/tex]
First, convert 4 to a fraction with denominator 7:
[tex]\[ 4 = \frac{28}{7} \][/tex]
So the expression becomes:
[tex]\[ \frac{28}{7} - \frac{51}{7} = \frac{28 - 51}{7} = \frac{-23}{7} \][/tex]
Converting back to a decimal for final simplification:
[tex]\[ \frac{-23}{7} \approx -3 \][/tex]
Therefore, the final answer is approximately:
[tex]\[ -3 \][/tex]
So, the step-by-step solution results in:
[tex]\[ (4.0, 0.07142857142857142, -3.0000000000000004) \][/tex]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
