Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Let's solve these problems step-by-step:
### Part (a)
Given: [tex]\(\frac{15}{19} \div \frac{5}{3}\)[/tex]
To divide fractions, we multiply by the reciprocal of the divisor. So, we need to multiply [tex]\(\frac{15}{19}\)[/tex] by the reciprocal of [tex]\(\frac{5}{3}\)[/tex], which is [tex]\(\frac{3}{5}\)[/tex].
Thus,
[tex]\[ \frac{15}{19} \div \frac{5}{3} = \frac{15}{19} \times \frac{3}{5} \][/tex]
When multiplying fractions, we multiply the numerators together and the denominators together:
[tex]\[ \frac{15 \times 3}{19 \times 5} = \frac{45}{95} \][/tex]
Now, simplify [tex]\(\frac{45}{95}\)[/tex]:
1. Find the greatest common divisor (GCD) of 45 and 95, which is 5.
2. Divide the numerator and the denominator by 5:
[tex]\[ \frac{45 \div 5}{95 \div 5} = \frac{9}{19} \][/tex]
So, the result is:
[tex]\[ \frac{15}{19} \div \frac{5}{3} = \frac{9}{19} \][/tex]
#### Which equals approximately:
[tex]\[ 0.47368421052631576 \][/tex]
### Part (b)
Given: [tex]\(2 \div \frac{3}{5}\)[/tex]
To divide by a fraction, we multiply by its reciprocal. The reciprocal of [tex]\(\frac{3}{5}\)[/tex] is [tex]\(\frac{5}{3}\)[/tex].
Thus,
[tex]\[ 2 \div \frac{3}{5} = 2 \times \frac{5}{3} \][/tex]
Multiply 2 by [tex]\(\frac{5}{3}\)[/tex]:
[tex]\[ 2 \times \frac{5}{3} = \frac{2 \times 5}{3} = \frac{10}{3} \][/tex]
So, converting to a decimal:
[tex]\(\frac{10}{3}\)[/tex] equals approximately:
[tex]\[ 3.3333333333333335 \][/tex]
### Final Quotients:
a) [tex]\(\frac{15}{19} \div \frac{5}{3} = 0.47368421052631576\)[/tex]
b) [tex]\(2 \div \frac{3}{5} = 3.3333333333333335\)[/tex]
Thus, these are the detailed solutions:
[tex]\[ \begin{aligned} \text{(a)} \quad & \frac{15}{19} \div \frac{5}{3} \approx 0.47368421052631576 \\ \text{(b)} \quad & 2 \div \frac{3}{5} \approx 3.3333333333333335 \end{aligned} \][/tex]
### Part (a)
Given: [tex]\(\frac{15}{19} \div \frac{5}{3}\)[/tex]
To divide fractions, we multiply by the reciprocal of the divisor. So, we need to multiply [tex]\(\frac{15}{19}\)[/tex] by the reciprocal of [tex]\(\frac{5}{3}\)[/tex], which is [tex]\(\frac{3}{5}\)[/tex].
Thus,
[tex]\[ \frac{15}{19} \div \frac{5}{3} = \frac{15}{19} \times \frac{3}{5} \][/tex]
When multiplying fractions, we multiply the numerators together and the denominators together:
[tex]\[ \frac{15 \times 3}{19 \times 5} = \frac{45}{95} \][/tex]
Now, simplify [tex]\(\frac{45}{95}\)[/tex]:
1. Find the greatest common divisor (GCD) of 45 and 95, which is 5.
2. Divide the numerator and the denominator by 5:
[tex]\[ \frac{45 \div 5}{95 \div 5} = \frac{9}{19} \][/tex]
So, the result is:
[tex]\[ \frac{15}{19} \div \frac{5}{3} = \frac{9}{19} \][/tex]
#### Which equals approximately:
[tex]\[ 0.47368421052631576 \][/tex]
### Part (b)
Given: [tex]\(2 \div \frac{3}{5}\)[/tex]
To divide by a fraction, we multiply by its reciprocal. The reciprocal of [tex]\(\frac{3}{5}\)[/tex] is [tex]\(\frac{5}{3}\)[/tex].
Thus,
[tex]\[ 2 \div \frac{3}{5} = 2 \times \frac{5}{3} \][/tex]
Multiply 2 by [tex]\(\frac{5}{3}\)[/tex]:
[tex]\[ 2 \times \frac{5}{3} = \frac{2 \times 5}{3} = \frac{10}{3} \][/tex]
So, converting to a decimal:
[tex]\(\frac{10}{3}\)[/tex] equals approximately:
[tex]\[ 3.3333333333333335 \][/tex]
### Final Quotients:
a) [tex]\(\frac{15}{19} \div \frac{5}{3} = 0.47368421052631576\)[/tex]
b) [tex]\(2 \div \frac{3}{5} = 3.3333333333333335\)[/tex]
Thus, these are the detailed solutions:
[tex]\[ \begin{aligned} \text{(a)} \quad & \frac{15}{19} \div \frac{5}{3} \approx 0.47368421052631576 \\ \text{(b)} \quad & 2 \div \frac{3}{5} \approx 3.3333333333333335 \end{aligned} \][/tex]
Answer:To find the quotient \( \frac{2}{\frac{3}{5}} \), we interpret it as the multiplication of 2 by the reciprocal of \( \frac{3}{5} \).
First, find the reciprocal of \( \frac{3}{5} \):
\[
\text{Reciprocal of } \frac{3}{5} = \frac{5}{3}
\]
Now, multiply 2 by the reciprocal \( \frac{5}{3} \):
\[
2 \cdot \frac{5}{3} = \frac{2 \cdot 5}{3} = \frac{10}{3}
\]
Therefore, the quotient \( \frac{2}{\frac{3}{5}} \) simplifies to \( \frac{10}{3} \).
So, the answer for part b) is \( \boxed{\frac{10}{3}} \).
Step-by-step explanation:Sure, let's break down the steps to find the quotient \( \frac{2}{\frac{3}{5}} \).
We can rewrite the expression \( \frac{2}{\frac{3}{5}} \) as multiplication by the reciprocal of \( \frac{3}{5} \):
1. **Identify the expression:**
\[
\frac{2}{\frac{3}{5}}
\]
2. **Find the reciprocal of \( \frac{3}{5} \):**
\[
\text{Reciprocal of } \frac{3}{5} = \frac{5}{3}
\]
3. **Rewrite the division as multiplication:**
\[
\frac{2}{\frac{3}{5}} = 2 \cdot \frac{5}{3}
\]
4. **Perform the multiplication:**
\[
2 \cdot \frac{5}{3} = \frac{2 \cdot 5}{3} = \frac{10}{3}
\]
Therefore, \( \frac{2}{\frac{3}{5}} = \frac{10}{3} \).
The step-by-step process confirms that the quotient \( \frac{2}{\frac{3}{5}} \) simplifies to \( \frac{10}{3} \).
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
