Title: Solving Proportions in Mathematics --- **Introduction to Proportions:** A proportion is an equation that states that two ratios are equal. Solving proportions is an essential skill in mathematics as it applies to various real-world scenarios. This guide will take you through the steps to solve a given proportion for the unknown variable. --- **Example Problem:** Solve the proportion for \( m \): \[ \frac{4}{5} = \frac{32}{m} \] **Solution Steps:** 1. **Set Up the Proportion:** The proportion is given as: \[ \frac{4}{5} = \frac{32}{m} \] 2. **Cross-Multiply:** To solve for \( m \), cross-multiplication is used. This involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal: \[ 4m = 5 \times 32 \] 3. **Calculate the Products:** Perform the multiplication on the right side of the equation: \[ 4m = 160 \] 4. **Solve for \( m \):** Isolate the variable \( m \) by dividing both sides of the equation by 4: \[ m = \frac{160}{4} \] 5. **Simplify the Result:** Complete the division to find the value of \( m \): \[ m = 40 \] **Final Answer:** The value of \( m \) is 40. --- **Summary:** By following the steps of setting up the proportion, cross-multiplying, and solving the resulting equation, we determine that \( m = 40 \). Understanding these steps helps in solving proportion problems effectively. --- **Practice Problems:** Try solving these proportions on your own: 1. \[ \frac{3}{7} = \frac{9}{x} \] 2. \[ \frac{5}{8} = \frac{y}{24} \] Check your answers by following the outlined steps. Practice makes perfect! ---
Title: Solving Proportions in Mathematics --- **Introduction to Proportions:** A proportion is an equation that states that two ratios are equal. Solving proportions is an essential skill in mathematics as it applies to various real-world scenarios. This guide will take you through the steps to solve a given proportion for the unknown variable. --- **Example Problem:** Solve the proportion for \( m \): \[ \frac{4}{5} = \frac{32}{m} \] **Solution Steps:** 1. **Set Up the Proportion:** The proportion is given as: \[ \frac{4}{5} = \frac{32}{m} \] 2. **Cross-Multiply:** To solve for \( m \), cross-multiplication is used. This involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal: \[ 4m = 5 \times 32 \] 3. **Calculate the Products:** Perform the multiplication on the right side of the equation: \[ 4m = 160 \] 4. **Solve for \( m \):** Isolate the variable \( m \) by dividing both sides of the equation by 4: \[ m = \frac{160}{4} \] 5. **Simplify the Result:** Complete the division to find the value of \( m \): \[ m = 40 \] **Final Answer:** The value of \( m \) is 40. --- **Summary:** By following the steps of setting up the proportion, cross-multiplying, and solving the resulting equation, we determine that \( m = 40 \). Understanding these steps helps in solving proportion problems effectively. --- **Practice Problems:** Try solving these proportions on your own: 1. \[ \frac{3}{7} = \frac{9}{x} \] 2. \[ \frac{5}{8} = \frac{y}{24} \] Check your answers by following the outlined steps. Practice makes perfect! ---
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![Title: Solving Proportions in Mathematics
---
**Introduction to Proportions:**
A proportion is an equation that states that two ratios are equal. Solving proportions is an essential skill in mathematics as it applies to various real-world scenarios. This guide will take you through the steps to solve a given proportion for the unknown variable.
---
**Example Problem:**
Solve the proportion for \( m \):
\[
\frac{4}{5} = \frac{32}{m}
\]
**Solution Steps:**
1. **Set Up the Proportion:**
The proportion is given as:
\[
\frac{4}{5} = \frac{32}{m}
\]
2. **Cross-Multiply:**
To solve for \( m \), cross-multiplication is used. This involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal:
\[
4m = 5 \times 32
\]
3. **Calculate the Products:**
Perform the multiplication on the right side of the equation:
\[
4m = 160
\]
4. **Solve for \( m \):**
Isolate the variable \( m \) by dividing both sides of the equation by 4:
\[
m = \frac{160}{4}
\]
5. **Simplify the Result:**
Complete the division to find the value of \( m \):
\[
m = 40
\]
**Final Answer:**
The value of \( m \) is 40.
---
**Summary:**
By following the steps of setting up the proportion, cross-multiplying, and solving the resulting equation, we determine that \( m = 40 \). Understanding these steps helps in solving proportion problems effectively.
---
**Practice Problems:**
Try solving these proportions on your own:
1. \[
\frac{3}{7} = \frac{9}{x}
\]
2. \[
\frac{5}{8} = \frac{y}{24}
\]
Check your answers by following the outlined steps. Practice makes perfect!
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa53c426-a760-4829-b362-653d3877b060%2F92179e31-95ba-46ad-b183-32b2cae235e4%2Fdcgauc.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Solving Proportions in Mathematics
---
**Introduction to Proportions:**
A proportion is an equation that states that two ratios are equal. Solving proportions is an essential skill in mathematics as it applies to various real-world scenarios. This guide will take you through the steps to solve a given proportion for the unknown variable.
---
**Example Problem:**
Solve the proportion for \( m \):
\[
\frac{4}{5} = \frac{32}{m}
\]
**Solution Steps:**
1. **Set Up the Proportion:**
The proportion is given as:
\[
\frac{4}{5} = \frac{32}{m}
\]
2. **Cross-Multiply:**
To solve for \( m \), cross-multiplication is used. This involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal:
\[
4m = 5 \times 32
\]
3. **Calculate the Products:**
Perform the multiplication on the right side of the equation:
\[
4m = 160
\]
4. **Solve for \( m \):**
Isolate the variable \( m \) by dividing both sides of the equation by 4:
\[
m = \frac{160}{4}
\]
5. **Simplify the Result:**
Complete the division to find the value of \( m \):
\[
m = 40
\]
**Final Answer:**
The value of \( m \) is 40.
---
**Summary:**
By following the steps of setting up the proportion, cross-multiplying, and solving the resulting equation, we determine that \( m = 40 \). Understanding these steps helps in solving proportion problems effectively.
---
**Practice Problems:**
Try solving these proportions on your own:
1. \[
\frac{3}{7} = \frac{9}{x}
\]
2. \[
\frac{5}{8} = \frac{y}{24}
\]
Check your answers by following the outlined steps. Practice makes perfect!
---
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