High School

We appreciate your visit to Name tex qquad tex Date tex qquad tex Class tex qquad tex Proportion Notes RATIO tex tex tex qquad tex RATE tex tex tex qquad. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Name: [tex]$\qquad$[/tex]
Date: [tex]$\qquad$[/tex]
Class: [tex]$\qquad$[/tex]

**Proportion Notes**

- RATIO [tex]$=$[/tex] [tex]$\qquad$[/tex]
- RATE [tex]$=$[/tex] [tex]$\qquad$[/tex]
- UNIT RATE [tex]$=$[/tex] [tex]$\qquad$[/tex]
- PROPORTION [tex]$=$[/tex] [tex]$\qquad$[/tex]

**Proportion Examples**

1. [tex]$\frac{2}{5} = \frac{8}{20}$[/tex]
2. [tex]$\frac{400 \text{ calories }}{1 \text{ burger }} = \frac{1200 \text{ calories }}{3 \text{ burgers }}$[/tex]
3. [tex]$\frac{16}{20} = \frac{44}{55}$[/tex]

Proportions are almost always written in [tex]$\qquad$[/tex] form.

**Checking for Proportions:**

You can determine if two ratios form a proportion using two methods:

- Method 1: Simplify Both
- Method 2: Cross Products

[tex]\[
\begin{array}{l}
\frac{16}{40} \quad \div \quad - = - \\
\frac{20}{50} \quad \div \quad - = -
\end{array}
\][/tex]

So, [tex]$\frac{16}{40} \quad \frac{20}{50}$[/tex] is a [tex]$\qquad$[/tex]

[tex]$40 \cdot 20 \quad ? \quad 50 \cdot 16$[/tex]

[tex]$\qquad$[/tex] [tex]$=$[/tex] [tex]$\qquad$[/tex] [tex]$\frac{20}{50}$[/tex] is a [tex]$\qquad$[/tex]

**Checking for Proportions - Practice Problems:**

Determine whether each of the pairs of ratios forms a proportion:

a. [tex]$\frac{2}{6} \quad \frac{8}{24}$[/tex]
b. [tex]$\frac{6}{10} \quad \frac{9}{12}$[/tex]
c. [tex]$\frac{21}{30} \quad \frac{35}{50}$[/tex]
d. [tex]$\frac{1.8}{7.5} \quad \frac{1.2}{5}$[/tex]

Answer :

Sure! Let's determine whether each pair of ratios forms a proportion by using the cross-multiplication method. Cross-multiplication is a way to compare two fractions or ratios by multiplying the numerator of one ratio by the denominator of the other ratio. If the products are equal, the pairs form a proportion.

### Step-by-Step Solution:

a. Check if [tex]\(\frac{2}{6}\)[/tex] and [tex]\(\frac{8}{24}\)[/tex] form a proportion.

1. Perform cross-multiplication:
- Multiply 2 (numerator of the first ratio) by 24 (denominator of the second ratio).
- Multiply 6 (denominator of the first ratio) by 8 (numerator of the second ratio).

2. Calculate the products:
- [tex]\(2 \times 24 = 48\)[/tex]
- [tex]\(6 \times 8 = 48\)[/tex]

3. Compare the products: [tex]\(48 = 48\)[/tex]

Since the products are equal, [tex]\(\frac{2}{6}\)[/tex] and [tex]\(\frac{8}{24}\)[/tex] do form a proportion.
Result: True

---

b. Check if [tex]\(\frac{6}{10}\)[/tex] and [tex]\(\frac{9}{12}\)[/tex] form a proportion.

1. Perform cross-multiplication:
- Multiply 6 by 12.
- Multiply 10 by 9.

2. Calculate the products:
- [tex]\(6 \times 12 = 72\)[/tex]
- [tex]\(10 \times 9 = 90\)[/tex]

3. Compare the products: [tex]\(72 \neq 90\)[/tex]

Since the products are not equal, [tex]\(\frac{6}{10}\)[/tex] and [tex]\(\frac{9}{12}\)[/tex] do not form a proportion.
Result: False

---

c. Check if [tex]\(\frac{21}{30}\)[/tex] and [tex]\(\frac{35}{50}\)[/tex] form a proportion.

1. Perform cross-multiplication:
- Multiply 21 by 50.
- Multiply 30 by 35.

2. Calculate the products:
- [tex]\(21 \times 50 = 1050\)[/tex]
- [tex]\(30 \times 35 = 1050\)[/tex]

3. Compare the products: [tex]\(1050 = 1050\)[/tex]

Since the products are equal, [tex]\(\frac{21}{30}\)[/tex] and [tex]\(\frac{35}{50}\)[/tex] do form a proportion.
Result: True

---

d. Check if [tex]\(\frac{1.8}{7.5}\)[/tex] and [tex]\(\frac{1.2}{5}\)[/tex] form a proportion.

1. Perform cross-multiplication:
- Multiply 1.8 by 5.
- Multiply 7.5 by 1.2.

2. Calculate the products:
- [tex]\(1.8 \times 5 = 9.0\)[/tex]
- [tex]\(7.5 \times 1.2 = 9.0\)[/tex]

3. Compare the products: [tex]\(9.0 = 9.0\)[/tex]

Since the products are equal, [tex]\(\frac{1.8}{7.5}\)[/tex] and [tex]\(\frac{1.2}{5}\)[/tex] do form a proportion.
Result: True

I hope this helps explain whether each pair of ratios forms a proportion!

Thanks for taking the time to read Name tex qquad tex Date tex qquad tex Class tex qquad tex Proportion Notes RATIO tex tex tex qquad tex RATE tex tex tex qquad. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada