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Answer :
To determine whether the given expression is a proportion, follow these steps:
Expression Provided:
[tex]\[
\frac{1.8}{2} = \frac{18}{20}
\][/tex]
Step 1: Cross-Multiply
To check if two ratios form a proportion, we use cross-multiplication. In a proportion, the product of the means equals the product of the extremes. For the expression [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], the products to compare are [tex]\(a \times d\)[/tex] and [tex]\(b \times c\)[/tex].
Applying this to the current expression:
- Multiply the numerator of the first ratio by the denominator of the second ratio: [tex]\(1.8 \times 20\)[/tex].
- Multiply the denominator of the first ratio by the numerator of the second ratio: [tex]\(2 \times 18\)[/tex].
Step 2: Compare the Products
Calculate each product:
- [tex]\(1.8 \times 20 = 36\)[/tex]
- [tex]\(2 \times 18 = 36\)[/tex]
Since both products are equal ([tex]\(36 = 36\)[/tex]), the given equation is indeed a proportion.
Step 3: Identify the Means and Extremes
In a proportion, the means are the middle terms, and the extremes are the outer terms.
Given:
- [tex]\(\frac{1.8}{2} = \frac{18}{20}\)[/tex]
The means are [tex]\(2\)[/tex] and [tex]\(18\)[/tex], and the extremes are [tex]\(1.8\)[/tex] and [tex]\(20\)[/tex].
Thus, the expression [tex]\(\frac{1.8}{2} = \frac{18}{20}\)[/tex] is a proportion with means [tex]\(2\)[/tex] and [tex]\(18\)[/tex], and extremes [tex]\(1.8\)[/tex] and [tex]\(20\)[/tex].
Expression Provided:
[tex]\[
\frac{1.8}{2} = \frac{18}{20}
\][/tex]
Step 1: Cross-Multiply
To check if two ratios form a proportion, we use cross-multiplication. In a proportion, the product of the means equals the product of the extremes. For the expression [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], the products to compare are [tex]\(a \times d\)[/tex] and [tex]\(b \times c\)[/tex].
Applying this to the current expression:
- Multiply the numerator of the first ratio by the denominator of the second ratio: [tex]\(1.8 \times 20\)[/tex].
- Multiply the denominator of the first ratio by the numerator of the second ratio: [tex]\(2 \times 18\)[/tex].
Step 2: Compare the Products
Calculate each product:
- [tex]\(1.8 \times 20 = 36\)[/tex]
- [tex]\(2 \times 18 = 36\)[/tex]
Since both products are equal ([tex]\(36 = 36\)[/tex]), the given equation is indeed a proportion.
Step 3: Identify the Means and Extremes
In a proportion, the means are the middle terms, and the extremes are the outer terms.
Given:
- [tex]\(\frac{1.8}{2} = \frac{18}{20}\)[/tex]
The means are [tex]\(2\)[/tex] and [tex]\(18\)[/tex], and the extremes are [tex]\(1.8\)[/tex] and [tex]\(20\)[/tex].
Thus, the expression [tex]\(\frac{1.8}{2} = \frac{18}{20}\)[/tex] is a proportion with means [tex]\(2\)[/tex] and [tex]\(18\)[/tex], and extremes [tex]\(1.8\)[/tex] and [tex]\(20\)[/tex].
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