Answer :
To find the value of the numerator that makes the fractions [tex]\(\frac{18}{20}\)[/tex] and [tex]\(\frac{}{10}\)[/tex] equivalent, follow these steps:
1. Understand Equivalent Fractions: Two fractions are equivalent if they represent the same value. This means that they have the same ratio.
2. Set Up the Equation:
Given the fractions:
[tex]\[
\frac{18}{20} = \frac{x}{10}
\][/tex]
We need to find the value of [tex]\(x\)[/tex] that makes these fractions equal.
3. Simplify the Equation:
To find [tex]\(x\)[/tex], set up the proportion:
[tex]\[
\frac{18}{20} = \frac{x}{10}
\][/tex]
4. Cross-Multiply:
To solve for [tex]\(x\)[/tex], cross-multiply the fractions:
[tex]\[
18 \times 10 = 20 \times x
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
[tex]\[
180 = 20x
\][/tex]
Divide both sides by 20:
[tex]\[
x = \frac{180}{20}
\][/tex]
[tex]\[
x = 9
\][/tex]
So, the value of the numerator of the second fraction must be 9 for the fractions to be equivalent. Therefore, the equivalent fraction given [tex]\(\frac{18}{20}\)[/tex] would be [tex]\(\frac{9}{10}\)[/tex].
1. Understand Equivalent Fractions: Two fractions are equivalent if they represent the same value. This means that they have the same ratio.
2. Set Up the Equation:
Given the fractions:
[tex]\[
\frac{18}{20} = \frac{x}{10}
\][/tex]
We need to find the value of [tex]\(x\)[/tex] that makes these fractions equal.
3. Simplify the Equation:
To find [tex]\(x\)[/tex], set up the proportion:
[tex]\[
\frac{18}{20} = \frac{x}{10}
\][/tex]
4. Cross-Multiply:
To solve for [tex]\(x\)[/tex], cross-multiply the fractions:
[tex]\[
18 \times 10 = 20 \times x
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
[tex]\[
180 = 20x
\][/tex]
Divide both sides by 20:
[tex]\[
x = \frac{180}{20}
\][/tex]
[tex]\[
x = 9
\][/tex]
So, the value of the numerator of the second fraction must be 9 for the fractions to be equivalent. Therefore, the equivalent fraction given [tex]\(\frac{18}{20}\)[/tex] would be [tex]\(\frac{9}{10}\)[/tex].
