Answer :
Sure! Let's go through each pair of fractions to see which ones are equivalent. Two fractions are equivalent if they represent the same value, which can be determined by cross-multiplying and checking if the products are equal.
1. Pair: [tex]\(\frac{15}{25}\)[/tex] and [tex]\(\frac{24}{30}\)[/tex]
Cross-multiply:
- [tex]\(15 \times 30 = 450\)[/tex]
- [tex]\(24 \times 25 = 600\)[/tex]
Since 450 ≠ 600, these fractions are not equivalent.
2. Pair: [tex]\(\frac{14}{21}\)[/tex] and [tex]\(\frac{8}{20}\)[/tex]
Cross-multiply:
- [tex]\(14 \times 20 = 280\)[/tex]
- [tex]\(8 \times 21 = 168\)[/tex]
Since 280 ≠ 168, these fractions are not equivalent.
3. Pair: [tex]\(\frac{18}{45}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex]
Cross-multiply:
- [tex]\(18 \times 35 = 630\)[/tex]
- [tex]\(14 \times 45 = 630\)[/tex]
Since 630 = 630, these fractions are equivalent.
4. Pair: [tex]\(\frac{12}{35}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex]
These fractions already have the same denominator, making it easy to compare the numerators:
- 12 ≠ 14
So, these fractions are not equivalent.
Based on this analysis, the equivalent fraction pair is [tex]\(\frac{18}{45}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex], which corresponds to option 3.
1. Pair: [tex]\(\frac{15}{25}\)[/tex] and [tex]\(\frac{24}{30}\)[/tex]
Cross-multiply:
- [tex]\(15 \times 30 = 450\)[/tex]
- [tex]\(24 \times 25 = 600\)[/tex]
Since 450 ≠ 600, these fractions are not equivalent.
2. Pair: [tex]\(\frac{14}{21}\)[/tex] and [tex]\(\frac{8}{20}\)[/tex]
Cross-multiply:
- [tex]\(14 \times 20 = 280\)[/tex]
- [tex]\(8 \times 21 = 168\)[/tex]
Since 280 ≠ 168, these fractions are not equivalent.
3. Pair: [tex]\(\frac{18}{45}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex]
Cross-multiply:
- [tex]\(18 \times 35 = 630\)[/tex]
- [tex]\(14 \times 45 = 630\)[/tex]
Since 630 = 630, these fractions are equivalent.
4. Pair: [tex]\(\frac{12}{35}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex]
These fractions already have the same denominator, making it easy to compare the numerators:
- 12 ≠ 14
So, these fractions are not equivalent.
Based on this analysis, the equivalent fraction pair is [tex]\(\frac{18}{45}\)[/tex] and [tex]\(\frac{14}{35}\)[/tex], which corresponds to option 3.
