Answer :
Sure, let's go through how to create equivalent fractions with common denominators for each pair of fractions:
1. Fractions: [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex]
- To find a common denominator, multiply the denominators: [tex]\(5 \times 10 = 50\)[/tex].
- Convert [tex]\(\frac{2}{5}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{2}{5} \times \frac{10}{10} = \frac{20}{50}
\][/tex]
- Convert [tex]\(\frac{3}{10}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{3}{10} \times \frac{5}{5} = \frac{15}{50}
\][/tex]
2. Fractions: [tex]\(\frac{3}{7}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]
- To find a common denominator, multiply the denominators: [tex]\(7 \times 3 = 21\)[/tex].
- Convert [tex]\(\frac{3}{7}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{3}{7} \times \frac{3}{3} = \frac{9}{21}
\][/tex]
- Convert [tex]\(\frac{2}{3}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{2}{3} \times \frac{7}{7} = \frac{14}{21}
\][/tex]
By following these steps, we created equivalent fractions for each pair with a common denominator. The results are:
- [tex]\(\frac{20}{50}\)[/tex] and [tex]\(\frac{15}{50}\)[/tex]
- [tex]\(\frac{9}{21}\)[/tex] and [tex]\(\frac{14}{21}\)[/tex]
These equivalent fractions have the same denominators, which makes them easier to compare or combine if needed.
1. Fractions: [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex]
- To find a common denominator, multiply the denominators: [tex]\(5 \times 10 = 50\)[/tex].
- Convert [tex]\(\frac{2}{5}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{2}{5} \times \frac{10}{10} = \frac{20}{50}
\][/tex]
- Convert [tex]\(\frac{3}{10}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{3}{10} \times \frac{5}{5} = \frac{15}{50}
\][/tex]
2. Fractions: [tex]\(\frac{3}{7}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]
- To find a common denominator, multiply the denominators: [tex]\(7 \times 3 = 21\)[/tex].
- Convert [tex]\(\frac{3}{7}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{3}{7} \times \frac{3}{3} = \frac{9}{21}
\][/tex]
- Convert [tex]\(\frac{2}{3}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{2}{3} \times \frac{7}{7} = \frac{14}{21}
\][/tex]
By following these steps, we created equivalent fractions for each pair with a common denominator. The results are:
- [tex]\(\frac{20}{50}\)[/tex] and [tex]\(\frac{15}{50}\)[/tex]
- [tex]\(\frac{9}{21}\)[/tex] and [tex]\(\frac{14}{21}\)[/tex]
These equivalent fractions have the same denominators, which makes them easier to compare or combine if needed.