Answer :
To match each fraction on the left with an equivalent fraction on the right, you can follow these steps:
1. Understand Equivalent Fractions:
- Equivalent fractions are fractions that represent the same value or proportion, even though they may look different.
- To determine if two fractions are equivalent, you can simplify both to their simplest form and see if they match.
2. Simplify Fractions:
- Simplifying a fraction means reducing it to its simplest form where the numerator and denominator have no common factors other than 1.
3. Perform the Matching:
- Match for [tex]\(\frac{1}{2}\)[/tex]:
- Simplify [tex]\(\frac{17}{34}\)[/tex]:
- The greatest common divisor (GCD) of 17 and 34 is 17.
- [tex]\(\frac{17}{34} \div \frac{17}{17} = \frac{1}{2}\)[/tex].
- Therefore, [tex]\(\frac{1}{2}\)[/tex] matches with [tex]\(\frac{17}{34}\)[/tex].
- Match for [tex]\(\frac{2}{3}\)[/tex]:
- Simplify [tex]\(\frac{32}{48}\)[/tex]:
- The GCD of 32 and 48 is 16.
- [tex]\(\frac{32}{48} \div \frac{16}{16} = \frac{2}{3}\)[/tex].
- Therefore, [tex]\(\frac{2}{3}\)[/tex] matches with [tex]\(\frac{32}{48}\)[/tex].
- Match for [tex]\(\frac{3}{4}\)[/tex]:
- Simplify [tex]\(\frac{18}{24}\)[/tex]:
- The GCD of 18 and 24 is 6.
- [tex]\(\frac{18}{24} \div \frac{6}{6} = \frac{3}{4}\)[/tex].
- Therefore, [tex]\(\frac{3}{4}\)[/tex] matches with [tex]\(\frac{18}{24}\)[/tex].
- Match for [tex]\(\frac{4}{5}\)[/tex]:
- Simplify [tex]\(\frac{36}{45}\)[/tex]:
- The GCD of 36 and 45 is 9.
- [tex]\(\frac{36}{45} \div \frac{9}{9} = \frac{4}{5}\)[/tex].
- Therefore, [tex]\(\frac{4}{5}\)[/tex] matches with [tex]\(\frac{36}{45}\)[/tex].
In summary, the matches are:
- [tex]\(\frac{1}{2}\)[/tex] matches with [tex]\(\frac{17}{34}\)[/tex].
- [tex]\(\frac{2}{3}\)[/tex] matches with [tex]\(\frac{32}{48}\)[/tex].
- [tex]\(\frac{3}{4}\)[/tex] matches with [tex]\(\frac{18}{24}\)[/tex].
- [tex]\(\frac{4}{5}\)[/tex] matches with [tex]\(\frac{36}{45}\)[/tex].
1. Understand Equivalent Fractions:
- Equivalent fractions are fractions that represent the same value or proportion, even though they may look different.
- To determine if two fractions are equivalent, you can simplify both to their simplest form and see if they match.
2. Simplify Fractions:
- Simplifying a fraction means reducing it to its simplest form where the numerator and denominator have no common factors other than 1.
3. Perform the Matching:
- Match for [tex]\(\frac{1}{2}\)[/tex]:
- Simplify [tex]\(\frac{17}{34}\)[/tex]:
- The greatest common divisor (GCD) of 17 and 34 is 17.
- [tex]\(\frac{17}{34} \div \frac{17}{17} = \frac{1}{2}\)[/tex].
- Therefore, [tex]\(\frac{1}{2}\)[/tex] matches with [tex]\(\frac{17}{34}\)[/tex].
- Match for [tex]\(\frac{2}{3}\)[/tex]:
- Simplify [tex]\(\frac{32}{48}\)[/tex]:
- The GCD of 32 and 48 is 16.
- [tex]\(\frac{32}{48} \div \frac{16}{16} = \frac{2}{3}\)[/tex].
- Therefore, [tex]\(\frac{2}{3}\)[/tex] matches with [tex]\(\frac{32}{48}\)[/tex].
- Match for [tex]\(\frac{3}{4}\)[/tex]:
- Simplify [tex]\(\frac{18}{24}\)[/tex]:
- The GCD of 18 and 24 is 6.
- [tex]\(\frac{18}{24} \div \frac{6}{6} = \frac{3}{4}\)[/tex].
- Therefore, [tex]\(\frac{3}{4}\)[/tex] matches with [tex]\(\frac{18}{24}\)[/tex].
- Match for [tex]\(\frac{4}{5}\)[/tex]:
- Simplify [tex]\(\frac{36}{45}\)[/tex]:
- The GCD of 36 and 45 is 9.
- [tex]\(\frac{36}{45} \div \frac{9}{9} = \frac{4}{5}\)[/tex].
- Therefore, [tex]\(\frac{4}{5}\)[/tex] matches with [tex]\(\frac{36}{45}\)[/tex].
In summary, the matches are:
- [tex]\(\frac{1}{2}\)[/tex] matches with [tex]\(\frac{17}{34}\)[/tex].
- [tex]\(\frac{2}{3}\)[/tex] matches with [tex]\(\frac{32}{48}\)[/tex].
- [tex]\(\frac{3}{4}\)[/tex] matches with [tex]\(\frac{18}{24}\)[/tex].
- [tex]\(\frac{4}{5}\)[/tex] matches with [tex]\(\frac{36}{45}\)[/tex].
