Answer :
To solve the problem of finding which cards are equivalent to the expression [tex]\( 3 \frac{2}{5} - 1 \frac{4}{6} \)[/tex], let's go through the process step-by-step:
1. Convert Mixed Numbers to Improper Fractions:
- [tex]\( 3 \frac{2}{5} \)[/tex] is equivalent to [tex]\( 3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5} \)[/tex].
- [tex]\( 1 \frac{4}{6} \)[/tex] can be simplified first to [tex]\( 1 \frac{2}{3} \)[/tex], which equals [tex]\( \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \)[/tex].
2. Find a Common Denominator:
- To subtract these fractions, we need a common denominator. The least common multiple of 5 and 3 is 15.
- Convert [tex]\( \frac{17}{5} \)[/tex] to a fraction with a denominator of 15:
[tex]\[
\frac{17}{5} = \frac{17 \times 3}{5 \times 3} = \frac{51}{15}
\][/tex]
- Convert [tex]\( \frac{5}{3} \)[/tex] to a fraction with a denominator of 15:
[tex]\[
\frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15}
\][/tex]
3. Subtract the Fractions:
- Subtract [tex]\( \frac{25}{15} \)[/tex] from [tex]\( \frac{51}{15} \)[/tex]:
[tex]\[
\frac{51}{15} - \frac{25}{15} = \frac{26}{15}
\][/tex]
- Convert [tex]\( \frac{26}{15} \)[/tex] back to a mixed number:
- 26 divided by 15 is 1 with a remainder of 11, so:
[tex]\[
\frac{26}{15} = 1 \frac{11}{15}
\][/tex]
4. Identify the Equivalent Cards:
- We are looking for the cards which have values equivalent to [tex]\( 1 \frac{11}{15} \)[/tex] or approximately 1.733 in decimal form:
- Check the given card values:
- [tex]\( 3 \frac{12}{30} - 1 \frac{20}{30} \)[/tex] simplifies to [tex]\( 1 \frac{11}{15} \)[/tex].
- [tex]\( 1 \frac{22}{30} \)[/tex] simplifies to [tex]\( 1 \frac{11}{15} \)[/tex].
Based on these calculations, the cards that are equivalent to [tex]\( 3 \frac{2}{5} - 1 \frac{4}{6} \)[/tex] are:
- [tex]\( 3 \frac{12}{30} - 1 \frac{20}{30} \)[/tex]
- [tex]\( 1 \frac{22}{30} \)[/tex]
These are the correct answers because their values match the calculated difference [tex]\( 1 \frac{11}{15} \)[/tex].
1. Convert Mixed Numbers to Improper Fractions:
- [tex]\( 3 \frac{2}{5} \)[/tex] is equivalent to [tex]\( 3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5} \)[/tex].
- [tex]\( 1 \frac{4}{6} \)[/tex] can be simplified first to [tex]\( 1 \frac{2}{3} \)[/tex], which equals [tex]\( \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \)[/tex].
2. Find a Common Denominator:
- To subtract these fractions, we need a common denominator. The least common multiple of 5 and 3 is 15.
- Convert [tex]\( \frac{17}{5} \)[/tex] to a fraction with a denominator of 15:
[tex]\[
\frac{17}{5} = \frac{17 \times 3}{5 \times 3} = \frac{51}{15}
\][/tex]
- Convert [tex]\( \frac{5}{3} \)[/tex] to a fraction with a denominator of 15:
[tex]\[
\frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15}
\][/tex]
3. Subtract the Fractions:
- Subtract [tex]\( \frac{25}{15} \)[/tex] from [tex]\( \frac{51}{15} \)[/tex]:
[tex]\[
\frac{51}{15} - \frac{25}{15} = \frac{26}{15}
\][/tex]
- Convert [tex]\( \frac{26}{15} \)[/tex] back to a mixed number:
- 26 divided by 15 is 1 with a remainder of 11, so:
[tex]\[
\frac{26}{15} = 1 \frac{11}{15}
\][/tex]
4. Identify the Equivalent Cards:
- We are looking for the cards which have values equivalent to [tex]\( 1 \frac{11}{15} \)[/tex] or approximately 1.733 in decimal form:
- Check the given card values:
- [tex]\( 3 \frac{12}{30} - 1 \frac{20}{30} \)[/tex] simplifies to [tex]\( 1 \frac{11}{15} \)[/tex].
- [tex]\( 1 \frac{22}{30} \)[/tex] simplifies to [tex]\( 1 \frac{11}{15} \)[/tex].
Based on these calculations, the cards that are equivalent to [tex]\( 3 \frac{2}{5} - 1 \frac{4}{6} \)[/tex] are:
- [tex]\( 3 \frac{12}{30} - 1 \frac{20}{30} \)[/tex]
- [tex]\( 1 \frac{22}{30} \)[/tex]
These are the correct answers because their values match the calculated difference [tex]\( 1 \frac{11}{15} \)[/tex].
