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Answer :
Sure, let's solve this problem step-by-step:
To determine which cards are equivalent to [tex]\(3 \frac{2}{5} - 1 \frac{4}{6}\)[/tex], we first need to convert the mixed numbers to improper fractions and perform the subtraction.
1. Convert to Improper Fractions:
- [tex]\(3 \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5}\)[/tex]
- [tex]\(1 \frac{4}{6} = \frac{6}{6} + \frac{4}{6} = \frac{10}{6}\)[/tex]
2. Perform the Subtraction:
To subtract the improper fractions, we need a common denominator:
- The least common denominator (LCD) for 5 and 6 is 30.
- Convert [tex]\(\frac{17}{5}\)[/tex] to a fraction with a denominator of 30:
[tex]\[
\frac{17}{5} = \frac{17 \times 6}{5 \times 6} = \frac{102}{30}
\][/tex]
- Convert [tex]\(\frac{10}{6}\)[/tex] to a fraction with a denominator of 30:
[tex]\[
\frac{10}{6} = \frac{10 \times 5}{6 \times 5} = \frac{50}{30}
\][/tex]
- Subtract the fractions:
[tex]\[
\frac{102}{30} - \frac{50}{30} = \frac{52}{30}
\][/tex]
3. Simplify the Difference:
[tex]\(\frac{52}{30}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
[tex]\[
\frac{52}{30} = \frac{26}{15}
\][/tex]
Convert [tex]\(\frac{26}{15}\)[/tex] back to a mixed number:
[tex]\[
26 \div 15 = 1 \quad \text{remainder: } 11
\][/tex]
This gives [tex]\(1 \frac{11}{15}\)[/tex].
4. Compare with Given Cards:
Now, look for the equivalent result [tex]\(1 \frac{11}{15}\)[/tex] among the options provided. We convert each option to a decimal to check:
- [tex]\(3 \frac{2}{30}-1 \frac{4}{30} = 1 \frac{28}{30}\)[/tex]
- [tex]\(3 \frac{12}{30}-1 \frac{20}{30} = 1 \frac{22}{30}\)[/tex]
- [tex]\(3 \frac{10}{30}-1 \frac{24}{30} = 1 \frac{16}{30}\)[/tex]
- [tex]\(1 \frac{16}{30}\)[/tex]
- [tex]\(1 \frac{22}{30}\)[/tex]
- [tex]\(1 \frac{28}{30}\)[/tex]
None of these options match with [tex]\(1 \frac{11}{15}\)[/tex], so it looks like no card given in the options is equivalent to the subtraction result [tex]\(1 \frac{11}{15}\)[/tex].
I hope this helps! If you need further assistance, feel free to ask.
To determine which cards are equivalent to [tex]\(3 \frac{2}{5} - 1 \frac{4}{6}\)[/tex], we first need to convert the mixed numbers to improper fractions and perform the subtraction.
1. Convert to Improper Fractions:
- [tex]\(3 \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5}\)[/tex]
- [tex]\(1 \frac{4}{6} = \frac{6}{6} + \frac{4}{6} = \frac{10}{6}\)[/tex]
2. Perform the Subtraction:
To subtract the improper fractions, we need a common denominator:
- The least common denominator (LCD) for 5 and 6 is 30.
- Convert [tex]\(\frac{17}{5}\)[/tex] to a fraction with a denominator of 30:
[tex]\[
\frac{17}{5} = \frac{17 \times 6}{5 \times 6} = \frac{102}{30}
\][/tex]
- Convert [tex]\(\frac{10}{6}\)[/tex] to a fraction with a denominator of 30:
[tex]\[
\frac{10}{6} = \frac{10 \times 5}{6 \times 5} = \frac{50}{30}
\][/tex]
- Subtract the fractions:
[tex]\[
\frac{102}{30} - \frac{50}{30} = \frac{52}{30}
\][/tex]
3. Simplify the Difference:
[tex]\(\frac{52}{30}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
[tex]\[
\frac{52}{30} = \frac{26}{15}
\][/tex]
Convert [tex]\(\frac{26}{15}\)[/tex] back to a mixed number:
[tex]\[
26 \div 15 = 1 \quad \text{remainder: } 11
\][/tex]
This gives [tex]\(1 \frac{11}{15}\)[/tex].
4. Compare with Given Cards:
Now, look for the equivalent result [tex]\(1 \frac{11}{15}\)[/tex] among the options provided. We convert each option to a decimal to check:
- [tex]\(3 \frac{2}{30}-1 \frac{4}{30} = 1 \frac{28}{30}\)[/tex]
- [tex]\(3 \frac{12}{30}-1 \frac{20}{30} = 1 \frac{22}{30}\)[/tex]
- [tex]\(3 \frac{10}{30}-1 \frac{24}{30} = 1 \frac{16}{30}\)[/tex]
- [tex]\(1 \frac{16}{30}\)[/tex]
- [tex]\(1 \frac{22}{30}\)[/tex]
- [tex]\(1 \frac{28}{30}\)[/tex]
None of these options match with [tex]\(1 \frac{11}{15}\)[/tex], so it looks like no card given in the options is equivalent to the subtraction result [tex]\(1 \frac{11}{15}\)[/tex].
I hope this helps! If you need further assistance, feel free to ask.
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