Answer :
Sure! Let's break down the problem step-by-step:
1. Convert Mixed Numbers to Improper Fractions:
We start with the two mixed numbers: [tex]\(3 \frac{2}{5}\)[/tex] and [tex]\(1 \frac{4}{6}\)[/tex].
- [tex]\(3 \frac{2}{5}\)[/tex] can be converted as follows:
- Convert it into an improper fraction: it remains [tex]\(3 + \frac{2}{5}\)[/tex].
- [tex]\(1 \frac{4}{6}\)[/tex] can be simplified first:
- Simplify [tex]\(\frac{4}{6}\)[/tex] to [tex]\(\frac{2}{3}\)[/tex].
- Then the mixed number becomes [tex]\(1 + \frac{2}{3}\)[/tex].
2. Subtract the Fractions:
We need to subtract these two values:
[tex]\[
3 + \frac{2}{5} - \left(1 + \frac{2}{3}\right)
\][/tex]
3. Perform the Subtraction:
- Combine the whole numbers: [tex]\(3 - 1 = 2\)[/tex].
- Now subtract the fractions [tex]\(\frac{2}{5} - \frac{2}{3}\)[/tex]:
- Find a common denominator, which is 15.
- [tex]\(\frac{2}{5} = \frac{6}{15}\)[/tex] and [tex]\(\frac{2}{3} = \frac{10}{15}\)[/tex].
- Subtract the fractions: [tex]\(\frac{6}{15} - \frac{10}{15} = -\frac{4}{15}\)[/tex].
- Combine these results:
- [tex]\(2 + -\frac{4}{15} = 1 \frac{11}{15}\)[/tex].
4. Identify Equivalent Cards:
We compare this result, [tex]\(1 \frac{11}{15}\)[/tex], to the given options expressed with a denominator of 30. To do that, convert [tex]\(\frac{11}{15}\)[/tex] to a denominator of 30:
- [tex]\(\frac{11}{15} = \frac{22}{30}\)[/tex].
Then, compare with the provided options:
- [tex]\(1 \frac{22}{30}\)[/tex] matches our result of [tex]\(1 \frac{11}{15}\)[/tex].
Hence, the card that is equivalent to [tex]\(3 \frac{2}{5} - 1 \frac{4}{6}\)[/tex] is:
- [tex]\(1 \frac{22}{30}\)[/tex]
This is the correct answer!
1. Convert Mixed Numbers to Improper Fractions:
We start with the two mixed numbers: [tex]\(3 \frac{2}{5}\)[/tex] and [tex]\(1 \frac{4}{6}\)[/tex].
- [tex]\(3 \frac{2}{5}\)[/tex] can be converted as follows:
- Convert it into an improper fraction: it remains [tex]\(3 + \frac{2}{5}\)[/tex].
- [tex]\(1 \frac{4}{6}\)[/tex] can be simplified first:
- Simplify [tex]\(\frac{4}{6}\)[/tex] to [tex]\(\frac{2}{3}\)[/tex].
- Then the mixed number becomes [tex]\(1 + \frac{2}{3}\)[/tex].
2. Subtract the Fractions:
We need to subtract these two values:
[tex]\[
3 + \frac{2}{5} - \left(1 + \frac{2}{3}\right)
\][/tex]
3. Perform the Subtraction:
- Combine the whole numbers: [tex]\(3 - 1 = 2\)[/tex].
- Now subtract the fractions [tex]\(\frac{2}{5} - \frac{2}{3}\)[/tex]:
- Find a common denominator, which is 15.
- [tex]\(\frac{2}{5} = \frac{6}{15}\)[/tex] and [tex]\(\frac{2}{3} = \frac{10}{15}\)[/tex].
- Subtract the fractions: [tex]\(\frac{6}{15} - \frac{10}{15} = -\frac{4}{15}\)[/tex].
- Combine these results:
- [tex]\(2 + -\frac{4}{15} = 1 \frac{11}{15}\)[/tex].
4. Identify Equivalent Cards:
We compare this result, [tex]\(1 \frac{11}{15}\)[/tex], to the given options expressed with a denominator of 30. To do that, convert [tex]\(\frac{11}{15}\)[/tex] to a denominator of 30:
- [tex]\(\frac{11}{15} = \frac{22}{30}\)[/tex].
Then, compare with the provided options:
- [tex]\(1 \frac{22}{30}\)[/tex] matches our result of [tex]\(1 \frac{11}{15}\)[/tex].
Hence, the card that is equivalent to [tex]\(3 \frac{2}{5} - 1 \frac{4}{6}\)[/tex] is:
- [tex]\(1 \frac{22}{30}\)[/tex]
This is the correct answer!
