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Answer :
To compare 7.4 and [tex]\(7 \frac{2}{5}\)[/tex], we can follow these steps:
1. Convert the Mixed Number to a Decimal:
- The mixed number [tex]\(7 \frac{2}{5}\)[/tex] can be converted to a decimal.
- First, recognize that [tex]\(7 \frac{2}{5}\)[/tex] can be expressed as [tex]\(7 + \frac{2}{5}\)[/tex].
- Calculate [tex]\(\frac{2}{5}\)[/tex] which is equal to 0.4.
- Add this to 7 to get 7.4.
2. Converted Forms:
- The mixed number [tex]\(7 \frac{2}{5}\)[/tex] when converted to a decimal gives 7.4.
- Therefore, both the decimal number 7.4 and the converted mixed number 7.4 are equal.
3. Convert the Mixed Number to an Improper Fraction:
- To convert [tex]\(7 \frac{2}{5}\)[/tex] to an improper fraction, use the following steps:
- Multiply the whole number 7 by the denominator 5: [tex]\(7 \times 5 = 35\)[/tex].
- Add the numerator 2 to this result: [tex]\(35 + 2 = 37\)[/tex].
- This gives us the improper fraction [tex]\(\frac{37}{5}\)[/tex].
4. Compare as Fractions:
- The number 7.4 can also be written as a fraction [tex]\(\frac{37}{5}\)[/tex].
- Thus, both the decimal 7.4 and the mixed number [tex]\(7 \frac{2}{5}\)[/tex] are equal in numerical value.
In conclusion, both 7.4 and [tex]\(7 \frac{2}{5}\)[/tex] represent the same quantity, whether expressed as decimals or fractions.
1. Convert the Mixed Number to a Decimal:
- The mixed number [tex]\(7 \frac{2}{5}\)[/tex] can be converted to a decimal.
- First, recognize that [tex]\(7 \frac{2}{5}\)[/tex] can be expressed as [tex]\(7 + \frac{2}{5}\)[/tex].
- Calculate [tex]\(\frac{2}{5}\)[/tex] which is equal to 0.4.
- Add this to 7 to get 7.4.
2. Converted Forms:
- The mixed number [tex]\(7 \frac{2}{5}\)[/tex] when converted to a decimal gives 7.4.
- Therefore, both the decimal number 7.4 and the converted mixed number 7.4 are equal.
3. Convert the Mixed Number to an Improper Fraction:
- To convert [tex]\(7 \frac{2}{5}\)[/tex] to an improper fraction, use the following steps:
- Multiply the whole number 7 by the denominator 5: [tex]\(7 \times 5 = 35\)[/tex].
- Add the numerator 2 to this result: [tex]\(35 + 2 = 37\)[/tex].
- This gives us the improper fraction [tex]\(\frac{37}{5}\)[/tex].
4. Compare as Fractions:
- The number 7.4 can also be written as a fraction [tex]\(\frac{37}{5}\)[/tex].
- Thus, both the decimal 7.4 and the mixed number [tex]\(7 \frac{2}{5}\)[/tex] are equal in numerical value.
In conclusion, both 7.4 and [tex]\(7 \frac{2}{5}\)[/tex] represent the same quantity, whether expressed as decimals or fractions.
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