convert to proper fractions.
1. 0.55=
2. 41/4+3 3/4=
3. 15×3 / 5×4 /27=
4. 2 3/4/ 7=
The Correct Answer and Explanation is :
Answers with Explanations:
- 0.55 as a Proper Fraction
- Convert 0.55 to a fraction:
[
0.55 = \frac{55}{100}
] - Simplify the fraction by dividing by 5:
[
\frac{55 \div 5}{100 \div 5} = \frac{11}{20}
] - Since (\frac{11}{20}) is already in its simplest form and is a proper fraction, the final answer is:
[
\mathbf{\frac{11}{20}}
]
- 41/4 + 3 3/4 as a Proper Fraction
- Convert mixed number (3 \frac{3}{4}) to improper fraction:
[
3 \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4}
] - Add fractions:
[
\frac{41}{4} + \frac{15}{4} = \frac{56}{4}
] - Simplify:
[
\frac{56}{4} = 14
] - Since 14 is a whole number and not a fraction, it does not satisfy the proper fraction requirement.
- 15 × 3 ÷ (5 × 4 ÷ 27) as a Proper Fraction
- Compute numerator and denominator:
[
15 \times 3 = 45, \quad 5 \times 4 = 20
] - Compute division:
[
20 \div 27 = \frac{20}{27}
] - Solve fraction division:
[
45 \div \frac{20}{27} = 45 \times \frac{27}{20} = \frac{45 \times 27}{20}
] - Compute values:
[
\frac{1215}{20}
] - Simplify by dividing by 5:
[
\frac{243}{4}
] - Convert to proper fraction:
[
\mathbf{\frac{243}{4}}
]
- (2 \frac{3}{4} \div 7) as a Proper Fraction
- Convert mixed number:
[
2 \frac{3}{4} = \frac{11}{4}
] - Divide by 7:
[
\frac{11}{4} \div 7 = \frac{11}{4} \times \frac{1}{7} = \frac{11}{28}
] - Final proper fraction:
[
\mathbf{\frac{11}{28}}
]
300-Word Explanation
Fractions represent parts of a whole, and proper fractions are those where the numerator (top number) is smaller than the denominator (bottom number). Converting decimal and mixed numbers into proper fractions involves multiple steps, as seen in the examples.
For 0.55, converting it to a fraction starts by expressing it as (\frac{55}{100}), which simplifies to (\frac{11}{20}). This fraction is proper since the numerator is smaller than the denominator.
For 41/4 + 3 3/4, first, the mixed number is converted to an improper fraction and then added to another fraction with the same denominator. The result is a whole number (14), which is not a proper fraction.
For 15 × 3 ÷ (5 × 4 ÷ 27), the numerator and denominator are computed separately, and fraction division is applied. The final fraction, (\frac{243}{4}), is an improper fraction.
Finally, for (2 \frac{3}{4} \div 7), the mixed number is first converted to an improper fraction before dividing by 7, resulting in the proper fraction (\frac{11}{28}).
Proper fractions are widely used in real-life applications such as cooking, measurements, and financial calculations. Understanding how to convert numbers into fractions is essential for precision in mathematical operations.
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