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Sagot :
Let's solve the given fractions step-by-step.
1. What fraction of the day is 6 hours?
- A day consists of 24 hours.
- The fraction of the day that 6 hours represents is calculated by dividing the number of hours (6) by the total hours in a day (24).
[tex]\[ \text{Fraction of the day} = \frac{6}{24} = 0.25 \][/tex]
2. What fraction of the year is 3 months?
- A year consists of 12 months.
- The fraction of the year that 3 months represents is calculated by dividing the number of months (3) by the total months in a year (12).
[tex]\[ \text{Fraction of the year} = \frac{3}{12} = 0.25 \][/tex]
3. What fraction of a meter is 20 cm?
- There are 100 centimeters in a meter.
- The fraction of the meter that 20 cm represents is calculated by dividing the number of centimeters (20) by the total centimeters in a meter (100).
[tex]\[ \text{Fraction of a meter} = \frac{20}{100} = 0.2 \][/tex]
4. What fraction of numbers between 1 to 10 are even numbers?
- The even numbers between 1 and 10 are: 2, 4, 6, 8, 10.
- There are 5 even numbers and the total numbers between 1 and 10 are 10.
- The fraction of even numbers is calculated by dividing the number of even numbers (5) by the total numbers (10).
[tex]\[ \text{Fraction of even numbers} = \frac{5}{10} = 0.5 \][/tex]
5. What fraction of an hour is 20 minutes?
- There are 60 minutes in an hour.
- The fraction of the hour that 20 minutes represents is calculated by dividing the number of minutes (20) by the total minutes in an hour (60).
[tex]\[ \text{Fraction of an hour} = \frac{20}{60} = 0.3333333333333333 \][/tex]
6. Which fraction is greater: [tex]\(\frac{7}{13}\)[/tex] or [tex]\(\frac{6}{13}\)[/tex]?
- We compare the numerators since the denominators are the same:
[tex]\(\frac{7}{13}\)[/tex] = 0.5384615384615384
[tex]\(\frac{6}{13}\)[/tex] = 0.46153846153846156
Therefore, [tex]\(\frac{7}{13}\)[/tex] (0.5384615384615384) is greater than [tex]\(\frac{6}{13}\)[/tex].
7. What is the improper fraction of the mixed number [tex]\(3 \frac{1}{3}\)[/tex]?
- A mixed number consists of a whole number and a fraction.
- To convert [tex]\(3 \frac{1}{3}\)[/tex] to an improper fraction:
[tex]\[ 3 \frac{1}{3} = \frac{10}{3} \][/tex]
8. What is the mixed number form of the fraction [tex]\(\frac{13}{7}\)[/tex]?
- To convert [tex]\(\frac{13}{7}\)[/tex] into a mixed number:
- Divide 13 by 7 to get 1 with a remainder of 6.
- The mixed number form will be [tex]\(1 \frac{6}{7}\)[/tex].
9. Reduce the fraction [tex]\(\frac{24}{40}\)[/tex] to its lowest terms.
- The greatest common divisor (GCD) of 24 and 40 is 8.
- Divide both the numerator and the denominator by the GCD:
[tex]\[ \frac{24}{40} = \frac{24 \div 8}{40 \div 8} = \frac{3}{5} \][/tex]
10. Arrange in ascending order: [tex]\(\frac{6}{11}; \frac{3}{11}; \frac{7}{11}; \frac{9}{11}; \frac{4}{11}\)[/tex].
- Converting fractions into decimal for clarity:
[tex]\[ \frac{3}{11} \approx 0.2727, \quad \frac{4}{11} \approx 0.3636, \quad \frac{6}{11} \approx 0.5455, \quad \frac{7}{11} \approx 0.6364, \quad \frac{9}{11} \approx 0.8182 \][/tex]
- Ascending order:
[tex]\[ 0.2727, 0.3636, 0.5455, 0.6364, 0.8182 \][/tex]
[tex]\[ \text{Ascending order} = \left( \frac{3}{11}, \frac{4}{11}, \frac{6}{11}, \frac{7}{11}, \frac{9}{11} \right) \][/tex]
11. Arrange in descending order: [tex]\(\frac{5}{11}; \frac{5}{9}; \frac{5}{7}; \frac{5}{13}; \frac{5}{6}\)[/tex].
- Converting fractions into decimal for clarity:
[tex]\[ \frac{5}{6} \approx 0.8333, \quad \frac{5}{7} \approx 0.7143, \quad \frac{5}{9} \approx 0.5556, \quad \frac{5}{11} \approx 0.4545, \quad \frac{5}{13} \approx 0.3846 \][/tex]
- Descending order:
[tex]\[ 0.8333, 0.7143, 0.5556, 0.4545, 0.3846 \][/tex]
[tex]\[ \text{Descending order} = \left( \frac{5}{6}, \frac{5}{7}, \frac{5}{9}, \frac{5}{11}, \frac{5}{13} \right) \][/tex]
1. What fraction of the day is 6 hours?
- A day consists of 24 hours.
- The fraction of the day that 6 hours represents is calculated by dividing the number of hours (6) by the total hours in a day (24).
[tex]\[ \text{Fraction of the day} = \frac{6}{24} = 0.25 \][/tex]
2. What fraction of the year is 3 months?
- A year consists of 12 months.
- The fraction of the year that 3 months represents is calculated by dividing the number of months (3) by the total months in a year (12).
[tex]\[ \text{Fraction of the year} = \frac{3}{12} = 0.25 \][/tex]
3. What fraction of a meter is 20 cm?
- There are 100 centimeters in a meter.
- The fraction of the meter that 20 cm represents is calculated by dividing the number of centimeters (20) by the total centimeters in a meter (100).
[tex]\[ \text{Fraction of a meter} = \frac{20}{100} = 0.2 \][/tex]
4. What fraction of numbers between 1 to 10 are even numbers?
- The even numbers between 1 and 10 are: 2, 4, 6, 8, 10.
- There are 5 even numbers and the total numbers between 1 and 10 are 10.
- The fraction of even numbers is calculated by dividing the number of even numbers (5) by the total numbers (10).
[tex]\[ \text{Fraction of even numbers} = \frac{5}{10} = 0.5 \][/tex]
5. What fraction of an hour is 20 minutes?
- There are 60 minutes in an hour.
- The fraction of the hour that 20 minutes represents is calculated by dividing the number of minutes (20) by the total minutes in an hour (60).
[tex]\[ \text{Fraction of an hour} = \frac{20}{60} = 0.3333333333333333 \][/tex]
6. Which fraction is greater: [tex]\(\frac{7}{13}\)[/tex] or [tex]\(\frac{6}{13}\)[/tex]?
- We compare the numerators since the denominators are the same:
[tex]\(\frac{7}{13}\)[/tex] = 0.5384615384615384
[tex]\(\frac{6}{13}\)[/tex] = 0.46153846153846156
Therefore, [tex]\(\frac{7}{13}\)[/tex] (0.5384615384615384) is greater than [tex]\(\frac{6}{13}\)[/tex].
7. What is the improper fraction of the mixed number [tex]\(3 \frac{1}{3}\)[/tex]?
- A mixed number consists of a whole number and a fraction.
- To convert [tex]\(3 \frac{1}{3}\)[/tex] to an improper fraction:
[tex]\[ 3 \frac{1}{3} = \frac{10}{3} \][/tex]
8. What is the mixed number form of the fraction [tex]\(\frac{13}{7}\)[/tex]?
- To convert [tex]\(\frac{13}{7}\)[/tex] into a mixed number:
- Divide 13 by 7 to get 1 with a remainder of 6.
- The mixed number form will be [tex]\(1 \frac{6}{7}\)[/tex].
9. Reduce the fraction [tex]\(\frac{24}{40}\)[/tex] to its lowest terms.
- The greatest common divisor (GCD) of 24 and 40 is 8.
- Divide both the numerator and the denominator by the GCD:
[tex]\[ \frac{24}{40} = \frac{24 \div 8}{40 \div 8} = \frac{3}{5} \][/tex]
10. Arrange in ascending order: [tex]\(\frac{6}{11}; \frac{3}{11}; \frac{7}{11}; \frac{9}{11}; \frac{4}{11}\)[/tex].
- Converting fractions into decimal for clarity:
[tex]\[ \frac{3}{11} \approx 0.2727, \quad \frac{4}{11} \approx 0.3636, \quad \frac{6}{11} \approx 0.5455, \quad \frac{7}{11} \approx 0.6364, \quad \frac{9}{11} \approx 0.8182 \][/tex]
- Ascending order:
[tex]\[ 0.2727, 0.3636, 0.5455, 0.6364, 0.8182 \][/tex]
[tex]\[ \text{Ascending order} = \left( \frac{3}{11}, \frac{4}{11}, \frac{6}{11}, \frac{7}{11}, \frac{9}{11} \right) \][/tex]
11. Arrange in descending order: [tex]\(\frac{5}{11}; \frac{5}{9}; \frac{5}{7}; \frac{5}{13}; \frac{5}{6}\)[/tex].
- Converting fractions into decimal for clarity:
[tex]\[ \frac{5}{6} \approx 0.8333, \quad \frac{5}{7} \approx 0.7143, \quad \frac{5}{9} \approx 0.5556, \quad \frac{5}{11} \approx 0.4545, \quad \frac{5}{13} \approx 0.3846 \][/tex]
- Descending order:
[tex]\[ 0.8333, 0.7143, 0.5556, 0.4545, 0.3846 \][/tex]
[tex]\[ \text{Descending order} = \left( \frac{5}{6}, \frac{5}{7}, \frac{5}{9}, \frac{5}{11}, \frac{5}{13} \right) \][/tex]
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