SIMPLIFYING FRACTIONS SHEET 2 Write these fractions in their simplest form. 14 1) \frac{14}{20} = 9 3) \frac{9}{12} = 8 5) \frac{8}{18} = 4 2) \frac{4}{8} = 12 4) \frac{12}{15} = 14 6) \frac{14}{21} = 7) \frac{12}{16} = 8) \frac{10}{24} = 9) \frac{15}{35} = 10) \frac{13}{26} = 11) \frac{11}{55} = 12) \frac{9}{21} = 13) \frac{16}{26} = 14) \frac{20}{32} = 15) \frac{18}{24} = 16) \frac{21}{27} = 17) \frac{4}{32} = 18) \frac{25}{40} =
SIMPLIFYING FRACTIONS SHEET 2 Write these fractions in their simplest form. 14 1) \frac{14}{20} = 9 3) \frac{9}{12} = 8 5) \frac{8}{18} = 4 2) \frac{4}{8} = 12 4) \frac{12}{15} = 14 6) \frac{14}{21} = 7) \frac{12}{16} = 8) \frac{10}{24} = 9) \frac{15}{35} = 10) \frac{13}{26} = 11) \frac{11}{55} = 12) \frac{9}{21} = 13) \frac{16}{26} = 14) \frac{20}{32} = 15) \frac{18}{24} = 16) \frac{21}{27} = 17) \frac{4}{32} = 18) \frac{25}{40} =
The Correct Answer and Explanation is:
Correct Answers:
- \frac{14}{20} = \frac{7}{10}
- \frac{4}{8} = \frac{1}{2}
- \frac{9}{12} = \frac{3}{4}
- \frac{12}{15} = \frac{4}{5}
- \frac{8}{18} = \frac{4}{9}
- \frac{14}{21} = \frac{2}{3}
- \frac{12}{16} = \frac{3}{4}
- \frac{10}{24} = \frac{5}{12}
- \frac{15}{35} = \frac{3}{7}
- \frac{13}{26} = \frac{1}{2}
- \frac{11}{55} = \frac{1}{5}
- \frac{9}{21} = \frac{3}{7}
- \frac{16}{26} = \frac{8}{13}
- \frac{20}{32} = \frac{5}{8}
- \frac{18}{24} = \frac{3}{4}
- \frac{21}{27} = \frac{7}{9}
- \frac{4}{32} = \frac{1}{8}
- \frac{25}{40} = \frac{5}{8}
Explanation of Simplifying Fractions
Simplifying a fraction, also known as reducing it to its simplest or lowest terms, means finding an equivalent fraction where the numerator (the top number) and the denominator (the bottom number) are the smallest possible whole numbers. Although the fraction’s value remains the same, its representation becomes easier to understand.
The most effective method for simplifying a fraction involves finding the Greatest Common Divisor (GCD), which is also called the Greatest Common Factor (GCF). The GCD is the largest whole number that can divide into both the numerator and the denominator without leaving a remainder.
Here is the step-by-step process:
- Identify the Numerator and Denominator: Look at the fraction you need to simplify. For example, in problem 1, the fraction is 14/20. The numerator is 14 and the denominator is 20.
- Find the Greatest Common Divisor (GCD): Determine all the factors (numbers that divide evenly) for both the numerator and the denominator.
- Factors of 14 are: 1, 2, 7, 14.
- Factors of 20 are: 1, 2, 4, 5, 10, 20.
By comparing these lists, the largest number that appears in both is 2. Therefore, the GCD of 14 and 20 is 2.
- Divide by the GCD: Divide both the numerator and the denominator by the GCD you just found.
- 14 ÷ 2 = 7
- 20 ÷ 2 = 10
The result is the simplified fraction: 7/10.
A fraction is in its simplest form when the only common factor between the numerator and denominator is 1. This process ensures that you find that simplest form in a single, efficient step.
