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Fractions are generally used to define any whole number into equal parts. While writing a fraction, there are two numbers involved. The number at the top is called the numerator, while that at the bottom is called a denominator. There are three types of fractions. They are:

Proper Fractions:

In proper fractions, the denominator is greater than the numerator. For example: 3/4, 1/3

Improper Fractions:

As the name suggests, these fractions are “top-heavy” or the numerator is greater than the denominator. For example: 8/7, 5/2

Mixed Fractions:

Mixed fractions are another type of improper fractions where there is a whole number as well as a fraction part. For example: 1 1/3, 2 3/7

Simplifying a Fraction

To simplify a fraction, we divide the numerator and the denominator with the same whole number. When the fraction can’t be divided by the same whole number except 1, then it is said to be in its simplest form.

Steps to simplify a fraction:

  1. First, find a whole number that can completely divide the numerator and the denominator of the fraction (Greatest Common Factor). Once you get that number, divide the numerator and denominator and write the new fraction.
  2. Now, follow this step until you can’t divide it by the same whole number. Once you see that the only number that can divide the numerator and denominator is 1, you have achieved the simplest form.

Example:

  • Take the fraction 9/18
  • Let’s divide the numerator and denominator by 3, so the fraction becomes 3/6
  • Next, let’s divide it by 3 again, so the result is 1/2. This is the simplest form.

\(\frac{9}{18} = \frac{9 \div 3}{18 \div 3} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}\)

Or

\(\frac{9}{18} = \frac{9 \div 9}{18 \div 9} = \frac{1}{2}, \text{GCF}(9,18) = 9\)

Exercises for Simplifying Fractions

  1. \(\frac{40}{55} =\)
  2. \(\frac{75}{90} =\)
  3. \(\frac{33}{42} =\)
  4. \(\frac{12}{21} =\)
  5. \(\frac{20}{55} =\)
  6. \(\frac{60}{95} =\)
  7. \(\frac{15}{18} =\)
  8. \(\frac{95}{130} =\)
  9. \(\frac{24}{45} =\)
  10. \(\frac{36}{39} =\)

Answers

  1. \(\frac{40}{55} = \frac{8}{11}\)

    Solution:

    To simplify \(\frac{40}{55}\), you first need to find a number that both 40 and 55 are divisible by. Both are divisible by 5, so: \(\frac{40}{55} = \frac{40 \div 5}{55 \div 5} = \frac{8}{11}\)

  2. \(\frac{75}{90} = \frac{5}{6}\)

    Solution:

    To simplify \(\frac{75}{90}\), you first need to find a number that both 75 and 90 are divisible by. Both are divisible by 15, so: \(\frac{75}{90} = \frac{75 \div 15}{90 \div 15} = \frac{5}{6}\)

  3. \(\frac{33}{42} = \frac{11}{14}\)

    Solution:

    To simplify \(\frac{33}{42}\), you first need to find a number that both 33 and 42 are divisible by. Both are divisible by 3, so: \(\frac{33}{42} = \frac{33 \div 3}{42 \div 3} = \frac{11}{14}\)

  4. \(\frac{12}{21} = \frac{4}{7}\)

    Solution:

    To simplify \(\frac{12}{21}\), you first need to find a number that both 12 and 21 are divisible by. Both are divisible by 3, so: \(\frac{12}{21} = \frac{12 \div 3}{21 \div 3} = \frac{4}{7}\)

  5. \(\frac{20}{35} = \frac{4}{7}\)

    Solution:

    To simplify \(\frac{20}{35}\), you first need to find a number that both 20 and 35 are divisible by. Both are divisible by 5, so: \(\frac{20}{35} = \frac{20 \div 5}{35 \div 5} = \frac{4}{7}\)

  6. \(\frac{60}{95} = \frac{12}{19}\)

    Solution:

    To simplify \(\frac{60}{95}\), you first need to find a number that both 60 and 95 are divisible by. Both are divisible by 5, so: \(\frac{60}{95} = \frac{60 \div 5}{95 \div 5} = \frac{12}{19}\)

  7. \(\frac{15}{18} = \frac{5}{6}\)

    Solution:

    To simplify \(\frac{15}{18}\), you first need to find a number that both 15 and 18 are divisible by. Both are divisible by 3, so: \(\frac{15}{18} = \frac{15 \div 3}{18 \div 3} = \frac{5}{6}\)

  8. \(\frac{95}{130} = \frac{19}{26}\)

    Solution:

    To simplify \(\frac{95}{130}\), you first need to find a number that both 95 and 130 are divisible by. Both are divisible by 5, so: \(\frac{95}{130} = \frac{95 \div 5}{130 \div 5} = \frac{19}{26}\)

  9. \(\frac{24}{45} = \frac{8}{15}\)

    Solution:

    To simplify \(\frac{24}{45}\), you first need to find a number that both 24 and 45 are divisible by. Both are divisible by 3, so: \(\frac{24}{45} = \frac{24 \div 3}{45 \div 3} = \frac{8}{15}\)

  10. \(\frac{36}{39} = \frac{12}{13}\)

    Solution:

    To simplify \(\frac{36}{39}\), you first need to find a number that both 36 and 39 are divisible by. Both are divisible by 3, so: \(\frac{36}{39} = \frac{36 \div 3}{39 \div 3} = \frac{12}{13}\)