simplest form

Understanding Fractions

Definition of a Fraction in Simplest Terms

• A fraction is considered to be in simplest terms when:

  • The numerator (the top number) and the denominator (the bottom number) cannot be divided evenly by the same number, other than the number one.

Example of Simplest Terms

• Example:

  • The fraction five eighths ($\frac{5}{8}$) is in simplest terms because:

  • There is no number other than one that divides both five and eight evenly.

  • Conversely, two tenths ($\frac{2}{10}$) is not in simplest terms because:

  • Both the numerator (2) and the denominator (10) can be evenly divided by two.

    • Calculation:

    • $2 \div 2 = 1$

    • $10 \div 2 = 5$

  • Thus, $\frac{2}{10}$ simplifies to $\frac{1}{5}$, which is in simplest form.

Understanding Improper Fractions

• An improper fraction is not considered simplified until it is expressed in mixed number form.

Example of Finding the Simplest Form

• Example 1: Finding the simplest form of eight twenty-fourths ($\frac{8}{24}$).

  • Determine the largest number that divides both 8 and 24 evenly:

  • The largest number is 8.

  • Divide both the numerator and the denominator:

  • $8 \div 8 = 1$

  • $24 \div 8 = 3$

  • Therefore, eight twenty-fourths simplifies to one third ($\frac{1}{3}$).

• Example 2: Finding the simplest form of fifteen sixths ($\frac{15}{6}$).

  • First, convert 15 sixths into mixed number form:

  • Calculation:

    • $15 \div 6$ equals 2 with a remainder of 3.

  • Thus, the mixed number is two and three sixths ($2 \frac{3}{6}$).

  • Check if three sixths is in simplest terms:

  • Both 3 and 6 can be divided by 3:

    • $3 \div 3 = 1$

    • $6 \div 3 = 2$

  • Therefore, three sixths simplifies to one half ($\frac{1}{2}$).

  • Hence, fifteen sixths, when expressed as a mixed number in simplest terms, is two and one half ($2 \frac{1}{2}$).