Math Problem Statement

Writeequivalentfractionsfor 1 9 and 5 8 usingtheleastcommondenominator.

Type the fractions, using a slash ( / ) to separate the numerator and denominator.

1 9

5 8

Solution

To write equivalent fractions for 19\frac{1}{9} and 58\frac{5}{8} using the least common denominator (LCD):

  1. The denominators are 9 and 8.
  2. The least common denominator of 9 and 8 is 72 (since 9×8=729 \times 8 = 72).

Now, convert each fraction to have the denominator of 72:

19=1×89×8=872\frac{1}{9} = \frac{1 \times 8}{9 \times 8} = \frac{8}{72}

58=5×98×9=4572\frac{5}{8} = \frac{5 \times 9}{8 \times 9} = \frac{45}{72}

Thus, the equivalent fractions are:

19=872\frac{1}{9} = \frac{8}{72}

58=4572\frac{5}{8} = \frac{45}{72}

Do you want further details or have any questions?


Related Questions:

  1. How do you find the least common denominator for two fractions?
  2. Can the least common denominator ever be smaller than the product of the denominators?
  3. How do you simplify fractions after converting them to a common denominator?
  4. What is the difference between least common multiple (LCM) and least common denominator (LCD)?
  5. Why is it important to use the least common denominator instead of any common denominator?

Tip:

Always check if the denominators can be simplified or factored to find the least common denominator more efficiently.

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Math Problem Analysis

Mathematical Concepts

Fractions
Least Common Denominator (LCD)
Equivalent Fractions

Formulas

Least common denominator (LCD) = least common multiple (LCM) of the denominators
Equivalent fraction: (numerator × factor)/(denominator × factor)

Theorems

Concept of Least Common Multiple (LCM)

Suitable Grade Level

Grades 5-7