Learn to cancel common factors before multiplying to make calculations easier.
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Showing the cancellation marks (slashes) clearly is key to modeling the process.
Divide a numerator and a denominator by a common factor to keep numbers small.
Introduce the motivation for simplifying early.
Imagine you need to multiply .
You could multiply the numerators () and then the denominators (). But that gives you , a fraction with huge numbers that is tedious to simplify.
Simplifying 12/7 x 5/24.
Problem. Multiply the following fractions and express the product in its lowest form: .
Simplifying 14/15 x 25/42.
Let us use the same technique to multiply 14/15 and 25/42. First, we look for common factors between numerators and denominators. We can divide the numerator 14 and denominator 42 by . We can also divide the denominator 15 and the numerator 25 by . Multiplying the remaining simple numbers (1/3 and 5/3) gives us the final answer of .
Historical context on fraction simplification in India.
In India, the process of reducing a fraction to its lowest terms is known as apavartana. It was so well known that the Jaina scholar Umasvati used it as a simile in a philosophical work as early as 150 CE!
Evaluate 14/4 divided by 2 (as multiplication).
Adapt the problem into a multiplication problem, then evaluate it by cancelling common factors first:
State the multiplication expression you need to solve.
Identify which numerator and denominator share a common factor, and state the factor.
Rewrite the fractions after dividing by the common factor.
Show the multiplication of the new numerators and denominators.
Provide the final fraction in its lowest terms.