Organizing the Products: How to Sorting Results from Multiplying Fractions and Whole Numbers

When multiplying fractions by whole numbers, the results can vary widely.

Sorting these results helps in understanding patterns, comparing values, and organizing data. In this guide, we’ll explore the process of multiplying fractions by whole numbers and then sorting the outcomes.

Step-by-step Guide to Sorting Results from Multiplying Fractions and Whole Numbers:

1. Multiplication Process:

To multiply a fraction by a whole number:

– Multiply the numerator of the fraction by the whole number.

– Keep the denominator the same.

– Simplify the result if necessary, converting any improper fractions to mixed numbers.

2. Sorting the Results:

Once you have a list of products:

– Start by comparing the whole number parts of the mixed numbers or the numerators of the fractions.

– For results with the same whole number part, compare the fractional parts.

– Arrange the products in ascending (or descending) order based on your comparison.

3. Understanding Patterns:

As you sort, you might notice patterns. For instance, multiplying by larger fractions generally results in larger products, while multiplying by smaller fractions yields smaller products.

Example 1:

Multiply and sort the results of: \(2 \times \frac{1}{4}\), \(2 \times \frac{3}{4}\), and \(2 \times \frac{1}{2}\).

Solution:

– \(2 \times \frac{1}{4} = \frac{2}{4} = \frac{1}{2}\)

– \(2 \times \frac{3}{4} = \frac{6}{4} = 1 \frac{1}{2}\)

– \(2 \times \frac{1}{2} = 1\)

Sorting in ascending order: \(1, \frac{1}{2}, 1 \frac{1}{2}\)

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Example 2:

Multiply and sort the results of: \(3 \times \frac{2}{5}\), \(3 \times \frac{4}{5}\), and \(3 \times \frac{1}{5}\).

Solution:

– \(3 \times \frac{2}{5} = \frac{6}{5} = 1 \frac{1}{5}\)

– \(3 \times \frac{4}{5} = \frac{12}{5} = 2 \frac{2}{5}\)

– \(3 \times \frac{1}{5} = \frac{3}{5}\)

Sorting in ascending order: \(\frac{3}{5}, 1 \frac{1}{5}, 2 \frac{2}{5}\)

Practice Questions:

1. Multiply and sort the results of: \(4 \times \frac{1}{3}\), \(4 \times \frac{2}{3}\), and \(4 \times \frac{1}{6}\).

2. Multiply and sort the results of: \(5 \times \frac{3}{8}\), \(5 \times \frac{5}{8}\), and \(5 \times \frac{1}{8}\).

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Answers:

1. \(1 \frac{1}{3}, 2 \frac{2}{3}, \frac{2}{3}\) (in ascending order)

2. \(\frac{5}{8}, 1 \frac{7}{8}, 1 \frac{7}{8}\) (in ascending order)

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