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

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)

The Best Math Books for Elementary Students

Recommended EffortlessMath Books

For a full fractions workbook that builds fraction multiplication into a complete skill set, the Grade 5 Common Core Math for Beginners (resource currently unavailable) walks through every grade-5 fraction topic with worked examples. For state-test prep that hits fraction multiplication in test format, the Grade 5 FSA Math for Beginners (resource currently unavailable) covers the same skills in FSA question style.

Frequently Asked Questions

How do you multiply fractions by whole numbers?

Multiply the whole number by the numerator and keep the denominator. For 5 × 2/3, multiply 5 × 2 = 10, so the product is 10/3, or 3 1/3. Before you compute, check the direction: because 2/3 is less than 1, the answer must be smaller than 5. That quick check makes it easy to sort several products without working each one out first.

How do you multiply fractions by whole numbers and simplify?

Multiply first, then divide the numerator and denominator by their greatest common factor. For 6 × 3/8, you get 18/8, and dividing both parts by 2 gives 9/4, which is 2 1/4 as a mixed number. Simplifying before you sort a list of products helps, because 9/4 and 2 1/4 are much easier to compare with other results than 18/8.

How do you multiply proper fractions by whole numbers?

A proper fraction has a numerator smaller than its denominator, so it is less than 1. Multiply the whole number by the numerator and keep the denominator: 8 × 3/4 = 24/4 = 6. The product is always smaller than the whole number you started with. When sorting products of the same whole number, the bigger the proper fraction, the bigger the result, so 8 × 1/4 < 8 × 1/2 < 8 × 3/4.

How do you do a mixed fraction times a whole number?

Change the mixed number to an improper fraction, then multiply. For 4 × 1 2/3, rewrite 1 2/3 as 5/3, then 4 × 5/3 = 20/3 = 6 2/3. Since 1 2/3 is greater than 1, the product should be larger than 4, and it is. You can also multiply the parts separately: 4 × 1 = 4 and 4 × 2/3 = 8/3, and 4 + 2 2/3 = 6 2/3.

How do you multiply unit fractions by whole numbers?

A unit fraction has a numerator of 1, so the product is just the whole number over the denominator. For example, 7 × 1/2 = 7/2 = 3 1/2, and 7 × 1/7 = 1. When you sort unit-fraction products of the same whole number, a larger denominator means a smaller piece, so 7 × 1/8 is less than 7 × 1/4, which is less than 7 × 1/2.

How do you multiply fractions by whole numbers with cancellation?

Cancel a common factor between the whole number and the denominator before multiplying. In 12 × 5/6, the 12 and the 6 share a factor of 6, so 12 becomes 2 and 6 becomes 1, leaving 2 × 5/1 = 10. Without cancelling you would get 60/6, which also simplifies to 10. Cancelling keeps the numbers small and lowers the chance of an arithmetic slip.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• Add fractions with unlike denominators
• Add and subtract three fractions
• Fraction word problems
• Break fractions and mixed numbers apart
• Free Grade 5 FSA Math practice test