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Since we already know that a fraction with the same denominators can be added to each other, we can understand that multiplying fractions with the whole number, n, means adding the same fraction n times.
See the fact file below for more information on the multiplying fractions with the whole numbers or alternatively, you can download our 28-page Numbers and Operations – Fractions: Multiplying Fractions with Whole Numbers CCSS 4.NF.4 worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
- At the end of the lesson, the student will learn how to multiply fractions with whole numbers by understanding that the numerator can actually be decomposed into 1xa, wherein a is the actual value of the numerator.
A NOTE FOR THE TEACHER
- When multiplying fractions with whole numbers, take note of the following:
- The multiplier and the multiplicands are a whole number and a fraction, respectively.
- Remember that a whole number, n, can be written as n/1.
- A whole number as a multiplier means we only multiply in the numerator.
- The value of the denominator is left unbothered.
- Since we already know that a fraction with the same denominators can be added to each other, we can understand that multiplying fractions with the whole number, n, means adding the same fraction n times.
- Consider ¼ + ¼ .
- We know that the sum will be equal to 2/4 because 1 + 1 = 2.
- Therefore, 2 will be the value in the numerator.
- Here, we added the same fraction twice. So, we can understand that we multiplied the numerator by 2:
- When dealing with the multiplication of fractions, the rule is you multiply based on where it is located in the fraction.
- Numerators can only be multiplied by numerators; denominators can only be multiplied by denominators.
- We do not need to get any least common multiple whatsoever.
- So, let’s go back to understanding why whole numbers are only multiplied in the numerator.
- Consider the whole number 3.
- We know that there are 3 wholes in this value because 1 + 1 + 1 = 3.
- We know that 1 can be written in fraction form as 1/1, thus; having the whole number 3 means having 1/1 + 1/1 + 1/1 = 3/1.
- Since we know we only multiply based on whether it is located in the numerator or the denominator, we can now understand that whole numbers always multiply in the numerator values.
- Consider 2/10 x 4.
- We can understand it to be 2/5 added 4 times:
- 2/10 + 2/10 + 2/10 + 2/10 = 8/10
- We can also understand it to be:
- (2/10) x (4/1) = (2 x 4)/(10 x 1) = 8/10
- Visually, we can see that we can shade 2/10, 4 times in a fraction model.
- Therefore, any fraction, a/b, multiplied by any whole number, n, will be:
- (a/b) x n = (a/b) x (n/1) = (a x n) / b
Numbers and Operations – Fractions: Multiplying Fractions with Whole Numbers CCSS 4.NF.4 Worksheets
This is a fantastic bundle that includes everything you need to know about Numbers and Operations – Fractions: Multiplying Fractions with Whole Numbers across 25 in-depth pages. These are ready-to-use worksheets that align with the Common Core CCSS code 4.NF.4 for Numbers and Operations – Fractions: Multiplying Fractions with Whole Numbers.
Table of contents:
- A lesson plan
- Warm-up activity
- Math theory explained
- Assisted learning activities
- Independent learning activities
- Extension activities and games
- Answer keys
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Use With Any Curriculum
These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.