Adding Two Dimensional Vectors with Fractional Components: A Detailed Example
In this guide, we’ll explore the step-by-step process of adding two-dimensional vectors with fractional components, including the essential step of finding a common denominator by multiplying by 1 in different forms.
| Vector C = (3/5, 4/7) | Starting with vector C, with fractional components 3/5 and 4/7 in the x and y directions, respectively. |
| Vector D = (5/6, 2/3) | Next, vector D, with fractional components 5/6 and 2/3 in the x and y directions, respectively. |
| 3/5 * 6/6 + 5/6 * 5/5 | Multiply the x-components by 1 in different forms to find a common denominator: 3/5 * 6/6 (which is 1) and 5/6 * 5/5 (which is 1). |
| 18/30 + 25/30 = 43/30 | Add the x-components, resulting in 43/30 for the sum of the x-components. |
| 4/7 * 3/3 + 2/3 * 7/7 | Multiply the y-components by 1 in different forms to find a common denominator: 4/7 * 3/3 (which is 1) and 2/3 * 7/7 (which is 1). |
| 12/21 + 14/21 = 26/21 | Add the y-components, resulting in 26/21 for the sum of the y-components. |
| Resultant Vector = (43/30, 26/21) | The resultant vector, obtained by adding the x and y components of vectors C and D, is (43/30, 26/21). |
This detailed example of adding two-dimensional vectors with fractional components provides a clear and comprehensive explanation of the process, including the essential step of finding a common denominator by multiplying by 1 in different forms. By breaking down the process into individual steps, we make this essential mathematical concept accessible to students, educators, and professionals in various fields. Explore more mathematical guides and tutorials on our website to continue building your mathematical expertise!
Adding Two Dimensional Vectors with Fractional Components: A Detailed Example
In this guide, we’ll explore the step-by-step process of adding two-dimensional vectors with fractional components, including the essential step of finding a common denominator by multiplying by 1 in different forms.
| Vector C = (3/5, 4/7) | Starting with vector C, with fractional components 3/5 and 4/7 in the x and y directions, respectively. |
| Vector D = (5/6, 2/3) | Next, vector D, with fractional components 5/6 and 2/3 in the x and y directions, respectively. |
| 3/5 * 6/6 + 5/6 * 5/5 | Multiply the x-components by 1 in different forms to find a common denominator: 3/5 * 6/6 (which is 1) and 5/6 * 5/5 (which is 1). |
| 18/30 + 25/30 = 43/30 | Add the x-components, resulting in 43/30 for the sum of the x-components. |
| 4/7 * 3/3 + 2/3 * 7/7 | Multiply the y-components by 1 in different forms to find a common denominator: 4/7 * 3/3 (which is 1) and 2/3 * 7/7 (which is 1). |
| 12/21 + 14/21 = 26/21 | Add the y-components, resulting in 26/21 for the sum of the y-components. |
| Resultant Vector = (43/30, 26/21) | The resultant vector, obtained by adding the x and y components of vectors C and D, is (43/30, 26/21). |
This detailed example of adding two-dimensional vectors with fractional components provides a clear and comprehensive explanation of the process, including the essential step of finding a common denominator by multiplying by 1 in different forms. By breaking down the process into individual steps, we make this essential mathematical concept accessible to students, educators, and professionals in various fields. Explore more mathematical guides and tutorials on our website to continue building your mathematical expertise!
