Question

Describe how you would find partial products to multiply 6×2,194 then find the product

Answer 1

To find out the answer of the two multiplied products with the help of partial products we separate into unit based numbers so as to, for easier calculation and simplification with units of zeroes. So, in this case we are given the product of 6 times of 2,194.

Here we need to expand this product of higher number to zeroes and take aside the added numbers to come back to the original multiple of a product. That is:


`\huge{2,194}`


`\begin{bmatrix}2000 \\ + \\ 194 \end{bmatrix}`

We just separated and expanded the product to be multiplied by removing other units following it. Same goes for other units at Hundredth, tenth and unitary position.

Therefore,


`\begin{bmatrix}100 \\ + \\ 94 \end{bmatrix}`

For tenth term.


`\begin{bmatrix}90 \\ + \\ 4 \end{bmatrix}`

The terms after splitting and expanding the product before multiplication is:


`\begin{bmatrix}2000 \\ 100 \\ 90 \\ 4 \end{bmatrix}`

Multiply the product elements in individual manner and add the elements forged by individual multiplication to get the required solution.


`\therefore \quad \begin{bmatrix}2000 * 6 \\ 100 * 6 \\ 90 * 6 \\ 4 * 6 \end{bmatrix}`


`\begin{bmatrix}12000 \\ + \\ 600 \\ + \\ 540 \\ + \\ 24 \end{bmatrix}`


`\begin{bmatrix}12000 \\ + \\ 1140 \\ + \\ 24 \end{bmatrix}`


`\begin{bmatrix}12000 \\ + \\ 1164 \end{bmatrix}`


`\boxed{\mathbf{Final \: \: Answer \: = \: 13,164}}`

Hope it helps.

Answer 2

We need to find the products of 6×2,194 using partial products .

2,194 could be written in expended form as,

2194 = 2000 + 100 + 90 + 4.

Now, we need to multiply each of those number by 6 what we got after expanding.

2000 × 6 = 12000

100 × 6 = 600

90 × 6 = 540.

4 × 6 = 24.

Now, we can add all those products.

12000 + 600 + 540 + 24

= 13164.

Therefore, 6×2,194 = 13164.