# How do you rewrite 2 \times 37 as the sum of two products?

Jul 6, 2018

Set 37 as 100-63 giving: $2 \times 37 \to 2 \times \left(100 - 63\right)$

$\left[200\right] + \left[- 126\right]$

#### Explanation:

$2 \times \left(37\right) = 74$

'Split' the 37 (partition it) into the sum of any two numbers.

Just to be different I select such that one of them is negative.

Set $37 = \textcolor{red}{100 - 63}$ so we have:

$\textcolor{g r e e n}{2 \times \left(\textcolor{red}{37}\right) \textcolor{w h i t e}{\text{d")-> color(white)("d}} 2 \times \left(\textcolor{red}{100 - 63}\right)}$

Multiply everything inside the brackets by the 2 that is outside.

$\textcolor{g r e e n}{\left[2 \times \textcolor{red}{100}\right] + \left[2 \times \left(\textcolor{red}{- 63}\right)\right]}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Check}}$

$\left[200\right] - \left[126\right] = 74 \leftarrow \text{ As required}$

Jul 6, 2018

color(brown)(=> 2 * 30 + 2 * 7

#### Explanation:

$2 \cdot 37 = \left(2 \cdot \left(30 + 7\right)\right)$ Distributive Law

$\implies 2 \cdot 30 + 2 \cdot 7$

We can write many such sum of two products.

$\implies 60 + 14 = 74$