# How to present the order of factors and summands for the usual multiplication procedure

In the following multiplication example,

\begin{align} 34\;& \\\underline{\times\;\; 7\;}& \end{align}

first one would multiply the units digits, producing the partial product $28$ as follows:

\begin{align} \color{maroon}{2}\;\;\;\!\>\!\\ 34\;& \\\underline{\times\;\; 7\;}& \\\color{maroon}{8}\;& \end{align}

How would this partial product operation best be described?

$$( 4 \times 7 ) \qquad\text{or}\qquad ( 7 \times 4 )$$

Similarly, how would the next partial product operation, which adds the carry, best be described?

$$( 3 \times 7 ) + 2 \quad\text{or}\quad ( 7 \times 3 ) + 2 \quad\text{or}\quad 2 + ( 3 \times 7 ) \quad\text{or}\quad 2 + ( 7 \times 3 )$$

• I suppose it would depend on what your country's department of education says. Perhaps you should try to get a copy of their official textbook?
– JRN
Jul 18, 2018 at 23:59
• Thanks everyone for the edits and for your thoughtful answers and comments. Jul 20, 2018 at 14:36

Following your example, in the first step, reading downward the order is $4$ then $7$, so write $(4 \times 7)$. In the second step, the order is $2$ then $3$ then $7$, so write $2+(3 \times 7).$