Give reasons for each of the following steps:
16 + 31= ( 1. 10 + 6) + (3.10 + 1)
= ( 1. 10 + 3. 10) + (6 + 1)
= (1+ 3) 10 + (6+ 1)
= 4 .10 + 7
= 47
Step 1: Breaking down the numbers into place value form
To add 16 and 31, we can break down each number into its place value form. The number 16 can be written as (1 * 10) + (6 * 1), and the number 31 can be written as (3 * 10) + (1 * 1).
Step 2: Distributing the multiplication
Next, we distribute the multiplication to simplify the expression. We can rewrite the equation as (1 * 10 + 3 * 10) + (6 + 1).
Step 3: Simplifying the addition inside parentheses
Inside the parentheses, we perform the addition operation. So, (1 * 10 + 3 * 10) becomes (1 + 3) * 10, and (6 + 1) is simply 7.
Step 4: Simplifying the expression
Finally, we simplify the expression further. (1 + 3) * 10 is equal to 4 * 10, which is 40. Therefore, the expression becomes 40 + 7.
Step 5: Adding the final numbers
To get the final answer, we add 40 and 7 together. The sum of 40 + 7 is 47.