Swap the Letter, Find the Value

How can a calculation containing a letter have one exact answer? It looks like a puzzle... but the letter comes with a secret value. Swap that value into the right place, follow the operations, and the mystery disappears. Let's reveal how it works!

Evaluating means finding the value of an expression. You are given the letter's value, so you do not need to solve an equation or discover what the letter means. Your first job is simply to SUBSTITUTE. Replace the letter with the number supplied. Look at five a plus three, when a equals four. Put four where the a was. Now you have five times four, plus three. A number beside a letter means multiplication, even when no multiplication sign is printed. Make that hidden operation visible. Here is the trap. Five a does not become fifty-four when a is four. Do not join the five and four as neighbouring digits. Five a means five TIMES four, which is twenty. Then add three, giving twenty-three. Substitute first. Calculate second.

Now tackle a full eleven plus example. Evaluate six m minus nine when m equals seven. Seven is already supplied, so you are not trying to find m. You are finding the value of the whole expression. Begin with the substitution. Start with six m minus nine. Replace ONLY the m with seven. The six stays. The minus nine stays. Because six m means six times m, the new calculation is six times seven, minus nine. Check it carefully before you calculate. Multiplication comes first. Six times seven is forty-two, so the expression becomes forty-two minus nine. Now subtract... forty-two minus nine is thirty-three. Therefore, when m equals seven, six m minus nine has the value thirty-three. One neat substitution, one accurate calculation, answer found!

Keep this routine ready: replace the letter with its supplied value, show any hidden multiplication, then calculate in the correct order. Never stick the neighbouring numbers together. You are not solving for the letter... you are evaluating the expression. Swap, calculate, succeed!