Question

Using only the addition and multiplication operations with the numbers 1, 2, 3, and 4 each exactly once,

it is possible to build a numeric expression (with parentheses to show the order used to build the
expression) that evaluates to 21. For example, 1 + ((2 + 3) · 4) is one such expression.
a. Build two more numeric expressions that evaluate to 21 using the criteria above. Both must be
different from the example given.
b. In both of your expressions, replace 1 with a, 2 with b, 3 with c, and 4 with d to get two algebraic
expressions. For example, a + ((b + c) · d) shows the replacements for the example given.

Answer 1

Answer and Step-by-step explanation:

criteria: addition and multiplication operations only

1 + ((2 + 3) · 4) = 21

a. Build two more numeric expressions that evaluate to 21 using the criteria above.

1) (1+2).(3+4) = 3.7 = 21

2) (1+2+4).3 = 7.3 = 21

b. In both of your expressions, replace 1 with a, 2 with b, 3 with c, and 4 with d to get two algebraic expressions.

1) (a+b).(c+d)

2) (a+b+d).c