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Quiz 1
1. Write as an algebraic expression: "12 more than a number".
Solution: Since "a number" describes a variable, let us use $x$ to denote it. Then "12 more than a number" means "12 more than x". We interpret "more than" as "addition" and so we get the algebraic expression
$$12 + x.$$
Note: if you chose a different symbol than "$x$", that's perfectly fine! All that matters is that you define your symbols.
2. Write an equation that represents "twice a number minus 2 is 15".
Solution: Here "a number" describes a variable, let us use $x$ to denote it. Then "twice a number minus 2 is 15" means "twice $x$ minus 2 is 15". Now "twice $x$" means $2x$. Recall the word "is" refers to the "$=$" sign. Therefore the sentence can be represented by the equation
$$2x - 2 = 15.$$
3. Which law(s) of algebra did I use to rewrite the expression $(a+b)(c+d)$ as $(c+d)(b+a)$?
Solution: First I used the commutative law of multiplication to write $(a+b)(c+d)=(c+d)(a+b)$. Now I apply the commutative law of addition to the expression $a+b$ to get $a+b=b+a$. Therefore we see
$$(a+b)(c+d)=(c+d)(b+a).$$
4. Evaluate $2x+7w$ where $x=2$ and $w=4$.
Solution: Substituting $x=2$ and $w=4$ into the algebraic expression $2x+7w$ yields
$$2(2)+7(4)=4+28=32.$$
5. Find the prime factorization of $48$.
Solution: Make a factorization tree or factor the number:
$$48 = 2(24) = 2(2)(12) = 2(2)(2)(6) = 2(2)(2)(2)(3).$$
Note: You may also express the final answer using exponents (we have not covered them yet!) as $2^4(3)$.
