Question

$\frac{1}{4}(15-6) + 3^{3}$ divided by 12


A) $2\frac{1}{2}$

B) 3

C) $4\frac{1}{2}$

D) $5\frac{7}{12}$

Answer 1

Answer:

$\textsf{C)} \quad 4\frac{1}{2}$

Step-by-step explanation:

PEMDAS

The PEMDAS rule is an acronym representing the order of operations in math:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Given expression:

$\dfrac{1}{4}(15-6)+\dfrac{3^3}{12}$

Carry out the operation inside the parentheses:

$\implies \dfrac{1}{4}(9)+\dfrac{3^3}{12}$

Carry out the exponent:

$\implies \dfrac{1}{4}(9)+\dfrac{3 \cdot 3 \cdot 3}{12}$

$\implies \dfrac{1}{4}(9)+\dfrac{9 \cdot 3}{12}$

$\implies \dfrac{1}{4}(9)+\dfrac{27}{12}$

Carry out the multiplication:

$\implies \dfrac{9}{4}+\dfrac{27}{12}$

Rewrite 27 as 3 · 9 and 12 as 3 · 4:

$\implies \dfrac{9}{4}+\dfrac{3 \cdot 9}{3 \cdot 4}$

Cancel the common term 3:

$\implies \dfrac{9}{4}+\dfrac{9}{4}$

$\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:$

$\implies \dfrac{9+9}{4}$

$\implies \dfrac{18}{4}$

Reduce the fraction by dividing the numerator and denominator by 2:

$\implies \dfrac{18 \div 2}{4 \div 2}$

$\implies \dfrac{9}{2}$

Rewrite 9 as 8 + 1:

$\implies \dfrac{8+1}{2}$

$\textsf{Apply the fraction rule} \quad \dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}:$

$\implies \dfrac{8}{2}+\dfrac{1}{2}$

Divide 8 by 2:

$\implies 4+\dfrac{1}{2}$

$\implies 4\frac{1}{2}$