Question

which expressions have a quotient of 6?
select all that apply.
a. $5.4 \div 0.9$
b. $0.54 \div 0.9$
c. $5.4 \div 0.09$
d. $0.54 \div 0.09$

Explanation:

Step1: Calculate A: \(5.4 \div 0.9\)

To divide decimals, we can multiply numerator and denominator by 10 to eliminate decimals: \(\frac{5.4\times10}{0.9\times10}=\frac{54}{9} = 6\). So A has a quotient of 6.

Step2: Calculate B: \(0.54 \div 0.9\)

Multiply numerator and denominator by 100: \(\frac{0.54\times100}{0.9\times100}=\frac{54}{90}=0.6\). So B does not have a quotient of 6.

Step3: Calculate C: \(5.4 \div 0.09\)

Multiply numerator and denominator by 100: \(\frac{5.4\times100}{0.09\times100}=\frac{540}{9}=60\). So C does not have a quotient of 6.

Step4: Calculate D: \(0.54 \div 0.09\)

Multiply numerator and denominator by 100: \(\frac{0.54\times100}{0.09\times100}=\frac{54}{9}=6\). So D has a quotient of 6.

Answer:

A. \(5.4 \div 0.9\), D. \(0.54 \div 0.09\)