Question

select all of the expressions equivalent to 3.5 ÷ 0.005. 35 ÷ 5 3500 ÷ 5 35 ÷ 0.05 (35/10) ÷ (5/100) (35/10) ÷ (5/1000)

Explanation:

Step1: Recall the rule of dividing decimals

To make the division of decimals easier, we can multiply both the dividend and the divisor by the same power of 10 to eliminate the decimal in the divisor. For \(3.5\div0.005\), we multiply both by 1000.
\(3.5\times1000 = 3500\), \(0.005\times1000 = 5\), so \(3.5\div0.005=(3.5\times1000)\div(0.005\times1000)=3500\div5\).

Step2: Check \(35\div0.05\)

Multiply both \(35\) and \(0.05\) by 100, we get \(35\times100 = 3500\), \(0.05\times100 = 5\), so \(35\div0.05=(35\times100)\div(0.05\times100)=3500\div5\), which is the same as \(3.5\div0.005\).

Step3: Check \(\frac{35}{10}\div\frac{5}{1000}\)

\(\frac{35}{10}=3.5\), \(\frac{5}{1000}=0.005\), so \(\frac{35}{10}\div\frac{5}{1000}=3.5\div0.005\).

Step4: Check other options

• For \(35\div5\), \(35\div5 = 7\), while \(3.5\div0.005 = 700\), so not equivalent.
• For \(\frac{35}{10}\div\frac{5}{100}\), \(\frac{35}{10}=3.5\), \(\frac{5}{100}=0.05\), \(3.5\div0.05 = 70

eq700\), so not equivalent.

Answer:

B. \(3500\div5\)
C. \(35\div0.05\)
E. \(\frac{35}{10}\div\frac{5}{1000}\)