Question

problem 1
select all of the expressions that are equivalent to
$4.5 \div 0.08$.
$\frac{45}{100} \div \frac{8}{100}$
$45 \div 8$
$\frac{450}{100} \div \frac{8}{100}$
$450 \div 8$
$45 \div 0.8$

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 non - zero number. According to the property of division: \(a\div b=(a\times n)\div(b\times n)\), where \(n
eq0\).

For the expression \(4.5\div0.08\):

• If we multiply both \(4.5\) and \(0.08\) by \(100\), we get \((4.5\times100)\div(0.08\times100)=450\div8\). Also, \(4.5=\frac{45}{10}\), \(0.08 = \frac{8}{100}\), and \(4.5\times100=\frac{45}{10}\times100 = 450=\frac{450}{100}\times100\), so \(\frac{450}{100}\div\frac{8}{100}\) is equivalent to \(4.5\div0.08\) (because dividing by a fraction is multiplying by its reciprocal, and when we have \(\frac{a}{c}\div\frac{b}{c}=\frac{a}{c}\times\frac{c}{b}=\frac{a}{b}\), here \(c = 100\), \(a = 450\), \(b = 8\)).
• If we multiply both \(4.5\) and \(0.08\) by \(10\), we get \((4.5\times10)\div(0.08\times10)=45\div0.8\).

Now let's check the other options:

• For \(\frac{45}{100}\div\frac{8}{100}\), \(\frac{45}{100}=0.45\), \(\frac{8}{100}=0.08\), so \(0.45\div0.08

eq4.5\div0.08\).

• For \(45\div8\), \(45\div8 = 5.625\), and \(4.5\div0.08=56.25\), \(45\div8

eq4.5\div0.08\).

Step2: Evaluate each option

• Option 1: \(\frac{45}{100}\div\frac{8}{100}=0.45\div0.08

eq4.5\div0.08\), so this option is incorrect.

• Option 2: \(45\div8 = 5.625\), \(4.5\div0.08 = 56.25\), so this option is incorrect.
• Option 3: \(\frac{450}{100}\div\frac{8}{100}=\frac{450}{100}\times\frac{100}{8}=\frac{450}{8}=450\div8\), and \(450\div8 = 56.25\), \(4.5\div0.08=56.25\), so this option is correct.
• Option 4: \(450\div8 = 56.25\), \(4.5\div0.08 = 56.25\), so this option is correct.
• Option 5: \(45\div0.8=\frac{45}{0.8}=\frac{45\times10}{0.8\times10}=\frac{450}{8}=56.25\), and \(4.5\div0.08 = 56.25\), so this option is correct.

Answer:

\(\frac{450}{100}\div\frac{8}{100}\), \(450\div8\), \(45\div0.8\) (i.e., the third, fourth, and fifth options)