Question

choose the two expressions that are equivalent to 3.9 ÷ 1.3. 39 ÷ 130 39 ÷ 13 390 ÷ 130 390 ÷ 13

Explanation:

Step1: Recall the rule of equivalent division

When we multiply or divide both the dividend and the divisor by the same non - zero number, the quotient remains the same. Mathematically, if we have \(a\div b\), then \((a\times k)\div(b\times k)=a\div b\) and \((a\div k)\div(b\div k)=a\div b\) for \(k
eq0\).

Step2: Analyze \(3.9\div1.3\) and \(39\div13\)

Multiply both the dividend \(3.9\) and the divisor \(1.3\) by \(10\). We get \((3.9\times10)\div(1.3\times10)=39\div13\). So \(39\div13\) is equivalent to \(3.9\div1.3\).

Step3: Analyze \(3.9\div1.3\) and \(390\div130\)

Multiply both the dividend \(3.9\) and the divisor \(1.3\) by \(100\). We have \((3.9\times100)\div(1.3\times100) = 390\div130\). So \(390\div130\) is also equivalent to \(3.9\div1.3\).

Step4: Analyze \(39\div130\)

If we consider \(3.9\div1.3\), if we multiply the dividend by \(10\) and the divisor by \(100\), we get \(39\div130\). Since we multiplied the dividend and divisor by different numbers (\(10\) and \(100\)), the quotient will change. \(3.9\div1.3 = 3\), and \(39\div130=0.3\), so they are not equivalent.

Step5: Analyze \(390\div13\)

If we multiply the dividend \(3.9\) by \(100\) and the divisor \(1.3\) by \(10\), we get \(390\div13\). Since we multiplied the dividend and divisor by different numbers (\(100\) and \(10\)), the quotient will change. \(3.9\div1.3 = 3\), and \(390\div13 = 30\), so they are not equivalent.

Answer:

The two equivalent expressions are \(39\div13\) and \(390\div130\) (the checkboxes corresponding to \(39\div13\) and \(390\div130\) should be selected).