Question

1. \\(\frac{2}{3}(6a + 9) = 20.4\\) \\(\boxed{} + \boxed{} = \boxed{}\\) \\(a = \boxed{}\\)

Explanation:

Step1: Divide both sides by 2

To isolate the expression in the parentheses, we divide both sides of the equation \(\frac{2}{3}(6a + 9)=20.4\) by 2.
\(\frac{\frac{2}{3}(6a + 9)}{2}=\frac{20.4}{2}\)
Simplifying the left side, the 2 in the numerator and denominator cancels out for the fraction part, giving \(\frac{1}{3}(6a + 9)\), and the right side is \(10.2\). So we have \(\frac{1}{3}(6a + 9)=10.2\)

Step2: Multiply both sides by 3

To get rid of the fraction \(\frac{1}{3}\) on the left side, we multiply both sides of the equation \(\frac{1}{3}(6a + 9)=10.2\) by 3.
\(3\times\frac{1}{3}(6a + 9)=10.2\times3\)
The 3 in the numerator and denominator on the left side cancels out, leaving \(6a + 9\), and the right side is \(30.6\). So we have \(6a+9 = 30.6\)

Step3: Subtract 9 from both sides

To isolate the term with \(a\), we subtract 9 from both sides of the equation \(6a + 9=30.6\).
\(6a+9 - 9=30.6 - 9\)
Simplifying both sides, we get \(6a=21.6\)

Step4: Divide both sides by 6

To solve for \(a\), we divide both sides of the equation \(6a = 21.6\) by 6.
\(\frac{6a}{6}=\frac{21.6}{6}\)
Simplifying, we find that \(a = 3.6\)

Answer:

First, \(\frac{2}{3}(6a + 9)\div2=20.4\div2\) gives \(\frac{1}{3}(6a + 9)=10.2\); then \(3\times\frac{1}{3}(6a + 9)=10.2\times3\) gives \(6a + 9 = 30.6\); then \(6a+9 - 9=30.6 - 9\) gives \(6a=21.6\); finally \(\frac{6a}{6}=\frac{21.6}{6}\) gives \(a = 3.6\)

The first blank (after dividing by 2) is \(10.2\), the second blank (the expression in parentheses after multiplying by 3) is \(30.6\), and \(a = 3.6\)