Question

3 the volume is 84m³. what is the missing dimension (x)?
4 solve 1\frac{3}{8}=\frac{\square}{\square} 2\frac{4}{5}=\frac{\square}{\square}
+\frac{1}{3}=\frac{\square}{\square} -\frac{1}{3}=\frac{\square}{\square}

Explanation:

Question 3

Step1: Recall the volume formula for a rectangular prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). Here, \(V = 84m^{3}\), \(l = 6m\), \(h=3\frac{1}{2}=\frac{7}{2}m\), and \(w = x\). So the equation is \(84=6\times x\times\frac{7}{2}\).

Step2: Simplify the right - hand side of the equation

First, calculate \(6\times\frac{7}{2}\). \(6\times\frac{7}{2}=\frac{6\times7}{2}=21\). The equation becomes \(84 = 21x\).

Step3: Solve for \(x\)

Divide both sides of the equation \(84 = 21x\) by 21. \(x=\frac{84}{21}\).

Step1: Convert the mixed number to an improper fraction

\(1\frac{3}{8}=\frac{1\times8 + 3}{8}=\frac{11}{8}\).

Step2: Find a common denominator

The common denominator of 8 and 3 is \(8\times3=24\). \(\frac{11}{8}=\frac{11\times3}{8\times3}=\frac{33}{24}\) and \(\frac{1}{3}=\frac{1\times8}{3\times8}=\frac{8}{24}\).

Step3: Add the fractions

\(\frac{33}{24}+\frac{8}{24}=\frac{33 + 8}{24}=\frac{41}{24}\).

Second part (\(2\frac{4}{5}-\frac{1}{3}\))

Step1: Convert the mixed number to an improper fraction

\(2\frac{4}{5}=\frac{2\times5+4}{5}=\frac{14}{5}\).

Step2: Find a common denominator

The common denominator of 5 and 3 is \(5\times3 = 15\). \(\frac{14}{5}=\frac{14\times3}{5\times3}=\frac{42}{15}\) and \(\frac{1}{3}=\frac{1\times5}{3\times5}=\frac{5}{15}\).

Step3: Subtract the fractions

\(\frac{42}{15}-\frac{5}{15}=\frac{42-5}{15}=\frac{37}{15}\).

Answer:

\(x = 4m\)

Question 4

First part (\(1\frac{3}{8}+\frac{1}{3}\))