Question

p2. use cross - multiplication to solve for the missing quantity in the proportion. round to one decimal place if necessary.
a. \\(\frac{x}{4}=\frac{3}{8}\\)
b. \\(\frac{5}{a}=\frac{30}{12}\\)
c. \\(\frac{25}{4}=\frac{k}{8}\\)
d. \\(\frac{4}{5}=\frac{12}{w}\\)
e. \\(\frac{x}{6}=\frac{3}{8}\\)
f. \\(\frac{3}{4}=\frac{x}{9}\\)
g. \\(\frac{5280}{h}=\frac{1}{3}\\)
h. \\(\frac{3.78}{1}=\frac{l}{8}\\)
i. \\(\frac{16}{100}=\frac{5}{p}\\)

Explanation:

Part a

Step1: Cross - multiply the proportion $\frac{x}{4}=\frac{3}{8}$

We know that for a proportion $\frac{a}{b}=\frac{c}{d}$, cross - multiplying gives $a\times d = b\times c$. So for $\frac{x}{4}=\frac{3}{8}$, we have $x\times8=4\times3$.

Step2: Solve for $x$

Simplify the right - hand side: $4\times3 = 12$. Then we have the equation $8x = 12$. Divide both sides by 8: $x=\frac{12}{8}=\frac{3}{2}=1.5$.

Step1: Cross - multiply the proportion $\frac{5}{A}=\frac{30}{12}$

Using the cross - multiplication rule $\frac{a}{b}=\frac{c}{d}\Rightarrow a\times d=b\times c$, we get $5\times12 = A\times30$.

Step2: Solve for $A$

Simplify the left - hand side: $5\times12=60$. Then we have the equation $30A = 60$. Divide both sides by 30: $A=\frac{60}{30}=2$.

Step1: Cross - multiply the proportion $\frac{25}{4}=\frac{K}{8}$

Applying cross - multiplication, we have $25\times8 = 4\times K$.

Step2: Solve for $K$

Simplify the left - hand side: $25\times8 = 200$. Then the equation is $4K=200$. Divide both sides by 4: $K=\frac{200}{4}=50$.

Answer:

$x = 1.5$

Part b