Question

lesson 6 extra
solve proportio
solve each proporti

1. \\(\frac{x}{15}=\frac{4}{5}\\)

1. \\(\frac{5}{t}=\frac{0.5}{0.3}\\)

1. \\(\frac{18}{4.5}=\frac{8}{f}\\)

Explanation:

Problem 1: $\boldsymbol{\frac{x}{15}=\frac{4}{5}}$

Step1: Cross - multiply

To solve the proportion $\frac{x}{15}=\frac{4}{5}$, we use the cross - multiplication property of proportions. If $\frac{a}{b}=\frac{c}{d}$, then $a\times d = b\times c$. So, $x\times5=15\times4$.

Step2: Solve for x

Simplify the right - hand side: $15\times4 = 60$. Then we have the equation $5x = 60$. Divide both sides of the equation by 5: $x=\frac{60}{5}=12$.

Step1: Cross - multiply

Using the cross - multiplication property for the proportion $\frac{5}{t}=\frac{0.5}{0.3}$, we get $5\times0.3=t\times0.5$.

Step2: Simplify and solve for t

First, calculate the left - hand side: $5\times0.3 = 1.5$. So the equation becomes $1.5 = 0.5t$. Divide both sides of the equation by $0.5$: $t=\frac{1.5}{0.5}=3$.

Step1: Cross - multiply

For the proportion $\frac{18}{4.5}=\frac{8}{f}$, cross - multiplying gives $18\times f=4.5\times8$.

Step2: Simplify and solve for f

Calculate the right - hand side: $4.5\times8 = 36$. So we have the equation $18f = 36$. Divide both sides of the equation by 18: $f=\frac{36}{18}=2$.

Answer:

$x = 12$

Problem 4: $\boldsymbol{\frac{5}{t}=\frac{0.5}{0.3}}$