Question

lesson check
you know how?
the nearest millimeter, a cell phone is 84 mm long
46 mm wide. what is the ratio of the width to the
th?
angle measures are in the ratio 5 : 9. write
essions for the two angle measures in terms of
ariable x.
is the solution of the proportion \\(\frac{20}{x} = \frac{5}{3}\\)?
\\(= \frac{13}{b}\\) complete each equivalent proportion.
\\(= \frac{7}{\square}\\) \t b. \\(\frac{a}{\square} = \frac{7}{\square}\\) \t c. \\(\frac{7}{a} = \frac{\square}{\square}\\)
do you understand?

1. vocabulary what is the difference between a ratio

and a proportion?

1. open - ended the lengths of the sides of a triangle

in the extended ratio 3 : 6 : 7. what are two possible
sets of side lengths, in inches, for the triangle?

1. error analysis what is the error

in the solution of the proportion
shown at the right?

1. what is a proportion that has

means 6 and 18 and extremes
9 and 12?
practice and problem - solving exercises
write the ratio of the first measurement to the second measurement.

1. length of a tennis racket: 2 ft 4 in.

length of a table tennis paddle: 10 in.

1. height of a table tennis net: 6 in.

height of a tennis net: 3 ft

1. diameter of a table tennis ball: 40 mm

diameter of a tennis ball: 6.8 cm

1. length of a tennis court: 26 yd

length of a table tennis table: 9 ft

1. baseball a baseball team played 154 regular season games. the ratio of the

number of games they won to the number of games they lost was \\(\frac{5}{2}\\). how many
games did they win? how many games did they lose?

1. the measures of two supplementary angles are in the ratio 5 : 7. what is the

measure of the larger angle?

1. the lengths of the sides of a triangle are in the extended ratio 6 : 7 : 9. the

perimeter of the triangle is 88 cm. what are the lengths of the sides?

1. the measures of the angles of a triangle are in the extended ratio 4 : 3 : 2. what is

the measure of the largest angle?
algebra solve each proportion.

1. \\(\frac{1}{3} = \frac{x}{12}\\) \t 18. \\(\frac{9}{5} = \frac{3}{x}\\) \t 19. \\(\frac{4}{x} = \frac{5}{9}\\) \t 20. \\(\frac{y}{10} = \frac{15}{25}\\)
2. \\(\frac{11}{14} = \frac{b}{21}\\) \t 23. \\(\frac{3}{5} = \frac{6}{x + 3}\\) \t 24. \\(\frac{y + 7}{9} = \frac{8}{5}\\) \t 25. \\(\frac{5}{x - 3} = \frac{10}{x}\\)

Explanation:

Let's solve problem 17: $\boldsymbol{\frac{1}{3} = \frac{x}{12}}$

Step 1: Cross - Multiply

To solve the proportion $\frac{1}{3}=\frac{x}{12}$, we use the cross - multiplication property of proportions. If $\frac{a}{b}=\frac{c}{d}$, then $a\times d = b\times c$. Here, $a = 1$, $b = 3$, $c=x$ and $d = 12$. So we have $1\times12=3\times x$.
$$1\times12 = 3x$$

Step 2: Solve for x

Simplify the left - hand side of the equation $1\times12 = 3x$ to get $12 = 3x$. Then divide both sides of the equation by 3 to isolate $x$.
$$x=\frac{12}{3}$$
$$x = 4$$

Answer:

$x = 4$