Question

write the ratio as a fraction in simplest form.

1. 24 videos : 10 pictures
2. \\(\frac{3}{4}\\) inches to \\(\frac{2}{3}\\) inches

use the ratio table to find the unit rate (2 labels are needed)
3.

songs	0	3	6	12
cost	$0	$1.80	$3.60	$7.20

tell whether the ratios form a proportion (show work to prove why or why not).

1. \\(\frac{4}{7}\\) and \\(\frac{24}{35}\\)
2. \\(\frac{11}{12}\\) and \\(\frac{33}{36}\\)

tell whether the rates form a proportion (show work to prove why or why not).

1. \\(\frac{25\text{ cars}}{5\text{ days}}\\) \\(\frac{60\text{ cars}}{12\text{ days}}\\)
2. \\(\frac{14\text{ books}}{2\text{ boxes}}\\) \\(\frac{20\text{ books}}{3\text{ boxes}}\\)

use table to write proportion
8.

	cashews	peanuts
dollars	12	16
pounds	3	p

solve the proportion

1. \\(\frac{4}{17} = \frac{x}{51}\\)
2. \\(\frac{8}{9} = \frac{p}{81}\\)

Explanation:

Step1: Write ratio as fraction

$\frac{24}{10}$

Step2: Simplify by GCD (2)

$\frac{24\div2}{10\div2}=\frac{12}{5}$

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Step1: Write ratio as fraction

$\frac{\frac{5}{4}}{\frac{2}{3}}$

Step2: Multiply by reciprocal

$\frac{5}{4} \times \frac{3}{2}=\frac{15}{8}$

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Step1: Pick pair to find unit rate

$\frac{\$1.80}{3\text{ songs}}$

Step2: Calculate cost per song

$\frac{1.80}{3}=0.60$

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Step1: Cross-multiply the ratios

$4 \times 35 = 140$, $7 \times 24 = 168$

Step2: Compare cross products

$140
eq 168$, so no proportion

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Step1: Cross-multiply the ratios

$11 \times 36 = 396$, $12 \times 33 = 396$

Step2: Compare cross products

$396 = 396$, so proportion exists

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Step1: Simplify each rate

$\frac{25}{5}=5$ cars/day, $\frac{60}{12}=5$ cars/day

Step2: Compare simplified rates

$5 = 5$, so proportion exists

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Step1: Simplify each rate

$\frac{14}{2}=7$ books/box, $\frac{20}{3}\approx6.67$ books/box

Step2: Compare simplified rates

$7
eq \frac{20}{3}$, so no proportion

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Step1: Set up proportion from table

$\frac{12}{3}=\frac{16}{p}$

Step2: Solve for $p$

$12p = 16 \times 3$, $12p=48$, $p=\frac{48}{12}=4$

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Step1: Cross-multiply to solve

$4 \times 51 = 17x$

Step2: Calculate $x$

$204 = 17x$, $x=\frac{204}{17}=12$

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Step1: Cross-multiply to solve

$8 \times 81 = 9p$

Step2: Calculate $p$

$648 = 9p$, $p=\frac{648}{9}=72$

Answer:

1. $\frac{12}{5}$
2. $\frac{15}{8}$
3. $\$0.60$ per song
4. The ratios do not form a proportion.
5. The ratios form a proportion.
6. The rates form a proportion.
7. The rates do not form a proportion.
8. $p=4$
9. $x=12$
10. $p=72$