Question

1. ratios, rates, proportions, percent score __/16 or ____%

a. john has 14 oranges and 7 apples. write the ratio of oranges to apples using three forms.

1. ______ 2. ____ 3. ____ score: __

b. what is the unit rate of oranges to apples? ____ score: __
c. what is an equivalent ratio to the rate given in question b? ____ score:____
d. percent skills – complete the table for decimals, fractions, percent

decimal	fraction	percent
.4
	\\(\frac{45}{100}\\)
		25%
score:	score:	score:

e. percent calculations

10% of 20 is:	130% of 100 is:	70% of 40 is:
score:	score:	score:

f. proportion problems – write a proportion and solve for the missing number.

1. if john drives his car 180 miles on 9 gallons of gas how many miles per gallon does his car use?
2. if sarah scores 8 goals in 10 soccer matches how many goals would she score in 15 matches?

Explanation:

Step1: Find orange-apple ratio forms

Oranges = 14, Apples = 7.

1. Colon form: $14:7$
2. Fraction form: $\frac{14}{7}$ (simplified to $\frac{2}{1}$)
3. Word form: $2$ to $1$ (simplified)

Step2: Calculate unit rate

Unit rate = $\frac{\text{Oranges}}{\text{Apples}} = \frac{14}{7} = 2$
Unit rate: 2 oranges per apple

Step3: Find equivalent ratio

Multiply both parts of $2:1$ by 2: $4:2$

Step4: Complete decimal-fraction-percent table

Row1 (Decimal = 0.4):

Fraction: $\frac{4}{10} = \frac{2}{5}$; Percent: $0.4 \times 100 = 40\%$

Row2 (Fraction = $\frac{45}{100}$):

Decimal: $\frac{45}{100} = 0.45$; Percent: $0.45 \times 100 = 45\%$

Row3 (Percent = 25%):

Decimal: $\frac{25}{100} = 0.25$; Fraction: $\frac{25}{100} = \frac{1}{4}$

Step5: Solve percent calculations

1. $10\% \text{ of } 20 = 0.10 \times 20 = 2$
2. $130\% \text{ of } 100 = 1.30 \times 100 = 130$
3. $70\% \text{ of } 40 = 0.70 \times 40 = 28$

Step6: Solve proportion problem 1

Let $x$ = miles per gallon. Proportion: $\frac{180}{9} = \frac{x}{1}$
$x = \frac{180}{9} = 20$

Step7: Solve proportion problem 2

Let $x$ = goals in 15 matches. Proportion: $\frac{8}{10} = \frac{x}{15}$
$x = \frac{8 \times 15}{10} = 12$

Answer:

A.

1. $14:7$
2. $\frac{2}{1}$
3. 2 to 1

B. 2 oranges per apple

C. $4:2$ (any equivalent ratio is acceptable)

D.

Decimal	Fraction	Percent
0.45	$\frac{45}{100}$	45%
0.25	$\frac{1}{4}$	25%

E.
10% of 20 is: 2
130% of 100 is: 130
70% of 40 is: 28

F.

1. Proportion: $\frac{180}{9} = \frac{x}{1}$; Answer: 20 miles per gallon
2. Proportion: $\frac{8}{10} = \frac{x}{15}$; Answer: 12 goals