Question 1

Write each ratio in two other ways. 6 to 5

Accepted Answer

C) $\frac { 6 } { 5 }$ ; $6 : 5$ correctly represents the ratio 6 to 5 in both fraction and ratio form, maintaining the same relationship.

Question 2

Write a ratio from the sentence and simplify it, possible. Frantisek adds 2 cans of milk to a can of soup.

Accepted Answer

The ratio of cans of milk to cans of soup is 2:1, meaning for every can of soup, there are 2 cans of milk added.

Question 3

Simplify the ladder ratio below. State whether it is a safe ladder ratio. If the ladder ratio is greater than 4:1 it is likely to tip. If the ladder ratio is less than 4:1, it is likely to slip. 12 feet to 2.4 feet

Accepted Answer

To simplify the ratio, we divide both values by the greatest common factor, which is 2. This gives us a ratio of 5:1. Since the ladder ratio is greater than 4:1, it is likely to tip. Therefore, the best choice is C.

Question 4

Change the units to like units with a unit analysis multiplication, and simplify the ratio. Useful facts:
1 yard = 3 feet
1 mile = 5,280 feet
1 yard = 36 inches
2 feet to 3 inches

Accepted Answer

The answer of Change the units to like units with...

Question 5

Solve. $\frac { 18 } { 24 } = \frac { n } { 8 }$

Accepted Answer

To solve this proportion, we can use cross-multiplication. That means we multiply the numerator of the first fraction by the denominator of the second fraction, and set it equal to the numerator of the second fraction times the denominator of the first fraction. In other words:

$$\frac{18}{24} = \frac{n}{8}$$

$$18 \cdot 8 = 24 \cdot n$$

$$144 = 24n$$

Dividing both sides by 24, we get:

$$n = 6$$

Therefore, the best choice is D, 6.

Question 6

Solve. Round to the nearest hundredth. $\frac { 3 } { 4 } = \frac { 11 } { n }$

Accepted Answer

To solve the equation $\frac{3}{4} = \frac{11}{n}$, cross-multiply to get $3n = 4 \times 11$. Simplifying, $3n = 44$, and dividing both sides by 3 gives $n = \frac{44}{3}$, which is approximately 14.67 when rounded to the nearest hundredth.

Question 7

Jasmin budgets the following each month: rent, $400; utilities, $140; food, $320; clothes, $110; car payment and insurance, $470; gasoline, $60; savings, $20; other $80. What percent of her total monthly budget does she spend on car payment and insurance?

Accepted Answer

To find the percent of the budget spent on car payment and insurance, we must first add up all the expenses:

Total monthly budget = $400 + $140 + $320 + $110 + $470 + $60 + $20 + $80 
= $1600

Now we can find the percentage spent on car payment and insurance:

Percentage spent on car payment and insurance = 
($470 ÷ $1600) × 100% ≈ 29.375% ≈ 29 $\frac {3}{8}$%

Therefore, the answer is (C).

Question 8

Write the staircase slope in fraction notation and simplify it to lowest terms. Both measures are in inches, so units may be disregarded. 6.25 to 11.75

Accepted Answer

To find the slope of the staircase, we need to divide the rise (vertical height) by the run (horizontal length). In this case, the rise is 11.75 - 6.25 = 5.5 inches, and the run is the length of the horizontal tread, which is not given. Therefore, we cannot simplify the fraction any further, and the answer is $\frac{5.5}{11}$ which reduces to $\frac{25}{47}$.

Question 9

Solve. $\frac { n } { 6 } = \frac { 5 } { 15 }$

Accepted Answer

To solve, we can cross-multiply to get $5n=90$, and then divide by 45 to get $n=2$. Therefore, the answer is choice C.

Question 10

Solve. Round to the nearest hundredth. $\frac { 1 } { 4 } = \frac { n } { 14 }$

Accepted Answer

To solve for $n$, cross-multiply: $1 \times 14 = 4 \times n$, which simplifies to $14 = 4n$. Dividing both sides by 4 gives $n = \frac{14}{4} = 3.5$.

Question 11

Notation can make problems look harder than they are. Water with formula H₂O has 2 atoms of hydrogen for each atom of oxygen. A molecule of nicotine, C₁₀H₁₄N₂, has 10 atoms of carbon, 14 atoms of hydrogen, and 2 atoms of nitrogen. What is the ratio of atoms in the following chemical formula? (Ca is calcium) CaCO₃

Accepted Answer

The formula CaCO₃ consists of one calcium atom, one carbon atom, and three oxygen atoms. Therefore, the ratio of atoms is 1 calcium:1 carbon:3 oxygen, which is option D.

Question 12

Write a ratio of fertilizer to water and simplify it, if possible. Useful facts:
16 tablespoons = 1 cup
16 cups = 1 gallon
Sylvia adds 8 tablespoons of plant fertilizer to a gallon of water.

Accepted Answer

First, convert the tablespoons of fertilizer and the gallon of water to the same unit. 8 tablespoons of fertilizer is half a cup (since 16 tablespoons = 1 cup), and 1 gallon of water is 16 cups. Therefore, the ratio of fertilizer to water is 1/2 cup to 16 cups, which simplifies to 1:32.

Question 13

Change 100 miles per hour to feet per second. Start with a fraction showing miles per hour, and then set up the unit analysis product of fractions. Useful facts:
5280 feet = 1 miles
60 seconds = 1 minute
60 minutes = 1 hour

Accepted Answer

To convert 100 miles per hour to feet per second, use the given conversions: $100 \frac{\text{miles}}{\text{hour}} \times \frac{5280 \text{ feet}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3600 \text{ seconds}} = 146 \frac{2}{3} \text{ feet per second}$.

Question 14

Write a ratio of water to fruit drink and simplify it, if possible. Sergei adds 2 cans of water to each can of frozen fruit drink.

Accepted Answer

The ratio of water to fruit drink is 2 cans of water for every 1 can of fruit drink, which simplifies to 2 to 1.

Question 15

Change the units to like units with a unit analysis multiplication, and simplify the ratio. Useful facts:
1,000 milliliters = 1 liter
1,000 meters = 1 kilometer
5,280 feet = 1 mile
750 meters to 2 kilometers

Accepted Answer

750 meters is 0.75 kilometers. The ratio of 0.75 kilometers to 2 kilometers is $\frac{0.75}{2} = \frac{3}{8}$.

Question 16

Write the ratio in two other ways. 9 : 8

Accepted Answer

The ratio 9:8 can be written as the fraction $\frac{9}{8}$ and in words as "9 to 8".

Question 17

Write each ratio in two other ways. $\frac { 5 } { 10 }$

Accepted Answer

The original ratio is already simplified, so we don't need to simplify further or create more fractions with different numerators. Choices A, B, D, and E all have different numerators, which means they are not equivalent ratios to the original. Therefore, the best choice is C, which is the same simplified ratio as the original.

Question 18

Solve. $\frac { 6 } { n } = \frac { 10 } { 15 }$

Accepted Answer

To solve the equation $\frac{6}{n} = \frac{10}{15}$, first simplify the fraction on the right side: $\frac{10}{15} = \frac{2}{3}$. Then, cross-multiply to solve for $n$: $6 \times 3 = 10 \times n$, which simplifies to $18 = 10n$. Dividing both sides by 10 gives $n = \frac{18}{10} = 1.8$, which is not among the options provided. It seems there was a mistake in my calculation. Let's correct that: Cross-multiplying correctly, we get $6 \times 15 = 10 \times n$, leading to $90 = 10n$. Dividing both sides by 10 gives $n = 9$, which matches option D.

Question 19

Find the slope ratio for the equation. $y = 1.75 x + 5.75$

Accepted Answer

The slope of the equation $y = mx + b$ is represented by $m$. For the equation $y = 1.75x + 5.75$, the slope $m = 1.75$, which can also be written as $\frac{7}{4}$.

Question 20

Solve. $\frac { 2 } { 6 } = \frac { 4 } { n }$

Accepted Answer

Cross-multiply to solve for $ n $: $ 2n = 24 $, so $ n = 12 $.

Quiz 4: Ratios, Rates, and Proportional Reasoning

Write each ratio in two other ways. 6 to 5

Write a ratio from the sentence and simplify it, possible. Frantisek adds 2 cans of milk to a can of soup.

Simplify the ladder ratio below. State whether it is a safe ladder ratio. If the ladder ratio is greater than 4:1 it is likely to tip. If the ladder ratio is less than 4:1, it is likely to slip. 12 feet to 2.4 feet

Change the units to like units with a unit analysis multiplication, and simplify the ratio. Useful facts: 1 yard = 3 feet 1 mile = 5,280 feet 1 yard = 36 inches 2 feet to 3 inches

Solve. 1824=n8\frac { 18 } { 24 } = \frac { n } { 8 }2418​=8n​

Solve. Round to the nearest hundredth. 34=11n\frac { 3 } { 4 } = \frac { 11 } { n }43​=n11​

Jasmin budgets the following each month: rent, $400; utilities, $140; food, $320; clothes, $110; car payment and insurance, $470; gasoline, $60; savings, $20; other $80. What percent of her total monthly budget does she spend on car payment and insurance?

Write the staircase slope in fraction notation and simplify it to lowest terms. Both measures are in inches, so units may be disregarded. 6.25 to 11.75

Solve. n6=515\frac { n } { 6 } = \frac { 5 } { 15 }6n​=155​

Solve. Round to the nearest hundredth. 14=n14\frac { 1 } { 4 } = \frac { n } { 14 }41​=14n​

Write a ratio of fertilizer to water and simplify it, if possible. Useful facts: 16 tablespoons = 1 cup 16 cups = 1 gallon Sylvia adds 8 tablespoons of plant fertilizer to a gallon of water.

Change 100 miles per hour to feet per second. Start with a fraction showing miles per hour, and then set up the unit analysis product of fractions. Useful facts: 5280 feet = 1 miles 60 seconds = 1 minute 60 minutes = 1 hour

Write a ratio of water to fruit drink and simplify it, if possible. Sergei adds 2 cans of water to each can of frozen fruit drink.

Change the units to like units with a unit analysis multiplication, and simplify the ratio. Useful facts: 1,000 milliliters = 1 liter 1,000 meters = 1 kilometer 5,280 feet = 1 mile 750 meters to 2 kilometers

Write the ratio in two other ways. 9 : 8

Write each ratio in two other ways. 510\frac { 5 } { 10 }105​

Solve. 6n=1015\frac { 6 } { n } = \frac { 10 } { 15 }n6​=1510​

Find the slope ratio for the equation. y=1.75x+5.75y = 1.75 x + 5.75y=1.75x+5.75

Solve. 26=4n\frac { 2 } { 6 } = \frac { 4 } { n }62​=n4​