Ratios and Rates Overview

A ratio table is a visual tool used to represent and solve problems involving equivalent ratios. It's like a chart that helps you see how different quantities relate to each other.

To create an equivalent ratio using a ratio table, you can either multiply or divide BOTH terms (the numbers in the ratio) in ONE column by the SAME amount. This ensures the ratio remains equivalent.

You can add or subtract numbers in two or more columns of a ratio table to find a specific equivalent ratio you need. It's like combining or removing parts to get the desired outcome.

Example: if you have a ratio 8:18, and need to find the equivalent ratio where the second term is 81, you can use the fact that 81 is a multiple of 9, and 9 is also a factor of 18.

A ratio that compares two quantities with different units.

A ratio that compares the amounts of two or more ingredients in a mixture.

The quantity with the largest value when comparing ratios.

The quantity with the smallest value when comparing ratios.

To simplify a ratio by dividing both parts by their greatest common factor.

The proportion of ingredients that results in the darkest shade of a mixture.

To find the amount of one quantity in a mixture when given the amount of another quantity and the ratio.

A measurement that expresses how far something can travel in a specific amount of time.

A ratio is a comparison of two quantities. Ratios can be expressed in several ways: using a colon - 3:4, as a fraction - 3/4, or using the word 'to' - 3 to 4.

Equivalent ratios have the same value, even if they are written with different numbers. For example, the ratios 1:2 and 2:4 are equivalent ratios.

A proportion is an equation that states that two ratios are equal. Proportion problems involve finding a missing value that makes the ratios equal.

To solve a proportion, you need to find the value of the missing variable so that the two ratios are equal. This can be done by cross-multiplying the numerators and denominators of the ratios.

A unit rate is a rate that has a denominator of 1. For example, 60 miles per hour is a unit rate because it expresses the distance traveled in one hour.

To find a unit rate, divide the numerator by the denominator. For example, to find the unit rate for a car that travels 120 miles in 2 hours, you divide 120 miles by 2 hours, which results in a unit rate of 60 miles per hour.

A rate is a comparison of two quantities with different units. For example, 60 miles per hour is a rate because it compares distance (miles) to time (hours).

A ratio problem involves using ratios to solve for an unknown quantity. This can be done by setting up a proportion and solving for the missing value.

Speed is the rate at which an object moves, usually measured in units like miles per hour (mph) or feet per second (fps).

To find the speed, divide the distance traveled by the time it took to travel that distance. Formula: Speed = Distance / Time

To find the distance traveled, multiply the speed by the time it took to travel that distance. Formula: Distance = Speed x Time

To find the time it took to travel a certain distance, divide the distance by the speed. Formula: Time = Distance / Speed

Average speed is the total distance traveled divided by the total time taken. It represents the overall speed over a longer period, even if the speed varied during that time.

The baseball traveled at 147.9 feet per second and took 0.41 seconds to reach home plate. Formula: Time = Distance / Speed; Time = 60.5 feet / 147.9 feet/second = 0.41 seconds

To find the average speed, divide the total distance traveled by the total time taken. Formula: Average Speed = Total Distance / Total Time

The hockey puck would take 1.2 seconds to travel the length of the rink. Formula: Time = Distance / Speed; Time = 200 feet / 166 feet/second = 1.2 seconds

To find the unit rate, divide the first quantity by the second quantity. This gives you the value of the first quantity for every single unit of the second quantity. Example: Divide $2.19 by 5 to find the cost per pound of potatoes.

To find equivalent ratios, multiply or divide both terms (the numbers in the ratio) by the same value. This keeps the ratio equivalent because the relationship between the quantities remains the same. Example: Multiply both numbers in the ratio 5 lbs to $2.19 by 2 to get the equivalent ratio: 10 lbs to $4.38.

You can find equivalent ratios by multiplying or dividing both terms (the numbers) in a ratio table by the same value. This helps to see the relationships between quantities and find missing values. Example: If you know the ratio is 2:5 in one row and 4:10 in another, you can see that the relationship is doubled in the second row.

If one pound equals 16 ounces, you need to solve 16 * 72.27 = 1156.32 ounces.

To find the time it takes to travel around the world at the speed of sound (760 miles per hour), divide the total distance (25,000 miles) by the speed (760 miles per hour): 25,000 miles / 760 miles per hour = 32.89 hours. Round to the nearest hour, the answer is 33 hours.

To calculate the cost of the diamond, multiply the weight of the diamond (41.3 carats) by the price per carat ($113,000): 41.3 carats * $113,000/carat = $4,666,900.

To calculate how long it takes light to travel from Earth to Mars, divide the distance (48,000,000 miles) by the speed of light (186,000 miles per second): 48,000,000 miles / 186,000 miles per second = 258 seconds. Round to the nearest second, the answer is 258 seconds.

To find out how much the basketball player earned for each minute of playing time, divide his total earnings ($1,000,000) by the total minutes played (76 games * 44 minutes/game = 3344 minutes): $1,000,000 / 3344 minutes = $299 per minute (rounded to the nearest dollar).

To determine the total cost of the gas, add the amount of gas used by each bus (26.1 gallons + 32.7 gallons = 58.8 gallons) and multiply that by the price per gallon ($1.229): 58.8 gallons * $1.229/gallon = $72.36.

The cost of the gas is rounded to the nearest cent, so the final answer is $72.36.

The given information is related to a world record but does not provide specific calculations or questions for flashcards.

This information is about a world record, but there are no specific measurable details or questions to turn into flashcards.