What is a ratio?

A ratio is a comparison between two quantities showing how many times one value contains or is contained within the other. For example, if there are 2 apples and 3 oranges, the ratio of apples to oranges is 2:3.

What is the formula for a proportion?

A proportion is an equation that states two ratios are equal. For example, if a:b = c:d, then a/b = c/d.

What is a quick trick to simplify a ratio?

To simplify a ratio, divide both terms by their greatest common divisor (GCD). For example, the ratio 8:12 simplifies to 2:3 by dividing both 8 and 12 by 4.

Solve: If the ratio of x to y is 3:5 and the sum of x and y is 40, what are the values of x and y?

x = 15 and y = 25.

What are the key properties of ratios?

1. A ratio remains unchanged if both terms are multiplied or divided by the same non-zero number. 2. Ratios can be compared like fractions. 3. If a/b = c/d, then the cross products ad = bc are equal.

What is the formula for the mean proportional between two numbers a and b?

The mean proportional between a and b is √(ab). For example, if a = 4 and b = 16, then the mean proportional is √(4 * 16) = √64 = 8.

What is a shortcut for solving problems involving multiple ratios?

To combine multiple ratios, use the product of numerators and denominators method. For example, if A:B = 2:3 and B:C = 4:5, you can find A:B:C by calculating A = 2, B = 3, and C = (3 * 5) / 4 = 15/4.

If the ratio of the ages of A to B is 4:5 and A is 20 years old, how old is B?

If the ratio A:B = 4:5, then B = (5/4) * A = (5/4) * 20 = 25 years old.

In a recipe, the ratio of flour to sugar is 3:2. If you have 6 cups of flour, how much sugar do you need?

Using the ratio 3:2, if flour = 6 cups, then sugar = (2/3) * 6 = 4 cups.

If a:b = 2:3 and b:c = 4:5, what is the combined ratio a:b:c?

First, find b in terms of a: b = (3/2)a. Now, substitute b into the second ratio: (3/2)a : c = 4:5. Thus, c = (5/4)(3/2)a = (15/8)a. Therefore, the combined ratio a:b:c = 16:24:30.