What is a ratio?

A ratio is a comparison of two quantities by division. It shows how much of one quantity there is compared to another. For example, the ratio of 4 to 5 can be written as 4:5.

How do you simplify a ratio?

To simplify a ratio, divide both terms of the ratio by their greatest common divisor (GCD). For instance, the ratio 8:12 can be simplified by dividing both terms by 4, resulting in 2:3.

What is a proportion?

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

If 3 apples cost $1.50, how much would 12 apples cost?

Hint: Use a proportion to solve.

Set up the proportion: 3 apples / $1.50 = 12 apples / x. Cross-multiply to get 3x = 18. Solving for x gives x = $6.00.

If the ratio of boys to girls in a class is 2:3 and there are 15 girls, how many boys are in the class?

Hint: Use the ratio to find the number of boys.

Set up the ratio: boys/girls = 2/3. Let the number of boys be x. Then, x/15 = 2/3. Cross-multiply to get 3x = 30, so x = 10. There are 10 boys in the class.

What is the cross-multiplication method in proportions?

Cross-multiplication is a method used to solve proportions. If a/b = c/d, then ad = bc. This means you can find the unknown term by setting the products equal.

In a recipe, the ratio of sugar to flour is 1:4. If you use 2 cups of sugar, how much flour do you need?

Hint: Set up a proportion based on the ratio.

Set up the ratio: sugar/flour = 1/4. Let the flour be x. Then, 2/x = 1/4. Cross-multiply to get 4 * 2 = 1 * x, so x = 8 cups of flour.

How do you find the missing term in a proportion?

To find the missing term in a proportion, use cross-multiplication. If a/b = c/x, then ad = bc. Solve for x by rearranging the equation.

If the ratio of cats to dogs is 5:2 and there are 30 cats, how many dogs are there?

Hint: Set up a proportion based on the ratio.

Set up the ratio: cats/dogs = 5/2. Let the number of dogs be x. Then, 30/x = 5/2. Cross-multiply to get 5x = 60, so x = 12 dogs.

What is the formula for finding the scale factor between two similar figures?

The scale factor is the ratio of any two corresponding lengths in similar figures. If figure A has a length of a and figure B has a corresponding length of b, the scale factor is a/b.

If a map is drawn at a scale of 1:100, what does this mean?

Hint: Think about the actual distance represented by the map.

A scale of 1:100 means that 1 unit on the map represents 100 units in reality. For example, 1 cm on the map equals 100 cm in real life.