Equivalent Ratios and Tape Diagrams

Front

What is an equivalent ratio?

Back

An equivalent ratio is a ratio that expresses the same relationship between two quantities, even if the numbers are different. For example, the ratios 4:5 and 12:15 are equivalent because they represent the same proportional relationship.

Front

How can you find an equivalent ratio?

Back

To find an equivalent ratio, you can multiply or divide both terms of the ratio by the same non-zero number. For example, to find an equivalent ratio for 2:3, you can multiply both terms by 2 to get 4:6.

Front

What is a tape diagram?

Back

A tape diagram is a visual representation of a ratio or a fraction that uses rectangles to show the relative sizes of the parts. It helps in understanding the relationship between quantities.

Front

How do you use a tape diagram to solve ratio problems?

Back

To use a tape diagram, draw rectangles to represent the quantities in the ratio. Divide the rectangles into equal parts based on the ratio, and then use the diagram to find unknown quantities by comparing the sizes of the parts.

Front

What is the ratio of 3 to 5 expressed as a fraction?

Back

The ratio of 3 to 5 can be expressed as the fraction 3/5.

Front

If 3/4 = x/12, how do you solve for x?

Back

To solve for x, cross-multiply: 3 * 12 = 4 * x. This gives you 36 = 4x. Then, divide both sides by 4 to find x = 9.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions, where the first term of the ratio is the numerator and the second term is the denominator. For example, the ratio 4:5 can be expressed as the fraction 4/5.

Front

How can you represent the ratio of two quantities using a tape diagram?

Back

To represent the ratio of two quantities using a tape diagram, draw a rectangle for each quantity, dividing them into equal parts that correspond to the ratio. The length of each rectangle reflects the size of each quantity.

Front

What is the first step in solving a problem involving equivalent ratios?

Back

The first step is to identify the known ratios and the unknown quantity you need to find. Then, determine if you can use multiplication or division to find the equivalent ratio.

Front

How do you check if two ratios are equivalent?

Back

To check if two ratios are equivalent, cross-multiply the terms. If the products are equal, the ratios are equivalent.