A ratio is a a comparison of two numbers. A proportion, which is an equation with a ratio on each side, states that two ratios are equal. We use ratios to compare values and to measure the intensity of their comparison. For example, total six puppies in which two are girls and four are boys. Then, the ratio will be 2:4 (girls : boys) and you can express it in fraction form as well like this 2/4. Proportions tell you two ratios are equal to each other or not. Here, we will use the example of the above to see how proportions work for our puppies. The first ratio of boys : girls that is 2:4. If we have next ratio is 4:8, you will see the proportional answer would be equal to each other that is 2/4 = 0.5 and 4/8 = 0.5. In this way, your ratios will be proportional by dividing them into the same way. The values become equal when things are proportional. The sizes of the things make a difference. Ratios become proportional when they express the similar relation. You can find out two ratios are proportional by writing them as fractions and then, you will simplify them. If simplified fractions are the same, it means the ratios are proportional. Ratios are always proportional when they show their relationship same. If you see two proportional ratios, you will write them as fractions and reduce them. In this case, ratios will become proportional when fractions are same. Example: Fractions are same that is 3/4 = 6/8. It means ratios will also have the same ratio that is 3 to 4 and 6:4. We will verify the statement to know the proportional ratio by cross product. 3 × 8 = 4 × 6. They both are equal as both sides have the same answer that is 24. A ratio shows a connection between two or a pair of digits. It determines the quantity of the first compared to the second. For instance, the ratio of the four legs of mammals is 4:1 and the ratio of humans from legs to noses is 2:1. You can write all the ratios in the fractional expression. That is why, we will compare three boys with five girls that you can write the ratios 3:5 or 3/5. Again, these examples have proved that ratios become equal while quantities are equal. For example, the ratio between 2/5 and 8/20 have a proportional relationship. Remember, equivalent fractions are 4/10 and 12/30 as you can simplify both by 2/5.
In these worksheets, your students will determine whether pairs of ratios are proportional. Two types of methods are presented. In the first method, students will use cross multiplication to verify equality. In the second method, they will simplify fractions to verify equality. The problems ask for yes or no answers; however, students may require additional paper in order to show their work. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. Ample worksheets are also provided for students to practice independently. When finished with this set of worksheets, students will be able to recognize whether a given set of ratios is proportional. These worksheets explain how to determine whether a given set of ratios is proportional. Sample problems are solved and practice problems are provided.
