It is sometimes difficult to imagine how you will use mathematical principles in real life. Ratios, which are actually mathematical relationships, are perfect examples of math in the real world. Grocery shopping, cooking and getting from place to place are three common, real-life situations in which ratios are not only prevalent but essential to correct, cost-effective performance.

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Outside of math class, it is easy to recognize ratios in the real world. Common examples include comparing prices per ounce while grocery shopping, calculating the proper amounts for ingredients in recipes and determining how long car trip might take. Other essential ratios include pi and phi (the golden ratio).

## Grocery Shopping

The grocery store is a good source of ratios in real life. While looking at the prices of various groceries, you can easily illustrate ratios using two different boxes of cereal. For example, if a 10-ounce box of cereal costs $3 and a 20-ounce box of cereal costs $5, the 20 ounce box is the better value because each ounce of cereal is cheaper. By dividing the number of ounces of cereal by the price, you demonstrate the relationship between amount and size. For the smaller box of cereal, each ounce costs 30 cents; for the larger box of cereal, each ounce of cereal costs 25 cents.

## Recipes and Cooking

You also use ratios in cooking. The relationships between the amounts of various ingredients in recipes are essential to cooking the most delicious meals. For example, to create the best tasting achiote oil, you combine 1 cup of olive oil with 2 tablespoons of achiote, or orange seeds. This is easy to visualize as a ratio of 1 cup oil to 2 tablespoons seeds.

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## Vacation Trips

The ubiquitous travel question "Are we there yet?" is another example of ratios. For example, while taking a road trip from New York City to Philadelphia, you must travel approximately 90 miles. Assuming the car travels at 60 miles per hour, convert the hour to 60 minutes. Then divide the total miles traveled (90 miles) by 60 minutes to demonstrate that the trip to Philadelphia requires one and a half hours by car.

## Special Ratios

Two special ratios consistently seen in real life are pi (3.14) and phi (1.618). Pi is the relationship between the circumference of a circle and its diameter. In the real world, pi is essential for calculating the circumference of a circular swimming pool using the diameter or radius.

Euclid originally determined phi, or the golden ratio, as a means to calculate line segments and relationships between shapes. The golden ratio is common in biological relationships. For example, the length of your forearm divided by the length your hand results in a number close to 1.618, or phi.