Problem 105 - Elementary Algebra

Question

The nutrition fact sheet at a fast food restaurant says the fish sandwich has 380 calories, and 171 calories are from fat. What percent of the total calories is from fat?

Step-by-Step Solution

Answer

45%

Step 1 - Identify the given values

Identify the total number of calories and the number of calories from fat. In this case, the total calories are 380 and the calories from fat are 171.

Step 2 - Set up the ratio

Divide the number of calories from fat by the total number of calories to set up the ratio. \[ \text{Ratio} = \frac{171}{380} \]

Step 3 - Convert the ratio to a percentage

Convert the ratio to a percentage by multiplying by 100. \[ \text{Percent of calories from fat} = \frac{171}{380} \times 100 \]

Step 4 - Perform the calculation

Compute the percentage: \[ \frac{171}{380} \times 100 \approx 45\]

Key Concepts

Ratio

Understanding ratios is essential in many areas of math and real life. A ratio compares two quantities. It tells us how much of one thing exists compared to another. For example, if you have a bowl with 3 apples and 2 oranges, the ratio of apples to oranges is 3:2. This can also be written as a fraction, like \( \frac{3}{2} \). In our exercise, we are comparing the calories from fat to the total calories. This ratio helps us understand the proportion of calories that come from fat compared to overall calories. When calculating ratios, always ensure both parts of the ratio are in the same unit before you proceed.

Calories

Calories measure the amount of energy food provides. Calories in food come from proteins, carbohydrates, and fats. In nutrition, keeping track of calorie intake helps manage diet and health. In our example, the total calories of the fish sandwich are 380, and calories from fat are 171. To find out what portion of these calories comes from fat, we need to calculate the percentage, which tells us how significant the calories from fat are in relation to the total calories.

Division

Division is a fundamental mathematical operation where you split a number into equal parts. In our ratio, we are dividing the calories from fat by the total calories: \( \frac{171}{380} \). This division helps us to understand a part relative to its whole. When performing division, ensure that you handle the numbers correctly to maintain accuracy. Understanding division will help you correctly interpret proportions and calculations in many areas of math and daily life.

Multiplication

Multiplication helps in scaling quantities. In our example, after setting up our initial ratio of \( \frac{171}{380} \), we multiplied by 100 to convert this ratio into a percentage, making it easier to understand and relate to. The multiplication step is crucial: \( \frac{171}{380} \times 100 \approx 45\). This calculation shows that approximately 45% of the total calories in the fish sandwich come from fat. Multiplying by 100 transforms our ratio into a form that most people can quickly understand and visualize.