Multiplying rational numbers has various applications in real-life scenarios and different fields. Here are some quick checks to understand these applications:
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Finance:
- Interest Calculation: If you earn \( \frac{1}{2} \) percent interest on an investment of $2000, the interest earned can be calculated as \( 2000 \times \frac{1}{2} = 1000 \) (convert percent to a decimal first).
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Cooking and Recipes:
- Scaling Recipes: If a recipe requires \( \frac{3}{4} \) cup of sugar and you want to make \( \frac{1}{2} \) of the recipe, you multiply \( \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} \) cups of sugar needed.
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Measurements:
- Area Calculation: To find the area of a rectangle with a length of \( \frac{3}{5} \) meters and width of \( \frac{2}{3} \) meters, the area is \( \frac{3}{5} \times \frac{2}{3} = \frac{6}{15} = \frac{2}{5} \) square meters.
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Distance and Speed:
- Travel Time: If a car travels at a speed of \( \frac{60}{1} \) miles per hour for \( \frac{1}{4} \) hour, the distance covered can be calculated by multiplying: \( \frac{60}{1} \times \frac{1}{4} = 15 \) miles.
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Chemistry:
- Concentration Calculation: If you need to mix solutions, and the needed concentration is \( \frac{1}{3} \) of a liter with \( \frac{2}{5} \) concentration of a certain chemical, the amount of that chemical is \( \frac{1}{3} \times \frac{2}{5} = \frac{2}{15} \) liters.
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Statistics:
- Probability: In probability, if the chance of an event occurring is \( \frac{1}{4} \) and the chance of another related event is \( \frac{1}{3} \), the combined probability of both events is \( \frac{1}{4} \times \frac{1}{3} = \frac{1}{12} \).
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Construction:
- Material Estimates: If you need \( \frac{2}{3} \) of a bag of cement to complete \( \frac{4}{5} \) of a project, the total cement used would be \( \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} \) bags.
These examples illustrate how multiplying rational numbers applies to everyday situations, enabling calculations in finance, cooking, measurements, travel, chemistry, statistics, and construction.