Equivalent rates help us understand relationships between quantities in a consistent and proportional way. They are widely used in real-life scenarios, such as calculating speed, comparing costs, or scaling recipes.
Example 1: Finding Missing ValuesA cyclist travels 12 miles in 3 hours. How far will they travel in 5 hours if the speed remains constant?
Calculate the rate of travel:
12÷3=4 miles per hour.
Multiply the rate by the new time:
4×5=20 miles.
Answer: The cyclist will travel 20
miles in 5 hours.
A bakery uses 6 eggs to bake 2 cakes. How many eggs are needed to bake 5 cakes?
Calculate the number of eggs per cake:
6÷2=3 eggs per cake.
Multiply by the number of cakes:
3×5=15 eggs.
Answer: The bakery needs 15 eggs to bake 5 cakes.
A plumber charges $45 for 3 hours of work. How much will they charge for 7 hours?
Calculate the charge per hour:
45÷3=15 dollars per hour.
Multiply by the total hours:
15×7=105 dollars.
Answer: The plumber will charge $105 for 7 hours of work.
Equivalent rates simplify everyday problem-solving by making it easy to calculate consistent relationships. Whether determining travel distances, scaling ingredients, or estimating costs, mastering equivalent rates ensures accuracy and efficiency in real-world tasks.
Let’s explore how equivalent rates can simplify real-world problems and help you solve them step by step with ease!
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