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Use unit rates to solve problems

A unit rate describes the amount of one quantity for exactly one unit of another, found by dividing corresponding quantities while preserving meaningful units, such as miles per hour or dollars per item. Learners use unit rates, equivalent ratios, tables, and equations to find unknown quantities, compare rates, and solve real-world problems with whole numbers, fractions, and decimals, distinguishing a per-one rate from a total; formal proportional functions and more complex rate models are beyond this scope.

Detailed Explanation: Use unit rates to solve problems

A unit rate tells how much of one quantity corresponds to exactly 1 unit of another quantity. Find it by dividing, and keep the units with your answer.

Example:
Six apples cost 4.50$. How much would 10 apples cost at the same rate?

  1. Find the cost for 1 apple.

    Divide the total cost by the number of apples:

$4.50÷6=$0.75\$4.50 \div 6 = \$0.75

The unit rate is 0.75\text{ per apple}}$.

  1. Use the unit rate to find the cost of 10 apples.

10 apples×$0.75 per apple=$7.5010\text{ apples} \times \$0.75\text{ per apple} = \$7.50
  1. Answer the question.

10 apples cost $7.50.\boxed{\text{10 apples cost }\$7.50.}

The 0.75$ is the cost for one apple, not the total cost. Multiplying it by the number of apples gives the total.

Learn by doing: Use unit rates to solve problems

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Ratios - Unit Rates, Solve for Rate


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