How can you write a unit rate if at least one term is a fraction? How is this different from writing a unit rate where both terms are whole numbers?
It is possible to divide fractions by fractions. You can write a unit rate dealing with fractions by using fraction division.
For example: If ½ of the apples are rotten in every ¾ of the boxes then the unit rate is: ⅔ rotten apples per box.
The only difference is that you are dealing with fractions.
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When writing a unit rate where at least one term is a fraction, you can follow these steps:
Step 1: Identify the quantities involved - you need to determine the two quantities that are being compared.
Step 2: Write the fraction - express the comparison between the two quantities as a fraction.
Step 3: Simplify the fraction - if possible, simplify the fraction by dividing the numerator and denominator by their greatest common divisor.
Step 4: State the unit rate - write the fraction as a ratio, where the numerator represents one of the quantities, and the denominator represents the other quantity.
For example, let's consider the question: "How can you write a unit rate if the distance is 1/4 mile and the time is 1/2 hour?"
Step 1: Identify the quantities involved - in this case, the distance is 1/4 mile, and the time is 1/2 hour.
Step 2: Write the fraction - express the comparison between the distance and time as a fraction: 1/4 mile per 1/2 hour.
Step 3: Simplify the fraction - we can simplify the fraction 1/4 by dividing both the numerator and denominator by their greatest common divisor, which is 1. This gives us 1/4.
Step 4: State the unit rate - write the fraction as a ratio: 1/4 mile per 1/2 hour can be stated as 1/4 mile per 1/2 hour.
Now, let's compare writing a unit rate where both terms are whole numbers. The process is similar, but since both terms are whole numbers, the fractions are not involved.
For example, let's consider the question: "How can you write a unit rate if the distance is 10 miles and the time is 2 hours?"
Step 1: Identify the quantities involved - in this case, the distance is 10 miles, and the time is 2 hours.
Step 2: Write the ratio - express the comparison between the distance and time as a ratio: 10 miles per 2 hours.
Step 3: Simplify the ratio - we can simplify the ratio by dividing both the numerator and denominator by their greatest common divisor, which is 2. This gives us 5 miles per 1 hour.
Step 4: State the unit rate - write the ratio as a unit rate: 5 miles per 1 hour can be stated as 5 miles per hour.
In summary, when at least one term is a fraction, you write a unit rate by expressing the comparison as a fraction and simplifying it if possible. When both terms are whole numbers, you write a unit rate by expressing the comparison as a ratio and simplifying it if needed.