Rewrite 3/4 : 1/8 as a unit rate

Rewrite 3/4 : 1/8 as a unit rate

The Correct Answer and Explanation is :

To rewrite the expression ( \frac{3}{4} : \frac{1}{8} ) as a unit rate, we first need to understand what a unit rate is. A unit rate compares two quantities where one of the quantities is expressed as “per one unit” of the other. For example, speed is often expressed as miles per hour, or cost can be expressed as dollars per item.

Step 1: Convert the ratio to a fraction.

The expression ( \frac{3}{4} : \frac{1}{8} ) is a ratio, which can be written as a fraction:

[
\frac{3}{4} : \frac{1}{8} = \frac{\frac{3}{4}}{\frac{1}{8}}
]

Step 2: Simplify the division of fractions.

To divide fractions, we multiply by the reciprocal of the second fraction. The reciprocal of ( \frac{1}{8} ) is ( \frac{8}{1} ), so:

[
\frac{\frac{3}{4}}{\frac{1}{8}} = \frac{3}{4} \times \frac{8}{1}
]

Now, multiply the numerators and denominators:

[
\frac{3 \times 8}{4 \times 1} = \frac{24}{4}
]

Step 3: Simplify the result.

Now, simplify the fraction ( \frac{24}{4} ):

[
\frac{24}{4} = 6
]

Step 4: Interpret the result as a unit rate.

The simplified result, 6, means that for every 1 unit of ( \frac{1}{8} ), there are 6 units of ( \frac{3}{4} ). In other words, the ratio ( \frac{3}{4} : \frac{1}{8} ) can be expressed as a unit rate of 6.

Final Answer:

The unit rate of ( \frac{3}{4} : \frac{1}{8} ) is 6. This tells us that for every unit of ( \frac{1}{8} ), there are 6 units of ( \frac{3}{4} ).

Explanation:

Unit rates help to simplify and compare quantities in practical terms, making them easier to interpret and apply. This problem demonstrates how we can transform a ratio into a unit rate through the process of division and multiplication. Understanding unit rates is essential in everyday calculations, such as calculating speed, cost per item, or distance per unit of time.