Which ratios have a unit rate greater than 1? Select …

Mathematics Questions

Which ratios have a unit rate greater than 1? Choose ALL that apply.

Short Answer

The process involves identifying various ratios of miles to hours, calculating their unit rates, and then determining which rates exceed 1. The ratios that have a unit rate greater than 1 are a) 4 miles : 3 1/3 hours, c) 9/8 miles : 5/6 hour, d) 9/5 miles : 3 hours, e) 2 1/2 miles : 3 hours, and f) 7 miles : 3/4 hour.

Step-by-Step Solution

Step 1: Identify the Ratios

Start by listing the ratios you need to evaluate for their unit rates. The ratios in question are:

  • a) 4 miles : 3 1/3 hours
  • b) 1/3 mile : 2 3/8 hours
  • c) 9/8 miles : 5/6 hour
  • d) 9/5 miles : 3 hours
  • e) 2 1/2 miles : 3 hours
  • f) 7 miles : 3/4 hour

Step 2: Calculate the Unit Rates

To find the unit rates of these ratios, divide the first quantity (miles) by the second quantity (hours). This gives you a numerical value that represents the rate per one hour:

  • a) 4 miles ‚àö‚àë 3 1/3 hours = 1.2
  • b) 1/3 mile ‚àö‚àë 2 3/8 hours = approximately 0.14
  • c) 9/8 miles ‚àö‚àë 5/6 hour = 1.35
  • d) 9/5 miles ‚àö‚àë 3 hours = 1.8
  • e) 2 1/2 miles ‚àö‚àë 3 hours = approximately 0.83
  • f) 7 miles ‚àö‚àë 3/4 hour = 9.33

Step 3: Determine Ratios with Unit Rate Greater than 1

Finally, compare each calculated unit rate to determine which are greater than 1. The ratios meeting this criteria are:

  • a) 4 miles : 3 1/3 hours
  • c) 9/8 miles : 5/6 hour
  • d) 9/5 miles : 3 hours
  • e) 2 1/2 miles : 3 hours
  • f) 7 miles : 3/4 hour

Hence, a), c), d), e), and f) have a unit rate greater than 1.

Related Concepts

Ratios

A relationship between two quantities that expresses how much of one quantity is present for each unit of another quantity.

Unit Rate

A rate that compares a quantity to one unit of another quantity, calculated by dividing the first quantity by the second quantity.

Greater Than 1

A comparison indicating that a value or quantity is larger than one, often used in evaluating performance or efficiency measures.

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