# Find the Unit Rate 256 Miles Per 8 Gallons

Find the Unit Rate 256 Miles Per 8 Gallons.

### Key Concepts

■ Finding equivalent rates.

■ Comparison of quantities in two means. • Using unit of measurement charge per unit in solving problems.

## 5.5 Empathise Rates and Unit of measurement Rates

To understand, what is a rate? Firstly, we have to know virtually ratio.

Ratio:
A ratio can exist defined every bit the comparison of 2 quantities. Ratio can be represented in three forms.

Example1:
In a class of xxx students, 12 are girls.
Write the ratio of number of boys to the total number of students in the class.

Solution
:

Number of boys = Total number of students – Number of girls

Number of boys = 30 – 12

Number of boys = xviii

The ratio will be xviii: 12. The three forms of representation of ratio volition exist as follows.

Example2
:

Rate:
A rate is likewise a ratio comparing two different quantities having different units.

Case:
A bike travels lx miles in 4 hours.

Explanation: Here, we observe that there is a comparison being done between 2 different quantities, i.due east., altitude and time, the units of which are unlike.

### v.v.one Find equivalent rates

Example 1:
The price of pears in a store A is listed every bit five pears for \$12. At the aforementioned rate, what would be the price for 25 pears and how many pears can we buy using \$84?

Method 1: Ratio table

Solution:

Step 1:
Grade a tabular array to write ratios that are equivalent to

5  pears \$ 12

Step 2:
Multiply both the terms of the ratio by a non-zero positive integer until we become 25 in the pears column and 84 in the dollars column.

Step 3:
On analyzing the table, we observe that 25 pears price \$60. Whereas \$84 tin can buy the states 35 pears.

Method 2

Solution:

1. To find the cost of 25 pears.

Step 1:
Write the rate as a fraction:

5   12

Step two:
Multiply both terms of the rate past the aforementioned not-zero number to find an equivalent rate.

b) To notice the number of pears that tin can exist bought using \$84.

Step 1:
Write the rate as a fraction:

v   12

Stride 2:
Multiply both terms of the rate by the same non-zero number to find an equivalent rate.

Hence, we conclude that 25 pears cost \$60. Whereas \$84 can buy us 35 pears.

### five.5.2 Compare quantities in two ways

Example 1:
A recipe for scrambled eggs uses ii tablespoons of milk for every 3 eggs. What are the two unit rates that could represent the recipe?

Solution:

• Find the unit rate in eggs per spoons.

The unit charge per unit in eggs per spoons is

i.five eggs1 spoons  one.v eggs1 spoons

• Detect the unit rate in spoons per eggs.

The unit rate in eggs per spoons is

0.half-dozen table spoons1 egg 0.half-dozen table spoons1 egg

## What is a unit rate?

Unit rate is an equivalent rate with a denominator of i.

or

A unit charge per unit is a charge per unit in which the comparison is made to one unit of measurement.

Examples of unit rates:

1. The rate of center beats in 72 times per minute.
1. There are 24 hours per mean solar day.
1. There are seven days in a week.
1. In that location are 12 months in a year.
1. There are 365 days in a year.

### Ratio and Unit Rate

A unit is a ratio that compares two measurements(units) and the second measurement is 1(per).

Notation:

Remember that the give-and-take ‘’per’’ is always associated with rates, mostly unit rates.

Instance i:
A canoeing society travels fourscore miles in 5 days. How far could they travel in 8 days, if they maintain the same speed?

Solution:

Step ane:
Find the unit charge per unit in miles per hour.

The unit rate is xvi/one or 16 miles per hour.

Step 2:
Utilise the unit rate to find how far the society travel in eight hours. Multiply the unit of measurement charge per unit past 8.

Therefore, the canoeing club can travel 128 miles in viii hours.

## Exercise:

1. A car uses 8 gallons of gas to travel SO miles. How far tin the car travel with 40 gallons of gas?

ii. Sierra tin can make 5 friendship bands in two hours. How long will she take to make fifteen such bands?

iii. Mary can type threescore words in iii minutes. How many words can she type in 12 minutes?

4. Hannah read xl pages in 60 minutes. What are two dissimilar unit rates that could represent the situation?

5. It took jasmine 25 minutes to run 10 laps. What are the two dissimilar unit rates that could represent the situation?

6. Eight pairs of gloves are required for 16 patients. What are two different unit rates that could correspond the situation?

viii. Dave runs 1000 meters in S minutes. How much tin he run in xx minutes?

9. Isabella flew 600 miles in 120 minutes. How many miles did she wing in sixty minutes?

ten. Lenin paid \$30 dollars for 6 pitas, what would he pay for 9 pizzas of the same society?

### What have we learned?

• Understand how to find equivalent rates.

• Empathize how to compare quantities in two ways.

• Understand how to use unit rates in solving problems.