**Converting units using ratios and proportions :**

We can use ratios and proportions to convert both customary and metric units.

Use the table below to convert from one unit to another within the same measurement system.

Each relationship in the table can be described by two ratios.

For example, because 1 quart = 2 pints, we can write two ratios 1 quart / 2 pints and 2 pints / 1 quart.

**Example 1 : **

An average human brain weighs 3 pounds. What is this weight in ounces ? Use a proportion to convert 3 pounds to ounces.

**Solution :**

**Step 1 :**

Identify the ratio that compares the units involved.

The units pounds and ounces are customary units of weight.

Find the relationship of those units in the weight section of the customary measurements table.

1 pound = 16 ounces

**Step 2 :**

Write a proportion.

Because 1 x 3 = 3, multiply 16 by 3.

A weight of 3 pounds is equal to 48 ounces.

**Example 2 : **

A moderate amount of daily sodium consumption is 2,000 milligrams. What is this mass in grams ? Use a proportion to convert 2,000 milligrams to grams.

**Solution :**

**Step 1 :**

Identify the ratio that compares the units involved.

The units, milligrams and grams, are metric units of mass.

Find the relationship of those units in the mass section of the metric measurements table :

1 gram = 1,000 milligrams.

**Step 2 :**

Write a proportion.

Because 1000 x 2 = 2000, multiply 1 by 2.

A mass of 2,000 milligrams is equal to 2 grams.

**Example 3 : **

The height of a doorway is 6 feet. What is the height of the doorway in inches ?

**Solution :**

**Step 1 :**

Identify the ratio that compares the units involved.

The units feet and inches are customary units of length.

Find the relationship of those units in the length section of the customary measurements table :

1 foot = 12 inches

**Step 2 :**

Write a proportion.

Because 1 x 6 = 6, multiply 12 by 6.

A length of 6 feet is equal to 72 inches.

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