ParaPro Math Study Guide: Measurement

This page of our free ParaPro Study Guide covers all types of measurements including time and money. You will learn about different units of measurement and how to convert between various units. After you have read through this material you can take the measurement review test to check your progress.

Time & Money

We can represent values of time and money in different ways but still the same meaning. Sometimes when we communicate time or money, we use phrases like ”quarter past 10” or ”half dollar.” In this lesson, you will learn how to correctly use these terms to represent time and money.

When a time ends with :15 or :45, we can say the time is a ”quarter til” or a ”quarter past” an hour. We can also describe 30 minutes as a ”1/2 hour” because 30 is half of 60. The following are examples:

  • 11:15 can be expressed as ”a quarter after 11” or ”15 minutes after 11”
  • 10:45 can be expressed as ”a quarter til 11” or ”15 minutes til 11”

There are different ways we can write money, like using cents, dollars, or symbols. Some examples include:

  • $1.00 = 100 cents = two half-dollars
  • Fifty cents = $0.50 = half dollar

Measurement & Conversion

Measurement is a way to find the size or amount of something. We can measure:

  • length — how long or short
  • weight — how heavy
  • time — how long
  • volume — how much capacity

Each of these measures has different units, and we will learn how to convert from one unit to another. Let’s go over some common conversions:

1 foot = 12 inches1 meter = 100 centimeters
1 mile = 5280 feet1 kilometer = 1000 meters
1 day = 24 hours1 hour = 60 minutes
1 pint = 2 cups2 pints = 1 quart
1 gram = 1000 milligrams1 pound = 16 ounces
1 inch = 2.54 centimeters1 yard = 3 feet
1 minute = 60 seconds1 week = 7 days
4 quarts = 1 gallon1 ton = 2000 pounds

The following steps will help you convert units:

1. Write the conversion ratio as a fraction:

$ \dfrac{12 \ \text{inches}}{1 \ \text{foot}}$

2. Set up a multiplication problem with what you are converting times the conversion ratio so that the same unit is on the top and bottom:

$3 \ \text{feet} \ \times \ \dfrac{12 \ \text{inches}}{1 \ \text{foot}}$ [notice that ’feet’ is on the top and bottom]

3. Cancel units on the top and bottom of the fractions so that you are left with only one unit (the one you are converting to):

$ \require{cancel} 3 \ \cancel{\text{feet}} \ \times \ \dfrac{12 \ \text{inches}}{1 \ \cancel{\text{foot}}}$ [notice that ’feet’ is on the top and bottom]

4. Multiply across and divide if needed:

$3 \ \times \ \dfrac{12 \ \text{inches}}{1} = 36 \ \text{inches}$

Example 1

Convert $2 \ \text{miles}$ into $ \text{feet}$.

Solution:

$\require{cancel} 2 \ \text{miles} \; \times \ \dfrac{5280 \ \text{feet}}{1 \ \text{mile}} ⇒ 2 \ \cancel{\text{miles}} \ \times \dfrac{5280 \ \text{feet}}{1 \ \cancel{\text{mile}}}$

$\require{cancel} ⇒ \dfrac{ 2 \times 5280 \ \text{feet}}{1} = 10,560 \ \text{feet}$

Example 2

Convert $360 \ \text{seconds}$ into $ \text{minutes}$.

Solution:

$\require{cancel} 360 \ \text{seconds} \; \times \ \dfrac{1 \ \text{minute}}{60 \ \text{seconds}} ⇒ 360 \ \cancel{\text{seconds}} \ \times \ \dfrac{1 \ \text{minute}}{60 \ \cancel{\text{seconds}}}$

$\require{cancel} ⇒ \dfrac{ 360 \ \text{minutes}}{60} = 6 \ \text{minutes}$

You should now have a good understanding of measurements, and how to convert between different units. Make sure that you are fully prepared for these types of ParaPro math questions with this measurement review test.


Measurement Review Test


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