Mixed Numbers And Improper Fractions English Language Essay

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A Fraction has two parts that tell us what it denotes. The first part is the top number or the numerator. The numerator is the number of pieces you have. The second part of a fraction is the bottom number called the denominator (THINK: "Down"ominator). The denominator is the number of pieces the whole thing is divided into.

Example: 3/4 means:

We have 3 pieces of something.

The whole thing is divided into 4 pieces.

Each piece is a quarter (1/4) of the whole thing.

There are three types of fraction:

[Picture may need to be redone. Taken from http://www.mathsisfun.com/improper-fractions.html]

We define the three types of fractions like this:

Proper Fractions [glossary term; a fraction where the top number is smaller than the bottom number. http://www.bing.com/Dictionary/search?q=define+proper+fraction&FORM=DTPDIA]

A proper fraction is a fraction with the numerator smaller than the denominator. In other words, the numerator is less than the denominator.

Examples: 1/3, 3/4, 2/7 1/2 etc.

This is the type of fraction we typically think of when we are sharing or splitting something up.

Improper Fractions [glossary term; a fraction where the top number is bigger than the top number. http://www.bing.com/Dictionary/search?q=define+improper+fraction&FORM=DTPDIA]

An improper fraction is a fraction that has a numerator larger than or equal to its denominator. In other words, the numerator is bigger than or the same size as the denominator. We can remember an improper fraction by thinking it's "top-heavy".

In the examples below, notice how the top number is bigger than the bottom number? That makes it an Improper Fraction.

Examples: 4/3, 11/4, 3/2, 7/4, 16/15, 99/5

The term "IMPROPER" suggests that you shouldn't use it or that it's incorrect in some way, but there is nothing wrong about Improper Fractions. As you move on to higher levels of mathematics, you will find improper fractions are very friendly to use.

We know that when the numerator is less than the denominator it is called a proper fraction. When the numerator is greater than the denominator it is called an improper fraction. What do we call the fraction when the numerator is equal to the denominator as in the example 4/4 ?

[Picture may need to be redone. Taken from http://www.mathsisfun.com/improper-fractions.html]

In this instance where the numerator is the same as the denominator, the number of pieces you have are the same as the number of pieces the whole is divided into. We define this as 1, just as a pizza is a WHOLE pizza when it has all of its slices.

Whenever you see the same number in the numerator as the denominator, remember that fraction equals 1.

Examples: 4/4 = 1 and 7/7 = 1

[BEGIN YOUR TURN perhaps this could be done as a drag and drop.]

Match each fraction with its appropriate term, PROPER, IMPROPER or WHOLE

Answers

5/8 PROPER

8/5 IMPROPER

8/8 WHOLE

7/6 IMPROPER

6/7 PROPER

7/7 WHOLE

21/5 IMPROPER

5/21 PROPER

21/21 WHOLE

3/100 PROPER

100/3 IMPROPER

100/100 WHOLE

[END YOUR TURN]

Mixed Fractions or Mixed Numbers [glossary term; a fraction number consisting of a proper fraction and a whole number together http://www.bing.com/Dictionary/search?q=define+mixed+number&FORM=DTPDIA]

A whole number and proper fraction together is a Mixed Fraction or also known as a Mixed Number.

Examples: 1 1/3, 2 1/4, 16 2/5

[Pictures may need to be redone. Taken from http://www.mathsisfun.com/improper-fractions.html]

1 3/4   1 1/4

=

 

2 3/8

A mixed number consists of an integer followed by a proper fraction.

Mixed fractions are typically used in everyday/normal conversation.

Remember that fractions are used to count a part of something or a group.

¼ of this 1 whole square is red.

Mixed numbers are used when you need to count whole things AND parts of things at the same time.

How many of the following squares are red?

There are 5 whole squares and part of another square.

We write it like this 5 1/4. When we read it or say it out loud we would day, "five and one fourth."

This is similar to writing 5 + ¼ , but, we don't write the "+" in written form. In word form addition is the same as the word AND.

[BEGIN YOUR TURN]

This would be a great spot for an interactive video like this onehttp://www.beaconlearningcenter.com/WebLessons/MixedNumbers/default.htm

[END YOUR TURN]

[BEGIN YOUR TURN]

This would be a great spot for an interactive game to play with mixed numbers like this one http://www.mrnussbaum.com/sal/index.html This is very fun stuff!

[END YOUR TURN]

[BEGIN REVIEW]

1. A mixed number is _________________ a number made up of a whole number and a fraction.

*Always

Sometimes

Never

Feed back: By definition

2. An improper fraction should never be used as an answer to a math problem.

True

*False

Feed back: Improper fractions will make solving math problems easier as you get into high levels of mathematics.

3. A proper fraction is _______________ used when you need to count whole things AND parts of things at the same time.

Always

Sometimes

*Never

Feed back: A proper fraction is a fraction that has a denominator larger than the numerator and is used when you are talking about pieces of 1.

4. Which is the correct mathematical description for the following picture?

*5/8

1 5/8

eight fifths

4 and 1/8

Feedback: the pizza is divided into 8 pieces. 5 of the pieces are showing. Use a proper fraction of 5/8.

5. How would you describe the following picture in words to your friend?

       

      

There are twelve fifteenths pentagons.

*There are two and two fifths pentagons.

There are two fifths pentagons.

There are two whole pentagons and a fraction more.

Feed back: There are two and two fifths pentagons. We use mixed fractions in everyday language.

[END REVIEW]

[BEGIN QUIZ]

1. A proper fraction is _________________ a number made up of a whole number and a fraction.

Always

Sometimes

*Never

Feed back: A proper fraction is a fraction that has a denominator larger than the numerator and is used when you are talking about pieces of 1.

2. Improper fractions are friendly to use in mathematics problems but are not used in everyday language.

*True

False

3. A mixed number is _______________ used when you need to count the fractional pieces of something.

Always

Sometimes

*Never

Feed back: Mixed numbers are used when you need to count whole things AND parts of things at the same time.

4. Which is the correct mathematical description for the following picture?

       

       

11/12

*5 1/2

six halves

five and one twoths

Feedback: There are 5 full circles denoting 5 wholes and 1/2 of another.

5. What term would you use to describe the number of blue blocks below to your friend?

         

proper fraction

improper fraction

*mixed number fraction

Feed back: Mixed numbers are used when you need to count whole things AND parts of things at the same time.

[END QUIZ]

[BEGIN TEST]

1. A proper fraction is _________________ a fraction where the numerator is larger than the denominator

Always

Sometimes

*Never

Feed back: A proper fraction is a fraction that has a denominator larger than the numerator and is used when you are talking about pieces of 1.

2. The term "Improper fraction" simply means the numerator is larger than the denominator.

*True

False

3. A mixed fraction is _______________ the same as a mixed number.

*Always

Sometimes

Never

Feed back: The terms mixed numbers and mixed fractions are interchangeable and used when you need to count whole things AND parts of things at the same time.

4. Which picture below represents the improper fraction 5/2?

*

Feedback: There are 5 full circles denoting 5 wholes and 1/2 of another.

5. What term would you use to describe the of the nail below to your friend?

proper fraction

improper fraction

*mixed number fraction

Feed back: Mixed numbers are used when you need to count whole things AND parts of things at the same time.

[END TEST]

CONCLUSION:

A Fraction has two parts that tell us what it denotes.

The first part is the top number or the numerator.

The numerator is the number of pieces you have.

The second part of a fraction is the bottom number called the denominator (THINK: "Down"ominator).

The denominator is the number of pieces the whole thing is divided into.

There are three types of fraction:

Proper Fractions

A proper fraction is a fraction with the numerator smaller than the denominator.

Improper Fractions

An improper fraction is a fraction that has a numerator larger than or equal to its denominator.

We can remember an improper fraction by thinking it's "top-heavy".

. As you move on to higher levels of mathematics, you will find improper fractions are very friendly to use.

Mixed Fractions or Mixed Numbers

A whole number and proper fraction together is a Mixed Fraction or also known as a Mixed Number

Mixed fractions are typically used in everyday/normal conversation.

Mixed numbers are used when you need to count whole things AND parts of things at the same time.

We write it like this 5 ¼

When we read it or say it out loud we would day, "five and one fourth."

.When is a fraction a WHOLE?

when the numerator is equal to the denominator as in the example 4/4 ?

Whenever you see the same number in the numerator as the denominator, remember that fraction equals 1.

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