# THE SET OF RATIONAL NUMBERS

**I. ADDITION WITH “ LIKE ” DENOMINATORS**

1/5 | + | 2/5 | = |

So,1/5 + 2/5 =

**II. ADDITION WITH “ UNLIKE ” DENOMINATORS**

But what if the fractions do not have the same
denominator?

For instance,1/3 + 1/4

But, how do we count this? We need to find a way to
combine the two drawings to find the sum.

Let’s “build-up” each fraction:

Now, compare these two lists and look for a “like”

denominator . What is it? ________

**AN INTERESTING PROPERTY**

If a/b and c/d are any two rational numbers, then

EXAMPLES: | Using the LCD |
Using the Above Property |

**III. MIXED NUMBERS
**Mixed numbers are numbers that are the

**sum**of an integer and a fractional part of an integer. For

example, if a nail is inches long, this means 2 inches

**plus an additional**3/4 inches. (It is

common to think that since 2y means 2 times y, that means 2 times3/4, but this is

**)**

*incorrect!* Change the following *mixed numbers to improper
fractions.*

Using the Coventional Algorithm |
Change with Meaning |

Change the following **improper fractions to mixed
numbers.**

Using the Coventional Algorithm |
Change with Meaning |

IV.

**PROPERTIES OF ADDITION FOR RATIONAL NUMBERS**

Given any two rational numbers a/b and c/d where , b and d
are non- zero integers :

1. Closure

2. Commutative

3. Associative

4. Additive Identity

5. Additive Inverse

For any rational number a/b there exists a unique

number ________ such that:

Name the additive inverse of the following:

**V. ADDITION OF MIXED NUMBERS (Know how to add using the
given mixed numbers)**

**VI. SUBTRACTION OF RATIONAL NUMBERS**

**SUBTRACTION OF RATIONAL NUMBERS**

If a/b and c/d are any rational numbers, then

**AN INTERESTING PROPERTY**

If a/b and c/d are any two rational numbers, then

**SUBTRACTION OF MIXED NUMBERS (Know how to subtract
using the given mixed numbers**

**VII. ESTIMATION WITH RATIONAL NUMBERS**

Many times when estimating with fractions, it is helpful
to round to a convenient fraction –

for instance:0,1/2,1/3,1/4,1/5,2/3,3/4,or 1.

For example, if you got 59 out of 80 questions correct on your test, this is about 60/80 or 6/8 or 3/4

Then we can conclude that 3/4 is a HIGH ESTIMATE.

(You actually got less than 3/4 of the test correct, since 59 < 60, then 59/80< 60/80 = 3/4).

Approximate each of the following using 0,1/4,1/3,1/2,3/4,or 1.Tell if your estimate is low or high .

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