Chapter 2Rational Numbers

Rational Numbers

Numbers that can be written as a fraction. Rational Numbers include:

Whole numbersZeroPositive and negative integersPositive and negative fractionsPositive and negative decimals

Comparing FractionsCompare ¾ and 5/8

Step 1: Find the lowest common denominator (the smallest number that both denominators will divide into evenly.) The lowest common denominator is 8.

Step 2: Change fourths to eighths by multiplying three fourths by two halves:

Step 3: Since the denominators are the same, the fraction with the larger number is greater.

Comparing the mixed numbers

Compare 1 3/5 and 1 2/3

Step 1: Change the mixed numbers to improper fractions.

Step 2: Find the lowest common denominator for the improper fractions. The lowest common denominator is 15.

Step 3: Change fifths to fifteenths and thirds to fifteenths.

Comparing DecimalsA decimal is the point after a whole number. A decimal is commonly used in monetary notations, such as $12.54.A decimal is also used to express a whole number and a fractions, such as one and a quarter pies expressed as 1.25 pies.

Comparing DecimalsDecimals preceded by zeros represent numbers less than one, such as a quarter of a pie, 0.25pies.BE SURE TO INCLUDE A LEADING ZERO TO THE LEFT OF THE DECIMAL FOR NUMBERS LESS THAN ONE.

A decimal can be read as ‘point’; 1.25 is read as ‘one point two five’It can also be read as ‘one and twenty-five hundredths’

Comparing Decimals

1 ,8 6 3 . 6 8 1 7 2 6

Comparing DecimalsCompare 4.1 and 4.11Step 1: Arrange numbers with decimal points directly under each other.

4.14.11

- Step 2:Fill in with zeros so they all have the same number of digits after the decimal point. Read the numbers as if the decimal points were not there.

4.10

4.114.1< 4.11

Comparing DecimalsCompare:7.2 and 7.028.55 and 8.55597.08 and 97.180.21 and 0.21117.1001 and 17.1011

Changing Fractions to Decimals

Change To change a fraction to a decimal, divide the top number by the bottom number . 8 √1Add a decimal point and a 0 after the 1 and divide.Continue adding 0s and dividing until there is no remainder.

•0.125

€

18

to a decimal.

Change the following fractions to decimals.4/55/85/118/9

€

523

€

178

Changing decimals to fractions.

Change 0.25 to a fraction.Copy the decimal without the point. This will be the top number of the fraction 25.The bottom number is a 1 with as many 0s after it as there are digits in the top number

€

25100

Two digitsTwo 0’s

You need to simplify the fraction.

€

25100

=14

Change the following decimals to fractions.0.550.750.710.35

Change the following decimals to mixed

numbers.7.12599.52.1316.95

Graphing Rational Numbers

Where would 4/3 fall on the number line?Convert the improper fraction to a mixed number.

That is 1/3 of the distance between the numbers 1 and 2. Estimate the distance by dividing the distances between points 1 and 3 into thirds.

€

43=113

Graphing Rational Numbers

Plot the value of -1.75 on the number line.Convert the value of -1.75 to a mixed number.

That is ¾ of the distance between the numbers -1 and -2. Estimate this distance by dividing the distance between -1 and -2 into fourths.

€

−1.75 = −134

Plot and label the following values on your

number line!A. 5/4B. 12/5 C. 2/3D. =3/2

Plot and label the following values on your

number line!0.250.91.92.6

Comparing Rational Numbers

When comparing numbers, use the greater than (>), less than (<), or equal to (=0 signs.The simplest way to compare numbers that are in different notations, like percent, decimals, and fractions, is to change all of them to one notation.

Decimals are the easiest to compare!!

Which is larger? Or 1.3Change to a decimal. 1.25, which is smaller

than 1.3.

Which is smaller?: 0.6 or 2/3?Change 2/3 to a decimal – 0.666… 0.6 is smaller than- 0.666… so 0.6 < 2/3

€

114

€

114