Addition and Subtraction of Rational Numbers Foundations of Algebra

Rational Numbers A rational number is a real number that can be written as a simple fraction (i.e. as a ratio.) Example: 1.5 is a rational number because 1.5 = 3/2 (it can be written as a fraction). Here are some more examples Number As a Fraction Rational? 55/1Yes 1.757/4Yes.0011/1000Yes /9Yes √2 (square root of 2) ?NO ! Oops! The square root of 2 cannot be written as a simple fraction. And there are many more such numbers, and because they are not rational they are called irrational.

Be Careful With "Mixed Fractions" You may be tempted to write an Improper Fraction (a fraction that is "top-heavy", i.e. where the top number is bigger then the bottom number) as a Mixed Fraction:Improper FractionMixed Fraction For example 7 / 4 = 1 3 / 4, shown here: But for mathematics the "Improper" form (such as 7 / 4 ) is actually better. Improper FractionMixed Fraction 7/47/4 1 3 / 4 =

Adding and Subtracting Rational Numbers Adding and Subtracting Rational Numbers may require you to combine numbers that are integers, decimals, and fractions. The rules for adding and subtracting positive and negatives numbers are the same for rational numbers. When you add or subtract fractions you must have a common denominator. Since the decimal system involves tenths, hundredths, thousandths, etc, the place-values used already represent common denominators. To add , we only need to be sure the decimal points are lined up so that the place-values are also lined up.

Find the sum. 1) (-0.26) = Line up the decimals and add (same signs). 2) Get a common denominator and subtract.

Find the difference. 3) Change subtraction to adding the opposite. Get a common denominator. Subtract and keep sign of the larger number.

Find the difference. 4) Get a common denominator and subtract. Change subtraction to adding the opposite.

Substitute for y: (-3.42) ) Solve 6.32 – y if y = -3.42

Extra Practice

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