Adding and Subtracting Rational Numbers Worksheet

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```					  Adding and Subtracting Rational Numbers Worksheet

Adding and Subtracting Rational Numbers Worksheet

Addition and subtraction are the hardest things you'll be doing with rational expressions
because, just like with regular fractions, you'll have to convert to common denominators.
Everything you hated about adding fractions, you're going to hate worse with rational
expressions. But stick with me; you can get through this!

To find the common denominator, I first need to find the least common multiple (LCM) of
the three denominators. (For old folks like me, whenever you see "LCM", think "LCD", or
"lowest common denominator". In this context, they're pretty much the same thing.) There
are at least a couple ways of doing this. You could use the "listing" method, where you list
the multiples of the three denominators, until you find a number that is in all three lists,
like this:

If you know how to add and subtract whole numbers, then you can add and subtract
decimals! Just be sure to line up the terms so that all the decimal points are in a vertical
line.

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Like fractions are fractions with the same denominator. You can add and subtract like
fractions easily - simply add or subtract the numerators and write the sum over the
common denominator.Before you can add or subtract fractions with different
denominators, you must first find equivalent fractions with the same denominator, like
this: Find the smallest multiple (LCM) of both numbers. Rewrite the fractions as equivalent
fractions with the LCM as the denominator. When working with fractions, the LCM is
called the least common denominator (LCD).

It's easy to add and subtract like fractions, or fractions with the same denominator. You
just add or subtract the numerators and keep the same denominator. The tricky part
comes when you add or subtract fractions that have different denominators. To do this,
you need to know how to find the least common denominator. In an earlier lesson, you
learned how to simplify, or reduce, a fraction by finding an equivalent, or equal, fraction
where the numerator and denominator have no common factors. To do this, you divided
the numerator and denominator by their greatest common factor.

In this lesson, you'll learn that you can also multiply the numerator and denominator by
the same factor to make equivalent fractions.

Example:-

prime factorization of 4 = 2 × 2
prime factorization of 6 = 2 × 3
LCD = 2 × 2 × 3 = 12

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Now that we have our least common denominator, we can make equivalent like fractions
by multiplying the numerator and denominator of each fraction by the factor(s) needed.
We multiply 3/4 by 3/3, since 3 times 4 is 12, and we multiply 1/6 by 2/2, since 2 times 6
is 12. This gives the equivalent like fractions 9/12 and 2/12. Now we can add the
numerators, 9 + 2, to find the answer, 11/12.

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Thank You

TutorCircle.com

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