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Alegbra 1A - Mixed Numbers











































-6 - 7 3/4 + (-2 2/3)=

Convert each mixed number to a fraction with the same denominator, add (or subtract) the fractions, and then convert the total back into a mixed number.

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Aug 28, 2011
Adding Mixed Numbers
by: Staff


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Part II


Convert the fraction 31/4 to a fraction with a denominator of 12

The denominator of the fraction (31)/4 is 4. To convert the denominator of 4 to a denominator of 12, we are going to multiply the 4 by 3.

As before, we cannot change the value of the fraction. We are going to multiply the numerator AND the denominator by 3. In other words, the fraction 31/4 will be multiplied by another fraction: 3/3. Note that 3/3 = 1, so we are actually multiplying by 1. The decimal value of the fraction (31)/4 will not change.

= (31/4)*(3/3)

When multiplying two fractions, multiply the two numerators and multiply the two denominators:

= (31*3)/(4*3)

7 3/4 = (31)/4 = (93)/12


Convert the fraction 8/3 to a fraction with a denominator of 12

The denominator of the fraction 8/3 is 3. To convert the denominator of 3 to a denominator of 12, we are going to multiply the 3 by 4.

As before, we cannot change the value of the fraction. We are going to multiply the numerator AND the denominator by 4. In other words, the fraction 8/3 will be multiplied by another fraction: 4/4. Note that 4/4 = 1, so we are actually multiplying by 1. The decimal value of the fraction 8/3 will not change.

= (8/3)*(4/4)

When multiplying two fractions, multiply the two numerators and multiply the two denominators:

= (8*4)/(3*4)

2 2/3 = 8/3 = (32)/12


This is a summary of the steps which have completed so far:

Original problem:

= - 6 - 7 3/4 + (-2 2/3)


Problem after converting the mixed numbers to improper fractions:

= - 6/1 - 31/4 - 8/3


Problem after converting the improper fractions to fractions with a common denominator:

= - (72)/12 - (93)/12 - (32)/12


Since each fraction has the same denominator, the fractions can finally be added. When adding fractions, only the numerators are added.

= (- 72 - 93 - 32)/12

= (-197)/12

This fraction cannot be reduced, but it can be converted into a mixed number.

To convert (-197)/12 to a mixed number, divide -197 by 12

= (-197)/12

= (-197) ÷ 12

= -16, remainder 5

= -16 5/12


The final answer is: -16 5/12 [or (-197)/12 or -16.4167]



Check the answer with a calculator:

= -6 - 7 3/4 + (-2 2/3)

= -6 - 7.75 + (-2.6667)

= -16.4167


Since -16.4167 is the same answer obtained by converting -16 5/12 to its decimal equivalent, the answer of -16 5/12 is correct.


Thanks for writing.

Staff
www.solving-math-problems.com



Aug 28, 2011
Adding Mixed Numbers
by: Staff


Part I

The question:

-6 - 7 3/4 + (-2 2/3) =


The answer:

-6 - 7 3/4 + (-2 2/3) =

There are three widely used methods of adding these mixed numbers: (1) add the whole numbers and the fractional components separately (- 6 - 7 - 2) + (-3/4 - 2/3); (2) convert the three numbers to their decimal equivalents, and then add the decimal equivalents (-6.0 - 7.75 -.6666…); (3) convert any mixed numbers to improper fractions, and then add the fractions.


I’m going to demonstrate the third method.

As you know, the numerators of fractions can be added directly if every fraction being added has the same denominator.

That is the approach I’m going to use.

I’m going to show you how to convert each mixed number to a fraction with the same denominator, add the fractions, and then convert the total back into a mixed number.


Begin by converting each number into an improper fraction.

6 = 6/1

7 ¾ = 31/4

2 2/3 = 8/3


You’re original problem now looks like this:

-6 - 7 3/4 + (-2 2/3)

= -6/1 - 31/4 - 8/3


We are still not quite ready to add the fractions, since fractions cannot be added directly unless the denominators of all three fractions are the same.

At this point, we have three different denominators: 1, 4, and 3

Computing a common denominator

We can compute a common denominator by multiplying the denominators of all three fractions:

Common denominator = 1 * 4 * 3 = 12

The next step is to convert each of the fractions (6/1, 31/4, and 8/3) to fractions with the denominator of 12.


Convert the fraction 6/1 to a fraction with a denominator of 12

The denominator of the fraction 6/1 is 1. To convert the denominator of 1 to a denominator of 12, we are going to multiply the 1 by 12.

However, simply multiplying the denominator by 12 would change the value of the fraction 6/1 to 6/12.

Since we cannot change the value of the fraction, we are going to multiply the numerator AND the denominator by 12. In other words, the fraction 6/1 will be multiplied by another fraction: 12/12. Note that 12/12 = 1, so we are actually multiplying by 1. The decimal value of the fraction 6/1 will not change.

= (6/1)*(12/12)

When multiplying two fractions, multiply the two numerators and multiply the two denominators:

= (6*12)/(1*12)

6 = 6/1 = (72)/12

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