Mary Jane Sterling - Algebra I All-in-One For Dummies

The box method is a very nicely structured process that has an added bonus. You can use it to find the least common denominator of two or more fractions, and you can also use it to find the greatest common factor of two or more numbers.

Consider the addition problem . You don’t want to multiply them all together. And, yes, you could look at multiples of the largest denominator. But, as an option, look at the box method.

1 Write the three denominators in an “upside-down” division box.

2 Outside the box, on the left, write a number that divides all of the denominators evenly.For this first try, I’ll use 2.

3 Divide 2 into each denominator, putting the quotients under the respective denominators.

4 Now put a division box around these quotients and find another divisor. Repeat the process until there are no more common factors.This time I chose 3. The order of choices doesn’t really matter.One more time:

5 You’re finished when the quotients don’t have any common factors. All three have to have the same common factor. You can’t divide just two of them.

So, what do you have here? First, you have the greatest common factor of the three numbers: . You multiply the divisors, the numbers down the left side, and get the biggest number that will divide all three numbers evenly.

But you’re looking for a common denominator! To get that, find the product of those three numbers in the GCF times the product of the three numbers left on the bottom.

The least common denominator is: . This method is a bit nicer than looking at all the multiples of 96.

Now that you have the tools necessary, you can investigate ways to perform binary operations on fractions. Addition and subtraction go together, because they both require common denominators. Multiplication and division are paired, because they can be performed without having to create the same denominator. And division is just “multiplication adjusted”!

You can add fractions together or subtract one from another if they have a common denominator. After you find the common denominator and change the fractions to their equivalents, you can add the numerators together or subtract them (keeping the denominators the same).

Adding and subtracting fractions takes a little special care. You can add quarts and gallons if you change them to the same unit. It’s the same with fractions. You can add thirds and sixths if you find the common denominator first.

To add or subtract fractions:

1 Convert the fractions so that they have the same value in the denominators.Find out how to do this in the section, “ Finding common denominators.”

2 Add or subtract the numerators.Leave the denominators alone.

3 Reduce the answer, if needed.

Q.In her will, Jane gave of her money to the Humane Society and of her money to other charities. How much was left for her children’s inheritance?

A.The fractions and aren’t compatible because the denominators don’t have any factors in common. The fraction has the larger denominator and can be written as or or , and so on. You can stop at because 3 divides 21 evenly: and . Add the numerators to get the total designation to charity in Jane’s will: . Subtract that total from the whole of Jane’s proceeds to find what portion is allotted to her children: . Jane’s children will be awarded of her estate.

Q.

A.First find the common denominator, 24, and then complete the addition:

Q.

A.You need a common denominator of 30:

The whole number parts are separated from the fractional parts to keep the numbers in the computations smaller. Be sure to apply the subtraction to both the whole number and fraction when needed.

Q.

A.In this problem, you see another option: you can change both mixed numbers to improper fractions. The common denominator is 56: