Q. Find the least common denominator for the two fractions A. 72. Look at the multiples of 24: 24, 48, 72, 96. You can stop with the multiple 72, because that’s also a multiple of 18. The LCD is 72.
Q. How would you write the fractions
A. The fractions
21
22 Rewrite the fractions
23 Rewrite the fractions
24 Rewrite the fractions
25 Rewrite the fractions
26 Rewrite the fractions
Using the box method
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
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:
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:
Applying Fractional Operations
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”!
Adding and subtracting fractions
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.
A. The fractions
