Originally Posted by

**JeffM** I think we need to start at the very beginning.

If you need to add or subtract two fractions with different denominators, you must first change one or both FRACTIONS to make the denominators equal. To change the denominator of a fraction, you must also make a corresponding change to the numerator. You make a corresponding change by multiplying (or dividing) both numerator and denominator by the SAME number.

$\dfrac{3}{7} = \dfrac{4 \times 3}{4 \times 7} = \dfrac{12}{28}.$

I suspect where you were getting off track was that you heard "change the denominator" without realizing that you also had to make the corresponding change to the numerator. What people SHOULD say is to change the fraction by multiplying or dividing both numerator and denominator by the same number.

You with me on this?

Now you may have to change both fractions to make the denominators equal, in which case you will be changing one fraction by multiplying that fraction's numerator and denominator by some number and changing the other fraction by multiplying that fraction's numerator and denominator by a different number. SAME number for numerator and denominator of the same fraction, but DIFFERENT numbers for different fractions.

$\dfrac{3}{16} + \dfrac{2}{3} =$

$\dfrac{3 \times 3}{3 \times 16} + \dfrac{16 \times 2}{16 \times 3} =$

$\dfrac{9}{48} + \dfrac{32}{48} =$

$\dfrac{41}{48}.$