[Photo by jimmiehomeschoolmom.]
Fractions confuse almost everybody. In fact, fractions probably cause more math phobia among children (and their parents) than any other topic before algebra. Middle school textbooks devote a tremendous number of pages to teaching fractions, and still many students find fractions impossible to understand. Standardized tests are stacked with fraction questions.
Fractions are a filter, separating the math haves from the luckless have nots. One major source of difficulty with fractions is that the rules do not seem to make sense. Can you explain these to your children?
Start with an easy one…
If you need a common denominator to add or subtract fractions…
- Why don’t you need a common denominator when you multiply?
When you multiply both terms (the numerator and denominator) of a fraction by the same number, you get an equivalent fraction:
When you divide both terms by the same number, you get an equivalent fraction:
Then why won’t it work to do this:
- Why, when you add the same number to both terms, don’t you get an equivalent fraction?
To multiply two fractions, you multiply the numerators and multiply the denominators:
To divide fractions, can you divide the numerators and divide the denominators?
…but it works only if you are careful to keep all the numbers in the right order. Remember that 3 ÷ 1 is NOT the same as 1 ÷ 3.
So then why can’t we do this?
- Why, when you need to add fractions, can’t you just add the numerators and add the denominators?
When you divide by a fraction, you can flip the fraction over and multiply:
When you multiply by a fraction, can you flip the fraction over and divide?
Yes, it works.
- Then why, when you have to subtract a fraction, can’t you just flip it over and add?
If you divide by flipping the fraction over and multiplying, does it matter which fraction you flip?
But if I flipped the other fraction:
NO ! !
Only the first equation is correct, so it definitely matters which fraction you flip.
- But why does it matter?
This is post #1 in the Fraction basics series.