Calculate seven-ninths minus four-sixths.
We’ll need to follow the procedure for adding and subtracting fractions starting
with step one: check for common denominators. Step one tells us that we need to check for a common denominator. We’re working
with seven-ninths and four-sixths. Our denominators are not the same; they’re not common.
Before we move on to step two, we’ll need to look at six and nine and find a
common denominator for them. I know that 18 is divisible by nine and six. I think that 18 would be a good
common denominator here. To move from nine to 18, we would multiply by two; nine times two equals 18. But if we multiply the bottom half of our fraction, if we multiplied the
denominator by two, we also need to multiply the numerator by that same number, which means
we’ll need to multiply seven times two.
Another way to write the fraction seven-ninths is fourteen eighteenths. They are equal in
value, just written differently. Six times three equals 18. And if I multiplied the denominator by three, I need to multiply the numerator
by three which means I need to multiply four times three. Twelve eighteenths is an equivalent fraction for four-sixths.
Back to step one, we were checking for a common denominator. We’ve now found the
common denominator and have converted these fractions so that we’re subtracting fourteen eighteenths minus
twelve eighteenths. It means we can move on to step two.
Step two says add or subtract numerators. Well, our problem is a subtraction
problem. That means we’ll subtract 14 minus 12. 14 minus 12 equals two, and the denominator doesn’t change. We leave that as 18.
Step three tells us to simplify this fraction, if we can. I noticed that two and
18 are both even numbers, which means they’re both divisible by two. I’ll need to divide the numerator and the denominator by two to simplify the
fraction. The simplified fraction of two eighteenths is one-ninth.
Seven-ninths minus four-sixths equals one-ninth.