Fractions
To add or subtract fractions, first adjust them so that they have a common denominator. This can be achieved by “cross-multiplying”, or multiplying each by the other's denominator.
Fractions can be adjusted by multiplying the numerator (top) and denominator (bottom) by the same value.has the same value as
The value of + isn't but rather,
+ Take the original fraction.
Cross multiply.
+ Work out the parentheses.
Add accordingly.
To multiply fractions, multiply numerators by numerators and denominators by denominators.
multiplied byis
To divide fractions, invert one of the fractions, then multiply them.
divided by= multiplied by=
It doesn't matter which fraction is inverted.
Always reduce fractions which aren't in their lowest terms
is equal toTo reduce a fraction, divide both the numerator and the denominator by a common factor. For example, both 3 and 6 are divisible by 3; thus, equals
An “improper fraction” is a fraction suchas in which the numerator exceeds the denominator.is the same asor 1.5.
Practice
Solve for the value of each of the
following.
1. +
2. ()
3. ÷
Answers to Practice Questions
1.
+ Take the initial equation.
+ “Cross multiply.” Multiply each fraction by the other's denominator.
+ Work out the parentheses.
+= Add the numerators - leave the denominators be.
= Reduce the final fraction by dividing both the numerator and denominator by 2, 3, or another common factor.
2.
To multiply fractions, multiply numerators by numerators and denominators by denominators - 2(1) over 9(3).
3.
To divide fractions, invert and multiply. This yields a result of 5(1) over 2(1).