Solving One-Step Linear Equations with Mixed Numbers: Multiplication
A mixed number is a number expressed as the sum of a whole number and a fractions , such as .
It is usually easier to do calculations with improper fractions than mixed numbers, but mixed numbers give a better idea of the size of a number. So you should know how to convert back and forth.
To solve an equation that has a mixed number coefficient, we convert the mixed number to an improper fraction as the first step.
We can solve linear equations when only multiplication or division is involved. If there's a coefficient in front of the variable, multiply by the reciprocal of that number to get a coefficient of .
Example :
Solve.
Rewrite the mixed numbers as improper fractions.
The inverse operation of division is multiplication.
To isolate the variable (to get a coefficient of ), multiply both sides by which is the reciprocal of .
Simplify.
Therefore, the solution is .
