The fraction 4/10 can be simplified to 2/5, so the expression in simplest form is / (5x 5)]. The new expression is then / (10x 5), which is not in simplest form. (x-2)/ (2x 3), the new numerator would be 4(x-2) and the new denominator would be (5x 2).The new expression, (10a 3)/20a can be simplified to ½ The numerator is 5a 3♲ or 10a 3, and the denominator is 4 ♵a or 20a.

Suppose the problem were (5a 3)/4 times 2/ (5a). The process of multiplication would be similar, so that a/9 times 7/10 would equal 7a/90. Suppose one ratio were a/9 and another were 7/10. The fraction 9/20 is in the simplest form, because there are no factors common to both 9 and 20 except for 1. To multiply ¾ by 3/5, multiply the numerators 3♳, and then multiply the denominators 4♵, to result in the new fraction or ratio of 9/20. The numerator 3 is in a ratio to the denominator 4. The fraction ¾ is a rational number, as is the fraction 3/5. Rational numbers are also known as fractions. Division is the inverse of multiplication, so multiply by the reciprocal (or inverse) of the divisor, and then simplify the expression. In order to multiply, first multiply the numerators, then the denominators, and then simplify the expression. The process of multiplying and dividing rational expressions is similar to multiplying and dividing rational numbers.

Rational expressions