Two numbers are multiplicative inverses of each other if the product of the numbers is one (1). Multiplicative Inverse is similar to the program MULTIPLY FRACTIONS except that you are to determine the second factor, which will be the multiplicative inverse of the first factor. Another name for multiplicative inverse is reciprocal The following image was made from Multiply with Lines Designer:
You can see from the picture that the first factor is 1 1/2 units in length. The second factor is the multiplicative inverse or reciprocal of the first factor. To determine the reciprocal, first write the first factor in fraction form as shown in MIXED NUMBERS TO FRACTION. The answer will be the reciprocal or inverse of the first factor. The numerator of the reciprocal will be the denominator of the first factor. The denominator will be the numerator of the first factor.
The numerator of the multiplicative inverse is 2 and the denominator is 3. This gives an answer of:
All the examples in Reciprocal demonstrate that a number multiplied by its inverse gives a product of 1. When you enter the inverse of the first factor correctly, an image of the product 1 will appear in yellow. Also, you will see the numerals for the first factor, the inverse and the product. Reciprocals greater than or equal to 1 may be written in mixed form or in fraction (a/b) form.
You can see from the image of the product that:
The inverse is the vertical distance, 2/3.
Multiplicative inverse is useful in division of fractions as you will see in the next topic in Visual Fractions, DIVIDE FRACTIONS.