This question type showed up 18 times this year (on average once per test). The average placement was at question # 34, with the median at question # 28.
Number Dojo Level: 79
The reciprocal of a number is also called its multiplicative inverse. You can divide 1 by any number to find the number's reciprocal. Also, the product of any number and its reciprocal is always 1. There are several types of questions that appear on number sense tests; I will demonstrate how to find the solution to each type.
To find the reciprocal of a:
- Whole number (Integer): Write it as a fraction's denominator, with 1 as the numerator
- Fraction: Flip it over. In other words, switch its denominator and numerator.
- Mixed Number: Convert it to an improper fraction, and then flip it over.
- Decimal: Convert it to a fraction, and then flip it over.
Be sure to pay attention to what's after the answer blank. The test writers will often ask for a specific type of answer, such as decimal, mixed number, or fraction.
Example 1: The multiplicative inverse of 5 is ___
- There is no specific type of answer required. Simply write a fraction with 5 on the bottom and 1 on the top. The answer is 1/5. (.2 would also be correct).
Example 2: The reciprocal of 3/7 is ___
- There is no specific type of answer required. Simply flip the fraction over and write 7/3. (2 1/3 would also be correct).
Example 3: The reciprocal of -5/8 is ___ (decimal)
- Flip the fraction over to get -8/5.
- Convert -8/5 to a decimal. (Review ConvFracDeci if necessary). The answer is -1.6.
Example 4: The multiplicative inverse of 7/16 is ___ (mixed number)
- Flip the fraction over to get 16/7.
- Convert to a mixed number. The answer is 2 2/7.
Example 5: The reciprocal of 1.3 is ___ (fraction)
- Convert the decimal to a fraction. (Review ConvDeciFrac if necessary). You get 13/10.
- Flip the fraction over to get 10/13.
Example 6: The reciprocal of -2.4 is ___ (fraction)
- Convert the decimal to a fraction: -24/10 = -12/5.
- Flip the fraction over to get -5/12.
Example 7: The multiplicative inverse of 0.4 is ___ (mixed number)
- Convert the decimal to a fraction: 4/10 = 2/5.
- Flip the fraction over to get 5/2.
- Convert it to a mixed number: 2 1/2.