Difference between revisions of "Find the Reciprocal"
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Reciprocals are helpful in all sorts of algebraic equations. For example when you are dividing one fraction by another you multiply the first by the Reciprocal of the 2nd. You might also need reciprocals when finding equations of lines. | Reciprocals are helpful in all sorts of algebraic equations. For example when you are dividing one fraction by another you multiply the first by the Reciprocal of the 2nd. You might also need reciprocals when finding equations of lines. | ||
| − | [[Category:Multiplication and Division]] | + | [[Category: Multiplication and Division]] |
[[Category:Fractions]] | [[Category:Fractions]] | ||
== Steps == | == Steps == | ||
===Finding the Reciprocal of a Fraction or Whole Number=== | ===Finding the Reciprocal of a Fraction or Whole Number=== | ||
| − | #Find the reciprocal of a fraction by flipping it. The definition of "reciprocal" is simple. To find the reciprocal of any number, just calculate "1 ÷ (that number)." For a fraction, the reciprocal is just a different fraction, with the numbers "flipped" upside down (inverted).<ref>http://www.mathsisfun.com/reciprocal.html</ref> | + | #Find the reciprocal of a fraction by flipping it. The definition of "reciprocal" is simple. To find the reciprocal of any number, just calculate "1 ÷ (that number)." For a fraction, the reciprocal is just a different fraction, with the numbers "flipped" upside down (inverted).<ref name="rf1">http://www.mathsisfun.com/reciprocal.html</ref> |
#*For instance, the reciprocal of <sup>3</sup>/<sub>4</sub> is '''<sup>4</sup>/<sub>3</sub>'''. | #*For instance, the reciprocal of <sup>3</sup>/<sub>4</sub> is '''<sup>4</sup>/<sub>3</sub>'''. | ||
#Write the reciprocal of a whole number as a fraction. Again, the reciprocal of a number is always 1 ÷ (that number). For a whole number, write that as a fraction; there's no point in calculating it out to a decimal. | #Write the reciprocal of a whole number as a fraction. Again, the reciprocal of a number is always 1 ÷ (that number). For a whole number, write that as a fraction; there's no point in calculating it out to a decimal. | ||
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#Change the division problem to use whole numbers. The first step to [[Divide-Decimals|dividing decimals]] is to move the decimal point until all the numbers involved are whole numbers. As long as you move the decimal point the same number of spaces for both numbers, you'll get the correct answer. | #Change the division problem to use whole numbers. The first step to [[Divide-Decimals|dividing decimals]] is to move the decimal point until all the numbers involved are whole numbers. As long as you move the decimal point the same number of spaces for both numbers, you'll get the correct answer. | ||
#*For example, you can take 1 ÷ 0.4 and rewrite it as 10 ÷ 4. In this case, you've moved each decimal place one space to the right, which is the same as multiplying each number by ten. | #*For example, you can take 1 ÷ 0.4 and rewrite it as 10 ÷ 4. In this case, you've moved each decimal place one space to the right, which is the same as multiplying each number by ten. | ||
| − | #Solve the problem using long division. Use [[Do | + | #Solve the problem using long division. Use [[Do Long Division|long division]] techniques to calculate the reciprocal. If you calculate it for 10 ÷ 4, you'll get the answer '''2.5''', the reciprocal of 0.4. |
== Tips == | == Tips == | ||
| − | *A numbers negative reciprocal is the same as the regular reciprocal, multiplied by negative one.<ref>http://www.mathwarehouse.com/negative-reciprocals/</ref> For instance, the negative reciprocal of <sup>3</sup>/<sub>4</sub> is -<sup>4</sup>/<sub>3</sub>. | + | *A numbers negative reciprocal is the same as the regular reciprocal, multiplied by negative one.<ref name="rf2">http://www.mathwarehouse.com/negative-reciprocals/</ref> For instance, the negative reciprocal of <sup>3</sup>/<sub>4</sub> is -<sup>4</sup>/<sub>3</sub>. |
| − | *The reciprocal is sometimes called the "multiplicative inverse."<ref>http://www.cliffsnotes.com/cliffsnotes/math/in-math-what-does--i-reciprocal-i-mean</ref> | + | *The reciprocal is sometimes called the "multiplicative inverse."<ref name="rf3">http://www.cliffsnotes.com/cliffsnotes/math/in-math-what-does--i-reciprocal-i-mean</ref> |
*The number 1 is its own reciprocal, since 1 ÷ 1 = 1. | *The number 1 is its own reciprocal, since 1 ÷ 1 = 1. | ||
| − | *The number 0 does not have a reciprocal, since 1 ÷ 0 is undefined.<ref | + | *The number 0 does not have a reciprocal, since 1 ÷ 0 is undefined.<ref name="rf1" /> |
== Related Articles == | == Related Articles == | ||
