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Here are a few recommended readings before getting started with this lesson.
Shortcuts exist to find the reciprocals of specific types of numbers such as natural numbers, integer numbers, fractions, and decimals.
Type | Reciprocal | Example |
---|---|---|
Natural number a | a1 | The reciprocal of 2 is 21. |
Integer numbers a, a=0 | a1 | The reciprocal of -6 is -61. |
Fraction ba, b=0 | ab | The reciprocal of 23 is 32. |
Decimal a | a1 | The reciprocal of 0.2 is 0.21. |
Dividing a fraction by another fraction is the same as multiplying the first fraction by the reciprocal of the second fraction.
ba÷dc=ba⋅cd
Tearrik was gifted an heirloom by his grandfather. It is a handmade kimono.
Tearrik wants to make a box to hold this beautiful kimono. He plans to cut a piece of wood that is 5 feet long. He wants the cuts to create equal parts.
Rewrite 5 as 15
ba÷dc=ba⋅cd
Multiply fractions
Multiply
Write as a sum
Write as a sum of fractions
Calculate quotient
Rewrite 6+41 as 641
Multiply fractions
Cancel out common factors
Simplify quotient
A diagram can be used to model the division of 5 by 54. Divide each foot of the 5-foot-long wood into 5 equal pieces.
Notice that each of the smaller parts represents a 51 of a foot. Then determine how many of the 54-foot-long pieces are contained within the wood.
There are 6 of them. The length of the remaining part is a 51 of a foot. Note that the remaining part is also 41 of 54. This confirms that the result found algebraically is correct.
Tearrik is excited about making the box. A problem arises, however. He realizes a bit of paint would look cool but he does not have any in his home. Tearrik is full of energy and starts to run to the nearest paint shop.
Tearrik runs 32 of the way from the garage to the nearest paint shop.
ba÷dc=ba⋅cd
Multiply fractions
Multiply
ba÷dc=ba⋅cd
Multiply fractions
Multiply