18
Reciprocal (mutually inverse) numbers
Textbook, pp. 73–77
GoalUnderstand reciprocal numbers and find the reciprocal of a given number.
New words
reciprocal (mutually inverse) numbers · o‘zaro teskari sonlarreciprocal · teskari sonproduct equal to 1 · ko‘paytma 1improper fraction · noto‘g‘ri kasr
Explanation
Two numbers whose product is 1 are reciprocal (mutually inverse) numbers. The reciprocal of a/b is b/a, because a/b · b/a = 1. The reciprocal of a natural number n is 1/n. For a mixed number, turn it into an improper fraction first: 2 1/4 = 9/4, whose reciprocal is 4/9. The number 0 has no reciprocal, since 0 times any number is 0, not 1. Reciprocals are needed to divide fractions.
Worked examples
The reciprocal of 3/7 is 7/3: 3/7 · 7/3 = 21/21 = 1. The reciprocal of 5 is 1/5.
2 1/4 = 9/4, so the reciprocal is 4/9. Check: 9/4 · 4/9 = 1.
Class activity
“Find the flip”: the teacher shows a fraction card, pupils write its reciprocal and swap with a partner to check that the product is 1.
Practice
1
Write the reciprocal of 5/8.
8/5
2
Find the reciprocal of 3 1/2.
2/7
3
In 3/4 · x = 1, find x.
4/3
4
Why does 0 have no reciprocal?
0 times any number is 0, never 1.