reciprocal | MathCelebrity Forum

# reciprocal

1. ### Solve 100 / 1/2

Solve 100 / 1/2 Dividing by a fraction is the same as multiplying by the reciprocal of the fraction: Reciprocal of 1/2 = 2 100 * 2 = 200
2. ### y varies directly as the reciprocal of x

y varies directly as the reciprocal of x The reciprocal of x is written as: 1/x The phrase varies directly means there exists a constant k such that y = k/x
3. ### product of a number and its reciprocal is increased by 7

product of a number and its reciprocal is increased by 7 The phrase a number means an arbitrary variable, let's call it x: x Its reciprocal means we take the reciprocal of x: 1/x product of a number and its reciprocal: x * 1/x x/x The x's cancel giving us: 1 is increased by 7 means we add...
4. ### How many 1/4 sheets are there in 5 sheets

How many 1/4 sheets are there in 5 sheets We divide 5 sheets by 1/4 sheets: 5/1/4 However, when we divide by a fraction, it's the same as multiplying by the reciprocal of the fraction: The reciprocal of 1/4 is 4/1, so we have: 5 * 4/1 = 20/1 = 20
5. ### Ande has 8 pints of milk. If he drinks 1/4 of a pint of milk each day, how long will the 8 pints of

Ande has 8 pints of milk. If he drinks 1/4 of a pint of milk each day, how long will the 8 pints of milk last him? Milk Days = Total Pints of Milk / pints drank per day Milk Days = 8 / 1/4 Dividing by a fraction is the same as multiplying by it's reciprocal. The reciprocal of 1/4 is 4/1, so...
6. ### the sum of x and its reciprocal

the sum of x and its reciprocal The reciprocal of x is found by dividing 1 by x: 1/x the sum of x and its reciprocal means we add 1/x to x: x + 1/x
7. ### M is the sum of a and its reciprocal

M is the sum of a and its reciprocal The reciprocal of a variable is 1 divided by the variable 1/a The sum of a and its reciprocal means we add: a + 1/a The phrase is means an equation, so we set M equal to the sum of a + 1/a: M = 1 + 1/a
8. ### How many one-fifths are there in 200?

How many one-fifths are there in 200? Using the rule of dividing by a fraction is the same as multiplying by the reciprocal, we have: 200 / 1/5 = 200 * 5 = 1000
9. ### the sum of the reciprocal of x and the reciprocal of y

the sum of the reciprocal of x and the reciprocal of y Reciprocal of x means 1 over x: 1/x Reciprocal of y means 1 over y: 1/y The sum means we add the two reciprocals together: 1/x + 1/y
10. ### The sum of the reciprocals of x and y

The sum of the reciprocals of x and y The reciprocal of a variable is found by taking 1 over the variable. Reciprocal of x = 1/x Reciprocal of y = 1/y The sum means we add the reciprocals together 1/x + 1/y
11. ### the sum of a and its reciprocal

the sum of a and its reciprocal The reciprocal of a is 1/a, so the sum is: a + 1/a
12. ### The square of a number added to its reciprocal

The square of a number added to its reciprocal The phrase a number means an arbitrary variable, let's call it x. the square of x mean we raise x to the power of 2. It's written as: x^2 The reciprocal of x is 1/x We add these together to get our final algebraic expression: x^2 + 1/x
13. ### If a/b = 2, what is the value of 4b/a?

If a/b = 2, what is the value of 4b/a? 4b/a = 4(b/a) If a/b = 2, then the reciprocal b/a = 1/2. So we have 4(1/2) = 2
14. ### the reciprocal of the product a and b

the reciprocal of the product a and b Take this algebraic expression in pieces: The product a and b means we multiply a times b ab The reciprocal means we take 1 over ab 1/ab
15. ### 5 more than the reciprocal of a number

5 more than the reciprocal of a number Take this algebraic expression in pieces: The phrase a number means an arbitrary variable, let's call it x. x The reciprocal of this number means we divide 1 over x: 1/x 5 more means we add 5 to 1/x 1/x + 5