Section 4.2 Part 2: Reciprocals and Dividing Fractions

What is the reciprocal of −1?

-1 −1⋅−1=1✓

What is the reciprocal of −4?

-1/4 To find the reciprocals, we keep the sign and invert the fractions. It follows that the reciprocal of −4 is −1/4.Check by multiplying the number and its reciprocal to find −4⋅−1/4 and 4/4=1✓

Divide: 16/45÷(−144).

-1/405

Divide: −3/17÷24/13.

-13/136 To divide fractions, multiply the first fraction by the reciprocal of the second and then simplify. −3/17÷24/13=−3/17⋅13/24 To multiply fractions, multiply the numerators, multiply the denominators, and then simplify by removing common factors. Notice that since the signs are different, the product is negative. -3/17*13/24= -3/17 *13/24 = 3*13/17*2*2*2*3 =-3*13/17*2*2*2*3 =-13/136

What is the reciprocal of −1/2? Provide your answer below:

-2

Divide: −9/5÷18/3.

-3/10

Divide: −3/24÷1/5n. Provide your answer below:

-5n/8 To divide fractions, multiply the first fraction by the reciprocal of the second and then simplify. −3/24÷15n=−3/24⋅5n To multiply fractions, multiply the numerators, multiply the denominators, and then simplify by removing any common factors. Notice that since the signs are different, the product is negative. −3/24⋅5n= −3⋅5n/24⋅1= −5n⋅3/8⋅3= −5n⋅3/8⋅3 =−5n8

What is the reciprocal of 1?

1 To find the reciprocals, we keep the sign and invert the fractions. It follows that the reciprocal of 1 is 1.Check by multiplying the number and its reciprocal to find 1*1=1 1/1= 1

What is the reciprocal of 2/11? Provide your answer below:

11/2

Divide: −6/38÷42/−15x.

15x/266 To divide fractions, multiply the first fraction by the reciprocal of the second and then simplify. To multiply fractions, multiply the numerators, multiply the denominators, and then simplify by removing any common factors. Notice that since the signs are the same, the product is positive.

Divide: −16/21÷112/−19.

19/147

What is the reciprocal of 1/4?

4 To find the reciprocals, we keep the sign and invert the fractions. It follows that the reciprocal of 14 is 4.Check by multiplying the number and its reciprocal to find 1/4⋅4 4/4=1 ✓

Divide: −14/27÷56/−m.

m/108 To divide fractions, multiply the first fraction by the reciprocal of the second and then simplify. To multiply fractions, multiply the numerators, multiply the denominators, and then simplify by removing any common factors. Notice that since the signs are the same, the product is positive.