Reciprocals with Equations

Dividing with Equations

Reciprocals

• We use reciprocals to solve multiplication/division equations that contain fractions.

Reciprocal Example

 $\frac{1}{3}$  

• To find the reciprocal, we simply FLIP the fraction!

Multiple Select

Choose the reciprocal of:

 $\frac{5}{7}$  

•  $\frac{5}{7}$  

•  $\frac{7}{5}$  

Multiple Select

Choose the reciprocal of:

 $\frac{2}{5}$  

•  $\frac{5}{2}$  

•  $\frac{2}{5}$  

Solving equations using reciprocals.

•  $\frac{3}{5}t\ =\ 6$  

•  $\frac{1}{7}t\ =\ 3$  

Multiple Choice

Solve for f. 
 $\frac{4}{5}y\ =\ 8$  

•  $\frac{32}{5}$  

• 10

Multiple Choice

Solve for f. 
 $\frac{1}{9}w\ =\ 6$  

• 54

•  $\frac{2}{3}$  
  

Dividing with Equations - be careful!

•  $\frac{a}{9\ }\ =\ 9$  

•  $\frac{1}{9}a\ =\ 8$  

Dividing with Equations - be careful!

•  $\frac{a}{9\ }\ =\ 8$  

•  $\frac{p}{5}\ =\ 5$  

Multiple Choice

Solve for the variable.
 $\frac{1}{3}n\ =\ 12$  

• 36

• 4

Open Ended

Solve for the variable.
 $\frac{y}{2}\ =\ 34$  

Multiple Choice

Solve for the variable. $-\frac{3}{2}a\ =\ \frac{7}{3}$  

• -14/9

• -9/14

• -21/6

Multiple Choice

 $\frac{3}{4}x\ =\ 7$  

• x= 9 1/3

• x = 21/4

• x = 5  1/4

Multiple Choice

Solve for the variable. $-\frac{z}{12}\ =\ 4$  

• -48

• -4

• 48

Multiple Choice

Solve for the variable. $\frac{c}{2}\ =\ -14$  

• 24

• -24

• -28

Multiple Choice

Solve the equation: 
x + 7 = 12

• x = 5
• x = 19
• x = -5
• x = 84

Multiple Choice

Solve the equation:

x - 4 = -3

• x = -7

• x = 1

• x = 12

• x = -12

Multiple Choice

Solve the equation:

x + 14 = -3

• x = 17

• x = -17

• x = 12