Exercise 65 Page 106

To find the missing numbers, let's identify the variables using our variable diamond and substitute the correct numbers into our pattern.

Diamond A

In Diamond A, we are given that C=-98 and A=7. Substituting these values into our pattern gives us the following equations. -98 &=7 * B D&= 7+B From the first equation, we can calculate B by isolating it on one side. We found B. Now, we can substitute it into the second equation to find D.

Now we can complete our first diamond.

Diamond B

In Diamond B, we are given values for A and B, and we want to find C and D. A= 3/2 and B=3/2 To do this, we can substitute the numbers in our pattern.

C= A * B D=A+B

(I), (II): A= 3/2, B= 3/2

C= 32 * 32 D= 32+ 32

MultFrac

(I): Multiply fractions

C= 3*32*2 D= 32+ 32

Multiply

(I):Multiply

C= 94 D= 32+ 32

▼

(I):Write fraction as a mixed number

Rewrite

(I):Rewrite 9 as 8+1

C= 8+14 D= 32+ 32

WriteSumFrac

(I):Write as a sum of fractions

C= 84+ 14 D= 32+ 32

CalcQuot

(I):Calculate quotient

C=2+ 14 D= 32+ 32

AddTerms

(I):Add terms

C=2 14 D= 32+ 32

AddFrac

(II): Add fractions

C=2 14 D= 62

CalcQuot

(II):Calculate quotient

C=2 14 D=3

We can now complete our second diamond.

Diamond C

In this case, we are given that C= 54 and B=- 52. Substituting these values into our pattern gives us the following equations. 5/4&=A * (-5/2) D &= A+ (-5/2) From the first equation, we can calculate A by isolating it on one side.

5/4=A* (-5/2)

MultPosNeg

a(- b)=- a * b

5/4=-5/2A

▼

Isolate A

MultEqn

LHS * 2=RHS* 2

5/4*2=-5A

DivEqn

.LHS /(-5).=.RHS /(-5).

5/4*2÷(-5)=A

MoveRightFacToNum

a/c* b = a* b/c

5*2/4÷(-5)=A

DivFracSL

.a/b /c.= a/b* c

5*2/4*(-5)=A

Multiply

Multiply

10/-20=A

ReduceFrac

a/b=.a /10./.b /10.

1/-2=A

MoveNegDenomToFrac

Put minus sign in front of fraction

-1/2=A

RearrangeEqn

Rearrange equation

A=-1/2

We found A. Now, we can substitute it into the first equation to find D.

D=A+(-5/2)

Substitute

A= -1/2

D= -1/2+(-5/2)

AddNeg

a+(- b)=a-b

D=-1/2-5/2

SubFrac

Subtract fractions

D=-1-5/2

SubTerm

Subtract term

D=-6/2

CalcQuot

Calculate quotient

D=-3

Now we can complete our third diamond.

Diamond D

In Diamond D, we are given that D=0 and A=-10. Substituting these values into our pattern gives us the following equations. C &=-10 * B 0&= -10 +B From the second equation, we can calculate B by isolating it on one side.

0=-10+B

AddEqn

LHS+10=RHS+10

10=B

RearrangeEqn

Rearrange equation

B=10

We found B. Now, we can substitute it into the second equation to find D.

C=-10* B

Substitute

B= 10

C=-10* 10

MultNegPos

(- a)b = - ab

C=-100

Let's complete our last diamond with these numbers.