Exercise 21 Page 13

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

Diamond A

Here we are given that C=15 and D=8. We want to find the numbers A and B. 15=A* B 8=A+B In this case, let's think of different pairs of numbers which multiply to give us 15. Notice that both numbers should be positive because they add to give 8, which is positive number. &15=1*15 &15=3*5 Let's check which, if any of these, will match the second condition as well.

&1+15=16 * & 3+5=8 The pair A=3 and B=5 works for the pattern. Therefore, this is the correct pair of numbers to complete the diamond.

Diamond B

In Diamond B, we are given values for A and B, and we want to find C and D. A= 3 and B=1 To do this, we can substitute the numbers in our pattern.

C= A * B D=A+B

(I), (II): A= 3, B= 1

C= 3 * 1 D= 3+ 1

MultByOne

(I): a * 1=a

C=3 D=3+1

AddTerms

(II): Add terms

C=3 D=4

We can now complete our second diamond.

Diamond C

In Diamond A, we are given that C=10 and A=5. Substituting these values into our pattern gives us the following equations. 10 &=5 * B D&= 5+B From the first equation, we can calculate B by isolating it on one side.

10=5* B

DivEqn

.LHS /5.=.RHS /5.

2=B

RearrangeEqn

Rearrange equation

B=2

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

D=5+B

Substitute

B= 2

D=5+ 2

AddTerms

Add terms

D=7

Now we can complete our third diamond.

Diamond D

In Diamond D, again we are given values for A and B, and we want to find C and D. A= 1/2 and B=1/3 To do this, we can substitute the numbers in our pattern.

C= A * B D=A+B

(I), (II): A= 1/2, B= 1/3

C= 12 * 13 D= 12+ 13

MultFrac

(I): Multiply fractions

C= 1*12*3 D= 12+ 13

Multiply

(I):Multiply

C= 16 D= 12+ 13

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Add fractions

ExpandFrac