Exercise 116 Page 117

Practice makes perfect

We want to complete the given Diamond Problem. Let's consider the given diagram and the pattern used in the problem!

We can fill the remaining corners when we find two rational numbers that sum up to 25 and have a product of 0. To find these numbers, let's think of different pairs of numbers that we can multiply to get 0 and calculate their sums till we find the pair that sums up to 25.

Product (xy)	Sum (x+y)	Is Sum Equal to 25?
0=1(0)	1+0=1	*
0=5(0)	5+0=5	*
0=25(0)	25+0=25	✓

Notice that we can complete our pattern when one factor is equal to 25 and the other is equal to 0. Let's complete our Diamond Problem!

Remember that this is one of the possible solutions. The Diamond Problem with x=0 and y=25 also corresponds to the pattern.

We are asked to complete the given Diamond Problem. Let's start by comparing the given diagram with the pattern used in the problem!

In the given diamond, x is 6. We can fill the remaining corners when we find a number corresponding to y such that the product xy is equal to - 30. xy= - 30 ⇒ 6y=- 30 Notice that we got an equation that we can solve for y. Let's do it!

6y=- 30

DivEqn

.LHS /6.=.RHS /6.

6y/6=- 30/6

CancelCommonFac

Cancel out common factors

6y/6=- 30/6

SimpQuot

Simplify quotient

y=- 30/6

MoveNegNumToFrac

Put minus sign in front of fraction

y=- 30/6

CalcQuot

Calculate quotient

y=- 5

We found that y is equal to - 5. Now we can calculate the value of the sum x+y.

x+y

SubstituteII

x= 6, y= - 5

6+( - 5)

AddNeg

a+(- b)=a-b

6-5

SubTerm

Subtract term

Finally, we can complete our Diamond Problem.

Let's take a look at the diagram and the pattern!

In the given diagram, x has a value of 11. We also know that the sum x+y is equal to 25. Let's use this information to find the value of y.

x+y= 25

Substitute

x= 11

11+y=25

SubEqn

LHS-11=RHS-11

11+y-11=25-11

SubTerms

Subtract terms

y=14

We found that y is equal to 14. Next, we can calculate the value of the product xy.

SubstituteII

x= 11, y= 14

11( 14)

Multiply

154

Now we can complete our Diamond Problem.

Let's start by analyzing the given diagram and the pattern used in the problem!

We can fill the remaining corners when we find two rational numbers that sum up to 31 and have a product of 234. To find these numbers, let's think of different pairs of numbers that we can multiply to get 234 and calculate their sums till we find the pair that sums up to 31.