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Core Connections: Course 2 View details

3. Section 3.3

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Exercise 123 Page 176

Practice makes perfect

We want to complete the given Diamond Problem by using the given pattern.

In the given diamond, y is - 5. We can fill the remaining corners when we find a number corresponding to x such that the product xy is equal to - 10. xy= - 10 ⇒ x (- 5)=10 Notice that we got an equation that we can solve for x. Let's do it!

x(- 5)=- 10

DivEqn

.LHS /- 5.=.RHS /- 5.

x(- 5)/- 5=- 10/- 5

CancelCommonFac

Cancel out common factors

x(- 5)/- 5=- 10/- 5

SimpQuot

Simplify quotient

x=- 10/- 5

DivNegNeg

- a/- b=a/b

x=10/5

CalcQuot

Calculate quotient

x=2

We found that x is equal to 2. Now we can calculate the value of the sum x+y.

x+y

SubstituteII

x= 2, y= - 5

2+( - 5)

AddNeg

a+(- b)=a-b

2-5

SubTerm

Subtract term

- 3

Finally, we can complete our Diamond Problem.

We want to complete the given Diamond Problem. To do so, we will use the given pattern.

In the given diagram, x is 3.4 and y is 10. We can fill the remaining corners by calculating the product and the sum of these numbers. Let's do it!

	x=2, y=3
Product (xy)	3.4( 10)=34
Sum (x+y)	3.4+ 10=13.4

Finally, we can complete our Diamond Problem.

We want to complete the given Diamond Problem. To do so, we will use the given pattern.

In the given diamond, x is 3 15. We can fill the remaining corners when we find a number corresponding to y such that the product xy is equal to 16. xy= 16 ⇒ (3 15)y=16 Notice that we got an equation that we can solve for y. Before do it, we will rewrite the mixed number as a fraction.

3 15

MixedToFrac

a bc=a* c+b/c

3* 5+1/5

Multiply

15+1/5

AddTerms

Add terms

16/5

Let's substitute the fraction on the equation for xy. xy= 16 ⇒ (16/5)y=16 Now, we will solve the equation for y. Let's do it!

(16/5)* y=16

▼

Solve for y

MultEqn

LHS * 5=RHS* 5

5 * (16/5)* y=5 * 16

FracMultDenomToNumber

a/5* 5 = a

(16)y=16 * 5

Multiply

(16)y=80

DivEqn

.LHS /16.=.RHS /16.

(16)y/16=80/16

CancelCommonFac

Cancel out common factors

(16)y/16=80/16

SimpQuot

Simplify quotient

y=80/16

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

▼

Evaluate

SubstituteII

x= 16/5, y= 5

16/5+ 5

NumberToFrac

a = 5* a/5

16/5+5 * 5/5

Multiply

16/5+25/5

AddFrac

Add fractions

16+25/5

AddTerms

Add terms

41/5

Now, let's write this fraction as a mixed number.

41/5

WriteSum

Write as a sum

40+1/5

WriteSumFrac

Write as a sum of fractions

40/5+1/5

CalcQuot

Calculate quotient

8+1/5

AddFrac

Add fractions

8 15

Finally, we can complete our Diamond Problem.

We want to complete the given Diamond Problem. To do so, we will use the given pattern.

In the given diamond, x is - 3. We can fill the remaining corners when we find a number corresponding to y such that the product xy is equal to 15. xy= 15 ⇒ (3)y=15 Notice that we got an equation that we can solve for y. Let's do it!

(- 3)* 15

▼

Solve for y

DivEqn

.LHS /- 3.=.RHS /- 3.

(- 3)y/- 3=80/15

CancelCommonFac

Cancel out common factors

(- 3)y/- 3=15/- 3

SimpQuot

Simplify quotient

y=15/- 3