Chapter Closure
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We know from the diagram that x= 56 and y=2 16. We can fill the remaining corners when we find the product and the sum of two numbers. Let's start with the sum!
x= 5/6, y= 2 16
a bc=a* c+b/c
Add fractions
Add terms
Calculate quotient
Next, we can calculate the product of two numbers.
x= 5/6, y= 2 16
a bc=a* c+b/c
Multiply fractions
Multiply
Write fraction as a mixed number
Let's complete our Diamond Problem!
We know from the diagram that x= 12 and y=6. We can fill the remaining corners when we find the product and the sum of two numbers. Let's start with the sum!
x= 1/2, y= 6
a = 2* a/2
Multiply
Add fractions
Add terms
Write fraction as a mixed number
Next, we can calculate the product of two numbers.
Let's complete our Diamond Problem!
| Product (xy) | Sum (x+y) | Is Sum Equal to - 10? |
|---|---|---|
| - 24=- 1(24) | - 1+24=23 | * |
| - 24=- 2(12) | - 2+12=10 | * |
| - 24=2(- 12) | 2+(- 12)=- 10 | ✓ |
Notice that we can complete our pattern when one factor is equal to 2 and the other is equal to - 12. Let's complete our Diamond Problem!
Remember that this is one of the possible solutions. The Diamond Problem with x=- 12 and y=2 also corresponds to the pattern.
| Product (xy) | Sum (x+y) | Is Sum Equal to 13? |
|---|---|---|
| - 48=- 1(48) | - 1+48=47 | * |
| - 48=- 2(24) | - 2+24=22 | * |
| - 48=-3( 16) | -3+( 16)=13 | ✓ |
Notice that we can complete our pattern when one factor is equal to - 3 and the other is equal to 13. Let's complete our Diamond Problem!
Remember that this is one of the possible solutions. The Diamond Problem with x=16 and y=- 3 also corresponds to the pattern.