Chapter Closure
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We can see that x is 15 and y is 23. To fill the remaining corners, we will calculate the product and the sum of these numbers. Let's start with the product.
Next, we can find the sum. To add fractions, they need to have the same denominator. Let's multiply the numerator and denominator of 15 by 3 and the numerator and denominator of 23 by 5. This will give both fractions the common denominator of 15.
x= 1/5, y= 2/3
a/b=a * 3/b * 3
a/b=a * 5/b * 5
Multiply
Add fractions
Add terms
We found the product and the sum of x and y.
| x=1/5, y=2/3 | |
|---|---|
| Product (xy) | 2/15 |
| Sum (x+y) | 13/15 |
Now we can complete our Diamond Problem.
| x=- 3, y=6 | |
|---|---|
| Product (xy) | - 3( 6)= - 18 |
| Sum (x+y) | - 3+ 6=3 |
Now we can complete our Diamond Problem.
In the given diagram, y has a value of 45. We also know that the sum x+y is equal to 2120. Let's use this information to find the value of x.
y= 4/5
LHS-4/5=RHS-4/5
4/5-4/5=0
a/b=a * 4/b * 4
Multiply
Subtract fractions
Subtract term
a/b=.a /5./.b /5.
Calculate quotient
We found that x is equal to 14. Next, we can calculate the value of the product xy.
x= 1/4, y= 4/5
Multiply fractions
Cancel out common factors
Simplify quotient
Now we can complete our Diamond Problem.
In the given diagram, y has a value of - 1. We also know that the sum x+y is equal to 11. Let's use this information to find the value of x.
y= - 1
a+(- b)=a-b
LHS+1=RHS+1
Add terms
We found that x is equal to 12. Next, we can calculate the value of the product xy.
x= 12, y= - 1
a(- b)=- a * b
Identity Property of Multiplication
Now let's complete our Diamond Problem.
