Core Connections Integrated II, 2015
CC
Core Connections Integrated II, 2015 View details
2. Section 1.2
Continue to next subchapter

Exercise 28 Page 20

Use the given pattern to complete each of the diamonds.


A.

B.

C.

D.

Practice makes perfect

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

Diamond A

In Diamond A, we are given values for A and B, and we want to find C and D. A= 6 and B=-11 To do this, we can substitute the numbers in our pattern.
C= A * B D=A+B

(I), (II): A= 6, B= -11

C= 6 * ( -11) D= 6+( -11)
C=-66 D=6+(-11)
C=-66 D=6-11
C=-66 D=-5
Now we can complete our first diamond.

Diamond B

In Diamond B, we are also given values for A and B, and we want to find C and D. A= -1 and B=-4 To do this, we can substitute the numbers in our pattern.
C= A * B D=A+B

(I), (II): A= -1, B= -4

C= -1 * ( -4) D= -1+( -4)
C=4 D=-1+(-4)
C=4 D=-1-4
C=4 D=-5
We can now complete our second diamond.

Diamond C

In this case, we are given that C=-6 and B=-2. Substituting these values into our pattern gives us the following equations. -6&=A * (-2) D &= A+ (-2) From the first equation, we can calculate A by isolating it on one side.
-6=A*(-2)
-6=-2A
-6/-2=A
3=A
A=3
We found A. Now, we can substitute it into the second equation to find D.
D=A+(-2)
D= 3+(-2)
D=3-2
D=1
Now we can complete our third diamond.

Diamond D

Here we are given that C= -8 and D=-7. We want to find the numbers A and B. -8=A* B -7=A+B In this case, let's think of different pairs of numbers which multiply to give us -8. Notice that, when we multiply them, we want to get a negative number. Therefore, we need the pair with one negative number. Multiplication of positive and negative number gives a negative number. &-8=-1*8 &-8=-2*4 &-8=-4*2 &-8=-8*1 Let's check which, if any of these, will match the second condition as well. &-1+8=7 * &-2+4=2 * &-4+2=-2 * & -8+1=-7 The pair A=-8 and B=1 works for the pattern. Therefore, this is the correct pair of numbers to complete the diamond.