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Core Connections Algebra 1, 2013

CC

Core Connections Algebra 1, 2013 View details

2. Section 1.2

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Exercise 51 Page 24

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= 1/2 and B=1/2 To do this, we can substitute the numbers in our pattern.

C= A * B D=A+B

(I), (II): A= 1/2, B= 1/2

C= 12 * 12 D= 12+ 12

(I): Multiply fractions

C= 14 D= 12+ 12

(II): Add fractions

C= 14 D=1

Now we can complete our first diamond.

Diamond B

In Diamond B, again we are given values for A and B, and we want to find C and D. A= 1/3 and B=3/4 To do this, we can substitute the numbers in our pattern.

C= A * B D=A+B

(I), (II): A= 1/3, B= 3/4

C= 13 * 34 D= 13+ 34

(I): Multiply fractions

C= 1*33*4 D= 13+ 34

(I): a/b=.a /3./.b /3.

C= 14 D= 13+ 34

▼

(II):Add fractions

(II):a/b=a * 4/b * 4

C= 14 D= 412+ 34

(II):a/b=a * 3/b * 3

C= 14 D= 412+ 912

(II):Add fractions

C= 14 D= 4+912

(II):Add terms

C= 14 D= 1312

▼

(II):Write fraction as a mixed number

(II):Rewrite 13 as 12+1

C= 14 D= 12+112

(II):Write as a sum of fractions

C= 14 D= 1212+ 112

(II):Calculate quotient

C= 14 D=1+ 112

(II):Add terms

C= 14 D=1 112

We can now complete our second diamond.

Diamond C

Again we are given values for A and B, and we want to find C and D. A= x and B=x To do this, we can substitute the numbers in our pattern.

C= A * B D=A+B

(I), (II): A= x, B= x

C= x * x D= x+ x

(I): Multiply

C=x^2 D=x+x

(II): Add terms

C=x^2 D=2x

Now we can complete our third diamond.

Diamond D

Here we are also given values for A and B, and we want to find C and D. A= a and B=b To do this, we can substitute the numbers in our pattern.

C= A * B D=A+B

(I), (II): A= a, B= b

C= a * b D= a+ b

(I): Multiply

C=ab D=a+b

Subchapter links

1.2.1 Describing a Graph p.19-21

1.2.2 Cube Root and Absolute Value Functions p.23-24

1.2.3 Function Machines p.27

1.2.4 Functions p.30-31

1.2.5 Domain and Range p.36