QuestionA. Verify $(3,125+3,168)+4,375=3,125+(3,168+4,375)$ using the associative property. B. Show $3,125+3,168+4,365=11,078-(550+692)$ . C. Prove $3,168+4,375+3,125=(3,168+3,125)$ . D. Confirm $(4,168+3,125)+4,375=3,125+(1,168+3,168)$ .

Studdy Solution

STEP 1

Assumptions1. The problems are asking us to verify if the left-hand side (HS) equals the right-hand side (RHS). . The operations involved are addition and subtraction, which obey the associative and commutative properties.

STEP 2

Let's start with problem A. First, we calculate the LHS.
$HS_A = (,125+,168)+4,375$

STEP 3

Perform the addition inside the parentheses first, then add the result to,375.
$HS_A =6,293+,375$

STEP 4

Calculate the LHS for problem A.
$HS_A =10,668$

STEP 5

Now, calculate the RHS of problem A.
$RHS_A =3,125+(3,168+4,375)$

STEP 6

Perform the addition inside the parentheses first, then add the result to3,125.
$RHS_A =3,125+,543$

STEP 7

Calculate the RHS for problem A.
$RHS_A =10,668$

STEP 8

For problem B, calculate the LHS.
$HS_B =3,125+3,168+4,365$

STEP 9

Calculate the LHS for problem B.
$HS_B =,658$

STEP 10

Now, calculate the RHS of problem B.
$RHS_B =,078-(550+692)$

STEP 11

Perform the addition inside the parentheses first, then subtract the result from11,078.
$RHS_B =11,078-,242$

STEP 12

Calculate the RHS for problem B.
$RHS_B =9,836$

STEP 13

For problem C, calculate the LHS.
$HS_C =3,168+,375+3,125$

STEP 14

Calculate the LHS for problem C.
$HS_C =10,668$

STEP 15

Now, calculate the RHS of problem C.
$RHS_C = (3,168+3,125)$

STEP 16

Perform the addition inside the parentheses.
$RHS_C =6,293$

STEP 17

For problem D, calculate the LHS.
$HS_D = (4,168+3,125)+4,375$

STEP 18

Perform the addition inside the parentheses first, then add the result to4,375.
$HS_D =7,293+4,375$

STEP 19

Calculate the LHS for problem D.
$HS_D =11,668$

STEP 20

Now, calculate the RHS of problem D.
$RHS_D =3,125+(,168+3,168)$

STEP 21

Perform the addition inside the parentheses first, then add the result to3,125.
$RHS_D =3,125+4,336$

STEP 22

Calculate the RHS for problem D.
$RHS_D =7,461$

STEP 23

Now, let's compare the LHS and RHS for each problem.
For problem A, LHS_A = RHS_A =10,668, so the equation is true.
For problem B, LHS_B =10,658 and RHS_B =9,836, so the equation is false.
For problem C, LHS_C =10,668 and RHS_C =6,293, so the equation is false.
For problem D, LHS_D =11,668 and RHS_D =7,461, so the equation is false.

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Studdy Solution

STEP 1

Assumptions1. The problems are asking us to verify if the left-hand side (HS) equals the right-hand side (RHS). . The operations involved are addition and subtraction, which obey the associative and commutative properties.

STEP 2

Let's start with problem A. First, we calculate the LHS.HSA=(,125+,168)+4,375HS_A = (,125+,168)+4,375HSA​=(,125+,168)+4,375

STEP 3

Perform the addition inside the parentheses first, then add the result to,375.HSA=6,293+,375HS_A =6,293+,375HSA​=6,293+,375

STEP 4

Calculate the LHS for problem A.HSA=10,668HS_A =10,668HSA​=10,668

STEP 5

Now, calculate the RHS of problem A.RHSA=3,125+(3,168+4,375)RHS_A =3,125+(3,168+4,375)RHSA​=3,125+(3,168+4,375)

STEP 6

Perform the addition inside the parentheses first, then add the result to3,125.RHSA=3,125+,543RHS_A =3,125+,543RHSA​=3,125+,543

STEP 7

Calculate the RHS for problem A.RHSA=10,668RHS_A =10,668RHSA​=10,668

STEP 8

For problem B, calculate the LHS.HSB=3,125+3,168+4,365HS_B =3,125+3,168+4,365HSB​=3,125+3,168+4,365

STEP 9

Calculate the LHS for problem B.HSB=,658HS_B =,658HSB​=,658

STEP 10

Now, calculate the RHS of problem B.RHSB=,078−(550+692)RHS_B =,078-(550+692)RHSB​=,078−(550+692)

STEP 11

Perform the addition inside the parentheses first, then subtract the result from11,078.RHSB=11,078−,242RHS_B =11,078-,242RHSB​=11,078−,242

STEP 12

Calculate the RHS for problem B.RHSB=9,836RHS_B =9,836RHSB​=9,836

STEP 13

For problem C, calculate the LHS.HSC=3,168+,375+3,125HS_C =3,168+,375+3,125HSC​=3,168+,375+3,125

STEP 14

Calculate the LHS for problem C.HSC=10,668HS_C =10,668HSC​=10,668

STEP 15

Now, calculate the RHS of problem C.RHSC=(3,168+3,125)RHS_C = (3,168+3,125)RHSC​=(3,168+3,125)

STEP 16

Perform the addition inside the parentheses.RHSC=6,293RHS_C =6,293RHSC​=6,293

STEP 17

For problem D, calculate the LHS.HSD=(4,168+3,125)+4,375HS_D = (4,168+3,125)+4,375HSD​=(4,168+3,125)+4,375

STEP 18

Perform the addition inside the parentheses first, then add the result to4,375.HSD=7,293+4,375HS_D =7,293+4,375HSD​=7,293+4,375

STEP 19

Calculate the LHS for problem D.HSD=11,668HS_D =11,668HSD​=11,668

STEP 20

Now, calculate the RHS of problem D.RHSD=3,125+(,168+3,168)RHS_D =3,125+(,168+3,168)RHSD​=3,125+(,168+3,168)

STEP 21

Perform the addition inside the parentheses first, then add the result to3,125.RHSD=3,125+4,336RHS_D =3,125+4,336RHSD​=3,125+4,336

STEP 22

Calculate the RHS for problem D.RHSD=7,461RHS_D =7,461RHSD​=7,461

STEP 23

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Let's start with problem A. First, we calculate the LHS.
$HS_A = (,125+,168)+4,375$

Perform the addition inside the parentheses first, then add the result to,375.
$HS_A =6,293+,375$

Calculate the LHS for problem A.
$HS_A =10,668$

Now, calculate the RHS of problem A.
$RHS_A =3,125+(3,168+4,375)$

Perform the addition inside the parentheses first, then add the result to3,125.
$RHS_A =3,125+,543$

Calculate the RHS for problem A.
$RHS_A =10,668$

For problem B, calculate the LHS.
$HS_B =3,125+3,168+4,365$

Calculate the LHS for problem B.
$HS_B =,658$

Now, calculate the RHS of problem B.
$RHS_B =,078-(550+692)$

Perform the addition inside the parentheses first, then subtract the result from11,078.
$RHS_B =11,078-,242$

Calculate the RHS for problem B.
$RHS_B =9,836$

For problem C, calculate the LHS.
$HS_C =3,168+,375+3,125$

Calculate the LHS for problem C.
$HS_C =10,668$

Now, calculate the RHS of problem C.
$RHS_C = (3,168+3,125)$

Perform the addition inside the parentheses.
$RHS_C =6,293$

For problem D, calculate the LHS.
$HS_D = (4,168+3,125)+4,375$

Perform the addition inside the parentheses first, then add the result to4,375.
$HS_D =7,293+4,375$

Calculate the LHS for problem D.
$HS_D =11,668$

Now, calculate the RHS of problem D.
$RHS_D =3,125+(,168+3,168)$

Perform the addition inside the parentheses first, then add the result to3,125.
$RHS_D =3,125+4,336$

Calculate the RHS for problem D.
$RHS_D =7,461$