We read your photo as:

Use the associative property to calculate the following: a) [(-6) + (4 + 2)] b) [3 + 7 + (-5)] c) [(6 + 4) + (-2)] d) [(-3) + 7 + 5]

Mathematics

ScanSolve AI Answer

Step-by-step solution

40 steps

Okay, Christina, let's work through these problems using the associative property.

The associative property of addition states that for any three numbers aa, bb, and cc, the way in which the numbers are grouped does not affect the sum: (a+b)+c=a+(b+c)(a + b) + c = a + (b + c).

Here are the calculations:

1. Use the associative property to calculate the following.

Part a· 4 steps

[(−6)+(4+2)][(-6) + (4 + 2)]

  1. Apply the associative property.

    ((−6)+4)+2=(−6)+(4+2)((-6) + 4) + 2 = (-6) + (4 + 2)

  2. Calculate the Left Hand Side (LHS).

    ((−6)+4)+2=(−2)+2=0((-6) + 4) + 2 = (-2) + 2 = 0

  3. Calculate the Right Hand Side (RHS).

    (−6)+(4+2)=(−6)+6=0(-6) + (4 + 2) = (-6) + 6 = 0

  4. Verify the equality.

    0=00 = 0

    The final value is 0\boxed{0}.

Part b· 4 steps

[3+7+(−5)][3 + 7 + (-5)]

  1. Apply the associative property.

    (3+7)+(−5)=3+(7+(−5))(3 + 7) + (-5) = 3 + (7 + (-5))

  2. Calculate the LHS.

    (3+7)+(−5)=10+(−5)=5(3 + 7) + (-5) = 10 + (-5) = 5

  3. Calculate the RHS.

    3+(7+(−5))=3+2=53 + (7 + (-5)) = 3 + 2 = 5

  4. Verify the equality.

    5=55 = 5

    The final value is 5\boxed{5}.

Part c· 4 steps

[(6+4)+(−2)][(6 + 4) + (-2)]

  1. Apply the associative property.

    (6+4)+(−2)=6+(4+(−2))(6 + 4) + (-2) = 6 + (4 + (-2))

  2. Calculate the LHS.

    (6+4)+(−2)=10+(−2)=8(6 + 4) + (-2) = 10 + (-2) = 8

  3. Calculate the RHS.

    6+(4+(−2))=6+2=86 + (4 + (-2)) = 6 + 2 = 8

  4. Verify the equality.

    8=88 = 8

    The final value is 8\boxed{8}.

Part d· 4 steps

[(−3)+7+5][(-3) + 7 + 5]

  1. Apply the associative property.

    ((−3)+7)+5=(−3)+(7+5)((-3) + 7) + 5 = (-3) + (7 + 5)

  2. Calculate the LHS.

    ((−3)+7)+5=4+5=9((-3) + 7) + 5 = 4 + 5 = 9

  3. Calculate the RHS.

    (−3)+(7+5)=(−3)+12=9(-3) + (7 + 5) = (-3) + 12 = 9

  4. Verify the equality.

    9=99 = 9

    The final value is 9\boxed{9}.

Part e· 4 steps

[(−4)+(6+2)][(-4) + (6 + 2)]

  1. Apply the associative property.

    ((−4)+6)+2=(−4)+(6+2)((-4) + 6) + 2 = (-4) + (6 + 2)

  2. Calculate the LHS.

    ((−4)+6)+2=2+2=4((-4) + 6) + 2 = 2 + 2 = 4

  3. Calculate the RHS.

    (−4)+(6+2)=(−4)+8=4(-4) + (6 + 2) = (-4) + 8 = 4

  4. Verify the equality.

    4=44 = 4

    The final value is 4\boxed{4}.

Part f· 4 steps

[3+(−7)+5][3 + (-7) + 5]

  1. Apply the associative property.

    (3+(−7))+5=3+((−7)+5)(3 + (-7)) + 5 = 3 + ((-7) + 5)

  2. Calculate the LHS.

    (3+(−7))+5=(−4)+5=1(3 + (-7)) + 5 = (-4) + 5 = 1

  3. Calculate the RHS.

    3+((−7)+5)=3+(−2)=13 + ((-7) + 5) = 3 + (-2) = 1

  4. Verify the equality.

    1=11 = 1

    The final value is 1\boxed{1}.

Part g· 4 steps

[(−9)+(3+11)][(-9) + (3 + 11)]

  1. Apply the associative property.

    ((−9)+3)+11=(−9)+(3+11)((-9) + 3) + 11 = (-9) + (3 + 11)

  2. Calculate the LHS.

    ((−9)+3)+11=(−6)+11=5((-9) + 3) + 11 = (-6) + 11 = 5

  3. Calculate the RHS.

    (−9)+(3+11)=(−9)+14=5(-9) + (3 + 11) = (-9) + 14 = 5

  4. Verify the equality.

    5=55 = 5

    The final value is 5\boxed{5}.

Part h· 4 steps

[(12+13)+(−10)][(12 + 13) + (-10)]

  1. Apply the associative property.

    (12+13)+(−10)=12+(13+(−10))(12 + 13) + (-10) = 12 + (13 + (-10))

  2. Calculate the LHS.

    (12+13)+(−10)=25+(−10)=15(12 + 13) + (-10) = 25 + (-10) = 15

  3. Calculate the RHS.

    12+(13+(−10))=12+3=1512 + (13 + (-10)) = 12 + 3 = 15

  4. Verify the equality.

    15=1515 = 15

    The final value is 15\boxed{15}.

Part h(i)· 8 steps

[(−3)+(9+11)][(-3) + (9 + 11)]

  1. Apply the associative property.

    ((−3)+9)+11=(−3)+(9+11)((-3) + 9) + 11 = (-3) + (9 + 11)

  2. Calculate the LHS.

    ((−3)+9)+11=6+11=17((-3) + 9) + 11 = 6 + 11 = 17

  3. Calculate the RHS.

    (−3)+(9+11)=(−3)+20=17(-3) + (9 + 11) = (-3) + 20 = 17

  4. Verify the equality.

    17=1717 = 17

    The final value is 17\boxed{17}.

    j) [(−12)+(13+10)][(-12) + (13 + 10)]

  5. Apply the associative property.

    ((−12)+13)+10=(−12)+(13+10)((-12) + 13) + 10 = (-12) + (13 + 10)

  6. Calculate the LHS.

    ((−12)+13)+10=1+10=11((-12) + 13) + 10 = 1 + 10 = 11

  7. Calculate the RHS.

    (−12)+(13+10)=(−12)+23=11(-12) + (13 + 10) = (-12) + 23 = 11

  8. Verify the equality.

    11=1111 = 11

    The final value is 11\boxed{11}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QUse the associative property to solve the following equations: a) [(−6) + (4 + 2)], b) [3 + 7…QUse the associative property to evaluate the following expressions: a) [(−6) + (4 + 2)] b) [3 + 7…QApply the associative property of addition to solve for the final value in the following problems…QSolve the following arithmetic expressions: a) −6 + (4 + 2) b) 3 + 7 + (−5) c) −2 + (6 + 4) d) −3…QSimplify the following expressions: a) 6 − 4 + 3, b) 15 − 4 imes 2, c) 10 + 16 / 8, d) 7 × 2 + (8…
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp