Step: 1

3 + (- 21)

[Original expression.]

Step: 2

|21| - |3| = 21 - 3

[Find the difference of absolute values.]

Step: 3

= 18

[Subtract.]

Step: 4

3 + (- 21) = - 18

[Since the absolute value of - 21 is greater, the sum is negative.]

Correct Answer is : - 18

Step: 1

- 2 3 + 5 6

[Original expression.]

Step: 2

= - 4 6 + 5 6

[Write the equivalent fractions with LCD 6 as the denominator.]

Step: 3

= - 4 + 5 6

[Add the numerators.]

Step: 4

= 1 6

Step: 5

The value of the fraction - 2 3 + 5 6 is 1 6 .

Correct Answer is : 1 6

Step: 1

[Write the expression.]

Step: 2

The LCM of 8 and 9 is 72, so the LCD of 7 8 and 8 9 is 72.

Step: 3

[Write equivalent fractions with a denominator of 72.]

Step: 4

= (63 72 ) + (64 72 )

[Simplify.]

Step: 5

= 6 3 + 6 4 7 2

[Write the sum over the common denominator.]

Step: 6

= 127 72

[Simplify.]

Step: 7

The sum of 7 8 and 8 9 is 127 72 .

Correct Answer is : 127 72

Step: 1

- 37 + 9

[Original expression.]

Step: 2

|- 37| - |9|

[Find the difference of the absolute values.]

Step: 3

= 37 - 9 = 28

[Subtract.]

Step: 4

- 37 + 9 = - 28

[Since - 37 has the greater absolute value, the sum is negative.]

Correct Answer is : - 28

Step: 1

- 4 + (- 7) + 6 + (- 2)

[Original expression.]

Step: 2

= - 4 - 7 + 6 + (- 2)

[To add - 7, subtract its opposite, 7.]

Step: 3

= - 4 - 7 + 6 - 2

[To add - 2, subtract its opposite, 2.]

Step: 4

= - (4 + 7 + 2) + 6

[Group numbers with same sign.]

Step: 5

= - 13 + 6

[Add inside the grouping symbols.]

Step: 6

= - 7

Correct Answer is : - 7

Step: 1

- 100 + 140 + (- 120) + 100

[Original expression.]

Step: 2

= - 100 + 140 - 120 + 100

[To add - 120, subtract its opposite 120.]

Step: 3

= - (100 + 120) + (140 + 100)

[Group numbers with same sign.]

Step: 4

= - 220 + 240

[Add inside the grouping symbols.]

Step: 5

= 20

Correct Answer is : 20

Step: 1

[Original expression.]

Step: 2

= 10 3 + 21 5

[Rewrite the mixed fractions as improper fractions.]

Step: 3

The LCM of 3 and 5 is 15, so the LCD of 10 3 and 21 5 is 15.

Step: 4

[Write equivalent fractions with a denominator of 15.]

Step: 5

= 5 0 + 6 3 1 5

[Write the sum over the common Denominator.]

Step: 6

= 113 15 .

[Simplify.]

Correct Answer is : 113 15

Step: 1

Work done by the person in the first week = 3 10

Step: 2

Work done by the person in the second week = 1 10

Step: 3

Total work done by the person in the past two weeks = 3 10 + 1 10

Step: 4

3 + 1 = 4

[Denominators are equal. So, add the numerators.]

Step: 5

Step: 6

[Divide.]

Step: 7

The work done by the person during the two weeks = 2 5 .

Correct Answer is : 2 5

Step: 1

10 + (- 11) + (- 37)

[Original expression.]

Step: 2

= 10 - 11 + (- 37)

[To add - 11, subtract its opposite, 11.]

Step: 3

= 10 - 11 - 37

[To add - 37, subtract its opposite, 37.]

Step: 4

= 10 - (11 + 37)

[Combine the negative numbers.]

Step: 5

= 10 - 48

[Add inside the grouping symbols.]

Step: 6

= -38

[Simplify.]

Correct Answer is : -38

Step: 1

[Original expression.]

Step: 2

= 16 3 + 31 5

[Rewrite the mixed fractions as improper fractions.]

Step: 3

The LCM of 3 and 5 is 15, so the LCD of 16 3 and 31 5 is 15.

Step: 4

[Write equivalent fractions with a denominator of 15.]

Step: 5

= (80+93) (15)

[Write the sum over the common Denominator.]

Step: 6

= 173 15

[Simplify.]

Correct Answer is : 173 15

Step: 1

Fraction of fence painted = Fraction of fence painted by Jake + Fraction of fence painted by Henry

= 3 12 + 5 12

[Substitute the values.]

Step: 2

= 3 + 5 1 2

[Write the sum of the numerators over common denominator.]

Step: 3

= 8 12 = 2 3

[Simplify the fraction.]

Step: 4

So, 2 3 of the fence is painted.

Correct Answer is : 2 3

Step: 1

To add two integers with different signs, consider the numbers as whole numbers and find their difference. Put the sign of the larger number to the result.

Step: 2

2 + (- 11)

[Original equation.]

Step: 3

11 - 2 = 9

[Consider the numbers as whole numbers and find their difference.]

Step: 4

2 + (- 11) = - 9

[As the larger number has negative sign, the result will also be negative.]

Correct Answer is : - 9

Step: 1

[Original expression.]

Step: 2

= 11 + (- 57)

[Substitute 11 for n .]

Step: 3

= - 46

[When two integers with different signs are added, the sum has the sign of the integer with the greater absolute value.]

Correct Answer is : - 46

Step: 1

5 + (- 47) + (- 4)

[Original expression.]

Step: 2

= 5 - 47 + (- 4)

[To add - 47, subtract its opposite, 47.]

Step: 3

= 5 - 47 - 4

[To add - 4, subtract its opposite, 4.]

Step: 4

= 5 - (47 + 4)

[Combine the negative numbers.]

Step: 5

= 5 - 51

[Add inside the grouping symbols.]

Step: 6

= - 46

[Simplify.]

Correct Answer is : - 46

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