Examples with solutions for All Operations in Signed Numbers: Number of terms

Exercise #1

30(2)+(8)+5= -30-(-2)+(-8)+5=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(x)=+ -(-x)=+

Now let's write the exercise in the appropriate way:

30+2+(8)+5= -30+2+(-8)+5=

28+(8)+5= -28+(-8)+5=

We'll locate negative 28 on the number line and go 8 steps left (since negative 8 is less than zero):

-27-27-27-28-28-28-29-29-29-30-30-30-31-31-31-32-32-32-33-33-33-34-34-34-35-35-35-36-36-36-37-37-37-38-38-38-39-39-39-40-40-40

We can see that we reached negative 36.

Now the exercise we got is:

36+5= -36+5=

We'll locate negative 36 on the number line and go 5 steps right (since 5 is greater than zero):

-27-27-27-28-28-28-29-29-29-30-30-30-31-31-31-32-32-32-33-33-33-34-34-34-35-35-35-36-36-36-37-37-37-38-38-38-39-39-39-40-40-40

We can see that we reached negative 31

Answer

31 -31

Exercise #2

30+4+(8)= -30+4+(-8)=

Video Solution

Step-by-Step Solution

Let's locate negative 30 on the number line and move 4 steps to the right (since 4 is greater than zero):

-27-27-27-28-28-28-29-29-29-30-30-30-31-31-31-32-32-32-33-33-33-34-34-34-35-35-35-36-36-36-37-37-37-38-38-38-39-39-39-40-40-40-26-26-26

We can see that we reached negative 26.

Now the exercise we got is:

26+(8)= -26+(-8)=

Now let's locate negative 26 on the number line and move 8 steps to the left (since negative 8 is less than zero):

-27-27-27-28-28-28-29-29-29-30-30-30-31-31-31-32-32-32-33-33-33-34-34-34-35-35-35-36-36-36-37-37-37-38-38-38-39-39-39-40-40-40-26-26-26

We can see that we reached negative 34

Answer

34 -34

Exercise #3

4+3+(6)+(9)= 4+3+(-6)+(-9)=

Video Solution

Step-by-Step Solution

First, let's look at the first exercise:

4+3 4+3

We will locate the number 4 on the axis, and move right three steps, where each step represents a whole number in the following way:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666777

We can see that we reached the number 7.

Now we get the exercise:

7+(6)+(9)= 7+(-6)+(-9)=

Let's look at the exercise:

7+(6)= 7+(-6)=

We will locate the number 7 on the axis, and move left six steps, where each step represents a whole number in the following way:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666777

We can see that we reached the number 1.

Now we got the exercise:

1+(9)= 1+(-9)=

We will locate the number 1 on the axis, and move left nine steps, where each step represents a whole number in the following way:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333-7-7-7-8-8-8-9-9-9

We can see that we reached the number minus 8.

Answer

8 -8

Exercise #4

(4)+2+(3)+(5)= (-4)+2+(-3)+(-5)=

Video Solution

Step-by-Step Solution

Let's start with the leftmost exercise:

(4)+2 (-4)+2

We'll locate negative 4 on the axis and move two steps to the right, where each step represents one whole number:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333

We can see that we've reached negative 2.

Now we'll get the exercise:

(2)+(3)+(5)= (-2)+(-3)+(-5)=

Let's focus on the exercise:

(2)+(3) (-2)+(-3)

We'll locate negative 2 on the axis and move three steps to the left, where each step represents one whole number:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333

We can see that we've reached negative 5.

Now we'll get the exercise:

(5)+(5)= (-5)+(-5)=

We'll locate negative 5 on the axis and move five steps to the left, where each step represents one whole number:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111-7-7-7-8-8-8-9-9-9-10-10-10

We can see that we've reached negative 10.

Answer

10 -10

Exercise #5

(30)+(2)+30+(5)= (-30)+(-2)+30+(-5)=

Video Solution

Step-by-Step Solution

First, let's organize the exercise in a way that will make it easier and more convenient to solve.

Notice that the number 30 appears twice in the exercise, so let's start with it:

(30)+30+(2)+(5)= (-30)+30+(-2)+(-5)=

Let's look at the exercise:

30+30 -30+30

Since we move left from zero to minus 30, and then return right 30 steps, we will arrive at the same number we started from: 0

-30-30-30000+30

Now let's continue the exercise in the following way:

0+(2)+(5)= 0+(-2)+(-5)=

We'll locate the number minus 2 on the number line, and move left five steps where each step represents one whole number:

-5-5-5000-1-1-1-2-2-2-3-3-3-4-4-4222111-8-8-8-7-7-7-6-6-6

We can see that we arrived at minus 7.

Answer

7 -7

Exercise #6

(10)+(3)+4+(12)= (-10)+(-3)+4+(-12)=

Video Solution

Step-by-Step Solution

First, let's look at the first exercise:

(10)+(3) (-10)+(-3)

We will locate the number minus 10 on the number line, and move left three steps, where each step represents one whole number:

-16-16-16-11-11-11-12-12-12-13-13-13-14-14-14-15-15-15-9-9-9-10-10-10

We can see that we reached the number minus 13.

Now we got the exercise:

(13)+4+(12)= (-13)+4+(-12)=

The next exercise is:

(13)+4 (-13)+4

We will locate the number minus 13 on the number line, and move right four steps where each step represents one whole number:

-16-16-16-11-11-11-12-12-12-13-13-13-14-14-14-15-15-15-9-9-9-10-10-10

We can see that we reached the number minus 9.

Now we got the exercise:

(9)+(12)= (-9)+(-12)=

We will locate the number minus 9 on the number line, and move left twelve steps where each step represents one whole number:

-16-16-16-11-11-11-12-12-12-13-13-13-14-14-14-15-15-15-9-9-9-10-10-10-21-21-21-20-20-20-19-19-19-18-18-18-17-17-17

We can see that the number we reached is minus 21.

Answer

21 -21

Exercise #7

25(5)+(6)4= 25-(-5)+(-6)-4=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(x)=+x -(-x)=+x

Let's write the exercise in the appropriate form:

25+5+(6)4= 25+5+(-6)-4=

Let's solve the exercise from left to right:

25+5=30 25+5=30

Now we get the exercise:

30+(6)4= 30+(-6)-4=

Let's remember the rule:

+(x)=x +(-x)=-x

Let's write the exercise in the appropriate form:

3064= 30-6-4=

Let's solve the exercise from left to right:

306=24 30-6=24

244=20 24-4=20

Answer

20 20

Exercise #8

15+5(4)+(9)+84= 15+5-(-4)+(-9)+8-4=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(x)=+x -(-x)=+x

We'll write the exercise in the appropriate form:

15+5+4+(9)+84= 15+5+4+(-9)+8-4=

Let's solve the exercise from left to right:

15+5=20 15+5=20

Now we'll get the exercise:

20+4+(9)+84= 20+4+(-9)+8-4=

Let's solve the exercise from left to right:

20+4=24 20+4=24

Now we'll get the exercise:

24+(9)+84= 24+(-9)+8-4=

Let's remember the rule:

+(x)=x +(-x)=-x

We'll write the exercise in the appropriate form:

249+84= 24-9+8-4=

Let's solve the exercise from left to right:

249=15 24-9=15

15+8=23 15+8=23

234=19 23-4=19

Answer

19 19

Exercise #9

27(7)+(6)+211= -27-(-7)+(-6)+2-11=

Video Solution

Step-by-Step Solution

First, we solve the multiplication exercise, that is where there is a plus or minus sign before another sign.

27+76+211= -27+7-6+2-11=

Now we solve as a common exercise from left to right:

27+7=20 -27+7=-20

206=26 -20-6=-26

26+2=24 -26+2=-24

2411=35 -24-11=-35

Answer

35 -35

Exercise #10

3+(12)+(38)+58= -3+(-\frac{1}{2})+(\frac{3}{8})+\frac{5}{8}=

Video Solution

Answer

52 -\frac{5}{2}

Exercise #11

12+34+15+(45)= -\frac{1}{2}+\frac{3}{4}+-\frac{1}{5}+(-\frac{4}{5})=

Video Solution

Answer

34 -\frac{3}{4}

Exercise #12

49+5+(2)+59= -\frac{4}{9}+5+(-2)+\frac{5}{9}=

Video Solution

Answer

289 \frac{28}{9}

Exercise #13

5+12+10+(34)= -5+-\frac{1}{2}+10+(-\frac{3}{4})=

Video Solution

Answer

154 \frac{15}{4}

Exercise #14

38(58)(12)= -\frac{3}{8}-(-\frac{5}{8})-(-\frac{1}{2})=

Video Solution

Answer

34 \frac{3}{4}

Exercise #15

147+(3)12(14)= -\frac{14}{7}+(-3)-\frac{1}{2}-(-\frac{1}{4})=

Video Solution

Answer

214 -\frac{21}{4}

Exercise #16

Solve:

416(38)+28+(14)= -\frac{4}{16}-(-\frac{3}{8})+\frac{2}{8}+(-\frac{1}{4})=

Video Solution

Answer

18 \frac{1}{8}