Relative numbers: answer key to 4th grade math exercises in PDF.

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The answer key to the 4th grade math exercises on relative numbers. Calculations with relative numbers including addition, subtraction, multiplication, division and use of the sign rule.

Exercise 1:

$A\,=\,(\,5\,-\,8\,)\times \,(-\,2\,-\,4\,)\\A=-3\times \,(-6)\\A=18\\.\,\\B\,=\,(-\,4\,)\,\times \,(-\,5\,)\,\times \,(-2\,)\,\times \,(-\,6\,+\,7)\\B=-4\times \,5\times \,2\times \,1\\B=-40\\.\,\\C\,=\,%5B\,9\,+\,2\,\times \,(-\,12\,)\,%5D: \,%5B\,3-(16-18)%5D\\C=(9-24): \,(3-(-2))\\C=(-15): \,5\\C=-3$

Exercise 2:

The sign of will be positive according to the sign rule -x- gives +.

The sign of will be negative because the sum of two negative numbers is negative.

the sign of the quotient $\frac{ab}{a+b}$ will be negative (according to the rigle of signs) because $\frac{+}{-}$ gives .

Exercise 3:

$A=(-14)-(-13)+(-7)=-14+13-7=-8\\B=(-4)-%5B(-3)-(-8)+(+7)%5D=-4-(-3+8+7)=-4-12=-16\\C=(-2)+(-3)\times \,(+5)=-2-3\times \,5=-2-15=-17\\D=(-9)-(-5)+%5B(-3)-(+2)\times \,(-3)%5D=-9+5+(-3+2\times \,3)=-4-3+6=-1\\E=(-4)-(3-7)+(-8)=-4-(-4)-8=-4+4-8=0$

Exercise 4:
1. .
$a+bc=(-6)+2\times \,(-4)=-6-8=-14$
2. $(a+b)\times \,c$ .
$(a+b)c=(-6+2)\times \,(-4)=-4\times \,(-4)=16$
3. $a+\frac{b}{c}$
$a+\frac{b}{c}=-6+\frac{2}{-4}=-6-2=-8$
4. $\frac{a+b}{c}$
$\frac{a+b}{c}=\frac{-6+2}{-4}=\frac{-4}{-4}=1$

Exercise 5:

How far down did it go?

$11\,-(-10)=11+10=21$

It went down 21 meters.

Exercise 6:
1. (+2)- (+8) – (-4) – (-3)
– c. 2 – 8 + 4 + 3=1

2. (-7) – (-3) + (+5) – (+4)
– a. – 7 + 3 + 5 – 4 = – 3

Exercise 7:
$a.\,(+2)\,+\,(-5)=2-5=-3\,\\b.\,(-3)\,+\,(+7)\,+\,(+3)=-3+7+3=4+3=7\,\\c.\,(-7)\,+\,(-2)\,+\,(+4)\,+\,(-1)=-7-2+4-1=-9+4-1=-5+1=-4\,\\d.\,(-\,3)\,-\,(-\,4)=-3+4=1\,\\e.\,(+7)\,-\,(-2)\,+\,(+4)=7+2+4=13\,\\f.\,(+5)\,+\,(-4)\,-\,(+7)=5-4-7=1-7=-6$

Exercise 8:
a. $\,(-2)\times \,3\,=-6$
b. $\,(-4)\times \,(-3)=12\,$
c. $\,(+2,5)\times \,(-5)\,=-12,5$
d. $\,(-2,4)\times \,(-1,5)=3,6\,$
e. $\,2\times \,(-1)\,\times \,(-3)=6$

Exercise 9:
$\,A=(-1)\times \,(-1)\times \,(+1)\times \,(-1)\,$ negative because an odd number with sign – .
$\,B=(+1)\times (-1)\times (+1)\times (+1)\times (-1)\\\times (-1)\times (+1)\times (-1)\times (-1)\\\times (+1)\times (+1)\times (-1)\,$ : positive because an even number with sign – .
If C is the product of 303 times the number -1. What is the sign of the number C?
It will be negative because 303 is odd.

Exercise 10:
$\,A\,=\,(-3)\times %5B3\,-\,(+5)%5D=-3\times (-2)=6$
$\,B\,=\,4\,-\,%5B5\times (-2)\,+\,(-2)%5D=4-(-10-2)=4-(-12)=4+12=16$
$\,C=\,-4\times \,%5B(3\,+\,(-4))\times (-\,2\,-\,(-3))%5D=-4\times (3-4)(-2+3)=-4\times \,(-1)\times \,1\,=4$

Exercise 11:
A=(- 5) + [(- 4) x ( – 2 ) + ( + 7)]
A=(- 5) + [(+8 ) + ( + 7)]
A=(- 5) +(+15)
A = 10
B=(- 4) x ( – 2)x( – 3) – ( – 3) x ( – 2)
B = -24 – (+6)
B= – 24 – 6
B= -30
C=(+ 6) – ( – 9) + (- 3) x [ ( – 5)x( -2) – 3]
C=6+9 + (- 3) x [ ( +10) – 3]
C=6+9 + (- 3) x 7
C=15 – 21
C= -6

Exercise 12:
1. $(+2)-\,(+8)\,-\,(-4)\,-\,(-3)$
– $c.\,2\,-\,8\,+\,4\,+\,3$

2. $(-7)\,-\,(-3)\,+\,(+5)\,-\,(+4)$
– $a.\,-\,7\,+\,3\,+\,5\,-\,4$

Exercise 13:
$a.\,(+2)\,+\,(-5)\,=\,-\,3\,\\b.\,(-3)\,+\,(+7)\,+\,(+3)\,=\,(+4)+(+3)=7\,\\c.\,(-7)\,+\,(-2)\,+\,(+4)\,+\,(-1)\,=\,(-9)+(+4)+(-1)=(-5)+(-1)=-6\,\\d.\,(-\,3)\,-\,(-\,4)\,=\,(-3)+(+4)=1\,\\e.\,(+7)\,-\,(-2)\,+\,(+4)=(+7)+(+2)+(+4)=(+9)+(+4)=13\,\\f.\,(+5)\,+\,(-4)\,-\,(+7)\,=\,(+5)+(-4)+(-7)=\,(+1)+(-7)=\,-\,6$

Exercise 14:
Perform the following multiplications:
a. $\,(-2)\times \,3=-6\,$
b. $\,(-4)\times \,(-3)=12\,$
c. $\,(+2,5)\times \,(-5)=-12,5\,$
d. $\,(-2,4)\times \,(-1,5)=3,6\,$
e. $\,2\times \,(-1)\,\times \,(-3)=6$

Exercise 15:
What is the sign of each of the following calculations:
$\,A=(-1)\times \,(-1)\times \,(+1)\times \,(-1)\,$ there are three minus signs, three is odd so the sign is negative.
$\,B=(+1)\times (-1)\times (+1)\times (+1)\times (-1)\times (-1)\times (+1)\times (-1)\times (-1)\times (+1)\times (+1)\times (-1)\,$ There are six minus signs, six is even so the sign is positive.
If C is the product of 303 times the number -1. What is the sign of the number C?

There are 303 minus signs, the integer 303 is odd so the sign is negative.

Exercise 16:
Perform the following calculations (pay attention to the order of priority of the operations):
$A\,=\,(-3)\times %5B3\,-\,(+5)%5D=(-3)\times \,(-2)=6$
$B\,=\,4\,-\,%5B5\times (-2)\,+\,(-2)%5D=4-(-10-2)=4-(-12)=4+12=16$
$C=\,-4\times \,%5B(3\,+\,(-4))\times (-\,2\,-\,(-3))%5D=-4\times \,%5B(-1)\times \,1%5D=-4\times \,(-1)=4$

Exercise 18:

$A=3+7-4\\{\color{DarkRed}\,A=6}$

$B=(-3)+(-4)\times ,(-6)+(-21):(-7)$ .

$B=-3+24+21:7\\B=-3+24+3\\{\color{DarkRed}\,B=24}$

$C=(-36):(-9)-%5B(-4)\times ,(-3)+(-21):(-3)%5D$

$C=+4-(+12+7)\\C=4-19\\{\color{DarkRed}\,C=-15}$

Exercise 19:

$A=(+3)\times (-2)\times (+4)\times (-1)\times (-2)\\A=-\,3\times 2\times \,4\times \,1\times \,2\\A=-48$

$B=(-2)\times (+5)\times (-1)\times (-5)\times (-2)\\B=+2\times 5\times 1\times 5\times 2\,\\B=+\,100$

$C=(-8)-4\times (+5)\\C=-8-20\\C=-28$

$D=5\times (-7+10)-12\\D=5\times (+3)-12\\D=+15-12\\D=3$

Exercise 20:

$U\,=\,16\,-\,5\,\times \,4=16-20=\,-4$
$V\,=\,8\,\times \,4\,-\,5\,\times \,6=32-30=2$

$W\,=\,9\,-\,3\,:\,3=9-1=8$

$X\,=\,-7\,\times \,(3\,+\,6)=(-7)\,\times \,9=\,-\,63$

$Y\,=\,(-2\,-\,4)\,\times \,(6\,-8)=-6\,\times \,(-2)=12$

$Z\,=\,7\,-\,%5B6\,-(3-8)%5D=7-%5B6-(-5)%5D=\,7-(6+5)=7-11=\,-\,4$

Exercise 21:

1. By what amount did it improve its results?

80 000-15 000 = 65 000 €

2. If its results increase by the same amount this year, what will its profit be next year?

65 000 – 15 000 = 50 000 €

Exercise 22:

Calculate:

$A=6+\frac{24-66}{3-9}$

$A=6+\frac{-42}{-6}$

${\color{DarkRed}\,A=13}$

$B=\frac{(-7)\times 8+6}{-21-(-2)\times 13}$

$B=\frac{-56+6}{-21+26}$

$B=\frac{-50}{5}$

${\color{DarkRed}\,B=-10}$

$C=\frac{12\times (1-5)}{-3-3}$

$C=\frac{12\times (-4)}{-6}$

$C=\frac{-48}{-6}$

${\color{DarkRed}\,C=8}$

Exercise 23:

Calculate:

$A=5\times 6-16: ,(-4)-(15-8,1)$

${\color{DarkRed}\,A=27,1}$

$B=(23-37)\times (14,2-16,7)$

$B=(-14)\times (-2,5)$

${\color{DarkRed}\,B=35}$

${\color{DarkRed}\,C=-3,7}$

Exercise 24:

$A=2\times \,3\times (-4)\times 0,5$

${\color{DarkRed}\,A=-12}$

$B=2\times \,(-1)\times 5\times (-5)$

${\color{DarkRed}\,B=50}$

$C=(-3)\times \,(-5)\times (-2)\times 5$

${\color{DarkRed}\,C=-150}$

$D=(-1)\times \,(-8)\times (-6)\times (-5)$

${\color{DarkRed}\,D=240}$

Answers to the exercises on relative numbers in 4th grade.

After having consulted the answers to these exercises on relative numbers in 8th grade, you can return to the exercises in 4th grade.

Eighth grade exercises.

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