Literal calculation: answer key to 5th grade math exercises in PDF.

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The answer key to the 5th grade math exercises on literal calculation. Simplify and reduce literal expressions using simple distributivity.

Exercise 1:

$D=2x+3+4\times \,2x+3\times \,5x+11\times \,2$

$F=5,3+2\times \,5x+3,2-3\times \,2x-1,6$

Exercise 2:

Let be the expression .

Calculate the value of E for :

a) ;

$E=7\times \,0-3=-3$

b) ;

$E=7\times \,3-3=18$

c) .

$E=7\times \,1,2-3=5,4$

Exercise 3:

A = 13xz=

B= 4×5 = 20

C= (4- )x3=

D= 4xaxb=

E = axb+7x +5=

F=5x( +3)=

G= x(y+2)=

Exercise 4:

First way:

$A=15\times \,17+15\times \,20$

$A=555\,m^2$

Second way:

$A=15\times \,37$

$A=555\,m^2$

Exercise 5:

a) $37\times \,102\,$

= $37\times (100+2)$

= $37\times 100+37\times 2$

b) $65\times \,99$

= $65\times \,100-65\times \,1$

Exercise 6:

Calculate the following expression for $a=7\,et\,b=5$ :

$A=2\times \,5(7-3)$

$A=10\times \,4$

Exercise 7:

$A=3\times \,a\times \,5$

$B=8\times \,a\times \,b\times \,3$

$C=2\times \,a+5\times \,a$

$D=3\times \,x-4\times \,y$

$E=3+2\times \,1,5\times \,\pi$

$E=3+3\pi$

Exercise 8:

1. Express the length of the rectangle in terms of .

2. Express the perimeter of the rectangle in terms of .

$P=2\times \,4x+2\times \,7=8x+14$

3. Calculate the perimeter when:

$x=5\,m$

$P=8\times \,5+14=54\,m$

$x=2\,m$

$P=8\times \,2+14=30\,m$

Exercise 9:

a) Write the price of a CD as a function of x.

x+2

b) Write the prices of a book as a function of x.

x+4

c) Paul buys 4 CDs, write the amount of his purchases as a function of x.

4(x+2)=4x+8

d) Louise buys 2 comic books and 2 books, write the amount of her purchases as a function of x.

2x+2(x+4)=2x+2x+8=4x+8

e) Show that Paul and Louise spent the same amount.

They have the same expense which corresponds to 4x+8 .

Exercise 10:

$3\,\times \,x\,+\,2=3x+2\,;\\\,a\,\times \,a\,-4=a^2-4\,;\,\\\,12\,\times \,8\,+\,x=96+x\,;\,\\\,5\,\times \,(x\,+\,2)=5x+10$

Exercise 11:

A USB stick costs x euros and a book costs 5 € more.
1. What is the price of 3 books ?

2. What is the price of 2 USB keys and 4 books?

Exercise 12:

Exercise 13:

The left length is b+2b+b=4b .

The bottom length is a+a+a=3a .

The length of the staircase is a+b+a+2b+a+b=3a+4b .

The perimeter is 4b+3a+3a+4b=6a+8b

Conclusion: the answer is E .

A) 3a+4b.

B) 3a+8b

C) 6a+4b

D) 6a+6b

E) 6a+8b

Exercise 14:

$1)\,a\times \,a+1,5a$

The total area of the rectangle .

$2)\,4a+3$

The perimeter of the rectangle.

$3)\,2(1,5+2a)$

The perimeter of the rectangle.

$4)\,a(1,5+a)$

Area of the rectangle.

Exercise 15:

Expression		Answer A	Answer B	Answer C
1	8(a + 3)	8 a + 3	8 a + 24	8 a + 83
2	5(x – 9)	5 x + 45	5 x – 9	5 x – 45
3	k(a + 9)	a + 9 k	k a + 9	k a + 9 k
4	$\pi$ (4 + R)	4 $\pi$ + $\pi$ R	4 $\pi$ + R	4 $\pi$ R

Exercise 16:

Julie wrote:

$5\,(x\,+\,3)\,=\,5\,x\,+\,3.$
Marc wrote:

$5\,(x\,+\,3)\,=\,5\,x\,+\,5\times \,3.$

Sonia wrote:

$5\,(x\,+\,3)\,=\,5\,x\,+\,8.$

Which of these three students correctly distributed 5?

Marc distributed correctly.

$5(x+3)=5\times \,x+5\times \,3=5x+15$

Exercise 17:

$A\,=\,7\,(x\,+\,8)=7x+56\,;\,\\\,B\,=\,7\,(a-4)=7a-28\,;\,\\\,C\,=\,8\,(x\,+\,3)=8x+24\,;\,\\\,D\,=\,6\,(y\,-\,3)=6y-18$

Exercise 18:

For x = 1 , perform the following calculations:

$A\,=\,-\,4x\,+\,7\,=-4\times \,1+7=3;\\\,B\,=\,3\,+\,4x\,-\,6\,=3+4-6=1;\,\\\,C\,=\,2\,(\,3x\,+\,5\,)=2(3\times \,1+5)\,=2\times \,8=16;\,\\\,D\,=\,5x^2\,-\,8x\,-6=5\times \,1^2-8\times \,1-6=5-8-6=-9$

Exercise 19:

$A=5\times \,x+5\times \,2$

${\color{DarkRed}\,A=5x+10}$

$B=3\times \,4y-3\times \,3$

${\color{DarkRed}\,B=12y-9}$

$C=7\times \,x-7\times \,5$

${\color{DarkRed}\,C=7x-35}$

$D=2\times \,4x-2\times \,3,4$

${\color{DarkRed}\,D=8x-6,8}$

The answer key to the exercises on literal calculation in 5th grade.

After having consulted the answers to these exercises on literal calculation in 5th grade, you can return to the exercises in 5th grade

Fifth grade exercises.

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