Literal calculation: corrected 5th grade math exercises in PDF.

Literal calculus with corrected exercises in 5th grade is still essential for student understanding. Thus, the latter must know the rules of notations and simplifications of an algebraic expression. In addition, it must apply simple distributivity to expand a literal expression.
These corrected exercises on literal calculation will allow the student to revise online and identify his mistakes in order to progress throughout the school year and fill in his gaps on literal calculation.
These materials are similar to the exercises in your textbook and conform to the national education programs.

Exercise 1:

Reduce (if possible) and delete the × signs:

A\,=\,5\,\times  \,x\,\times  \,y

B\,=\,3\times  \,6\,\times  \,x

C\,=\,6\,+\,10\,\times  \,x

D\,=\,7\times  \,x\,\times  \,y\,\times  \,2

E\,=\,3\,\times  \,x\,\times  \,x

F\,=\,3\,\times  \,x\,+\,5\,\times  \,y

G\,=\,5\,\times  \,x\,\times  \,x\,\times  \,3

K\,=\,%5B(a\,/\,4)\,+\,(b\,\times  \,2)%5D

L\,=\,3\,\times  \,a\,\times  \,b\,\times  \,a\,-\,c\,\times  \,4\,\times  \,a

M = 2 × (3 × x × 2 × y)

N = 8 × a + 15 × a – 3 × a

O = 19 x – 13 x + 11 x

P = 4 × b × 9 + 4 × a × ac × 3

Q = 2 × a × a + b × b × b

Exercise 2: literal calculation

Given that x = 8; y = 5 and z = 1 calculate :





Exercise 3:

Expand then reduce :








Exercise 4:

Calculate in two different ways:

A\,=\,3\,\times  \,5\,+\,3\,\times  \,2

B\,=\,6\,\times  \,2\,-\,5\,\times  \,2


D\,=\,4\,\times  \,5\,+\,4

Exercise 5: Literal calculation

Clever calculation:

A\,=\,45\,\times  \,99

B\,=\,2,7\,\times  \,3,6\,+\,2,7\,\times  \,6,4

C\,=\,18\,\times  \,101

Exercise 6:

An object of mass M, in kg, is suspended from a spring.

The length L, in cm, of the spring is given by the formula :

L=18+2\,\times  \,M.

1. What is the length of the spring when no object is suspended?

2. Calculate the length of the spring when an object of mass :
a. 2 kg b. 1,5 kg c.800 g

Literal calculation

Exercise 7: Literal calculation

This rectangle has a variable x dimension.
We consider the expressions :
E=8\,\times  \,x and F=2\,\times  \,x+16.
a. What do E and F represent for this rectangle?
b. Calculate the values of E and F for x = 3, then x= 5.

Literal calculation

Exercise 8:

This figure consists of a square and an isosceles triangle.
It has a variable x dimension.
We consider the expressions :

A=x+8;\,B=4\,\times  \,x;\,C=3\,\times  \,x+8.
a. What can each of these expressions be calculated for this figure?

b. Calculate the values of A, B and C for x = 5, then x=2.5.

Figure and literal calculation

Exercise 9:

A carpenter cuts out four identical squares from a rectangular board measuring 30 cm by 40 cm.
We don’t know the side of each cut square;
we note x the length of this side, in cm.

Rectangular board and literal calculation

a. Explain why the area A, in cm², of the remaining plate is A\,=\,1\,200\,-\,4\,\times  \,x^2.

b. Calculate this area for :

\bullet x=4 \bullet x=6

c. Is it possible that x = 20?

Exercise 10: Literal calculation

Pattern and literal calculation

a. How many small squares does pattern #6 have?

b. We consider the pattern number n.

Express, as a function of n, the number of small squares it contains.
c. How many small squares does pattern #100 have?

Exercise 11:

The stopping distance

The problem situation:

Maxime and Leïla are riding their scooters when a truck loses a pipe that blocks the road. Determine whether or not each teenager will be able to stop before this obstacle.

Work materials:
Documents, calculator, ruler.

Any research lead, even if not completed, will appear on the sheet.

Information about Maxime and Leïla :
Maxime is 19 years old and he drives at 63 kilometers per hour.
Leila is 16 years old and she drives at 45 kilometers per hour.
Maxime and Leïla are in the surroundings of Marseille and the weather is nice.

A site plan:

open problem

A formula:
d=k\,\times  \,(v:13,6)^2\,+\,v:3,6

d (stopping distance) is the distance, in m, covered before the vehicle stops;
v is the speed, in kilometers per hour, of the vehicle;
k is a number that depends on the weather conditions.
In good weather, k\,=\,0,08 and in rainy weather, k=\,0,14.

Exercise 12: literal calculation

Here is a calculation program.
1. Calculate the number obtained if we choose as starting number :

a.5 b. 1,2

c. 0 d.3,5

2. We note n the number chosen at the beginning.
Express the result as a function of n.

calculation program

Exercise 13:

program calculation 2

Exercise 14:

qcm on literal calculation

Exercise 15:

Mentally calculate the following numerical expressions:

A=13\times  \,11\\B=19\times  \,11\\C=15\times  \,21\\D=12\times  \,31\\E=43\times  \,101\\F=16\times  \,1\,001

Exercise 16:

Mentally calculate the expressions :

A=25\times  \,9\\B=16\times  \,9\\C=9\times  \,45\\D=17\times  \,19\\E=35\times  \,99\\F=14\times  \,999

Exercise 17: literal calculation

Mentally calculate each of the expressions for a\,=\,4.

A=5\times  \,a+8\\B=10-2\times  \,a\\C=4\times  \,(a+2)

Exercise 18:

Mentally calculate each expression for n\,=\,3.

A=n\times  \,(n+5)\\B=n\times  \,(10-n)\\C=n^2\\D=n^3\\E=3\times  \,n^2\\F=5+n^2\\G=2\times  \,n+4\times  \,n^2

Exercise 19:

We have the following literal expressions:

C=3(x+2) and D=2+5\times  \,x.

Calculate the values of C and D for :


Exercise 20: literal calculation

Mentally check if the equality 3\times  \,x-5=x+3 is true for :


Exercise 21:

In each case, say whether the equality is true for x\,=\,4.

a.\,\,8\times  \,x+5=37

b.\,\,6\times  \,x-3=7\times  \,x

c.\,\,2\times  \,(x+3)=18-x

d.\,\,9+3\times  \,x=5\times  \,x+1

See the answer key for this exercise.

Cette publication est également disponible en : Français (French) العربية (Arabic)

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