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 × a – c × 3

Q = 2 × a × a + b × b × b

Exercise 2: literal calculation

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

$A\,=\,5\,x\,+\,3$

$B\,=\,6\,x\,+\,2\,y\,-\,4\,z$

$G\,=\,8\,x\,+\,3\,-\,3\,y$

$H\,=\,x\,+\,y\,(3\,x\,-\,2\,y)$

Exercise 3:

Expand then reduce :

$A\,=\,8\,(x\,-\,3)$

$B\,=\,5\,(2\,x\,-\,6)$

$C\,=\,3\,x\,(2\,x\,-\,7)$

$G\,=\,4\,(2\,x\,+\,5)\,+\,3\,(x\,-\,6)$

$H\,=\,2\,(3\,x\,+\,4\,y\,-\,2)$

$I\,=\,2\,x\,(x\,+\,1)\,+\,x\,(5\,x\,-\,2)$

$J\,=\,2\,(3\,x\,+\,5)\,+\,4\,(2\,x\,+\,3)$

Exercise 4:

Calculate in two different ways:

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

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

$C\,=\,4\,(5-\,3)$

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

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

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.

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.

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.

a. Explain why the area , 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

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:

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, $k=\,0,14$ .