This site offers many math exercises to review the main concepts of middle school. It uses the calculator to display a detailed correction.

112 exercises
• N°1110 (Middle School) : Countdown is an arithmetic exercise that allows you to practice quick mental calculation in an efficient way. The goal is to reconstruct an integer using other integers and basic arithmetic operations (+,-,*,/).

Exercise example :

Use yellow numbers and blue arithmetic operators to calculate the target number.

## Countdown

1110 arithmetic_solver
• N°1111 (Middle School) : The purpose of this exercise is to compare two integers, using the appropriate comparison operator.

Exercise example :

Compare the following numbers: 751 ... 956.

1111
• N°1112 (Middle School) : The goal of this corrected exercise is to find the missing sign of an arithmetic expression, course reminders accompany this exercise.

Exercise example :

1112
• N°1113 (Middle School) : The purpose of this math activity is to calculate the percentage of an integer.

Exercise example :

What is the result of 10% of 80.

1113
• N°1114 (Middle School) : The objective of this numerical activity is to multiply a decimal number by 10,100,1000 or 0.1,0.01, or 0.001.

Exercise example :

What is the result of the following product: 836.912 * 0.001 ?

• N°1115 (Middle School) : The purpose of this exercise is to find the result of arithmetic operations (+, -, *, /) with integers.

Exercise example :

What is the result of the following operation 473+295 ?

• N°1116 (Middle School) : The purpose of this exercise on Euclidean division of two integers is to find the quotient and remainder.

Exercise example :

Compute the quotient and remainder of the Euclidean division of 621 by 45.

• N°1117 (Middle School) : The purpose of this exercise is to round a decimal number to a given precision.

Exercise example :

Give the rounding to 2 decimal places of : 11.445631.

• N°1118 (Middle School) : This graphical exercise allows to learn how to locate in the plane, to succeed, you just have to place at the right place a point of given abscissa.

Exercise example :

Point A is on the x-axis, its x-coordinate is 7. Place it correctly.

• N°1119 (Middle School) : The objective of this activity is to complete a "hole" operation, otherwise known as solving a simple equation.

Exercise example :

What is the missing number in the following expression : ...-5 = 4?

1119
• N°1122 (Middle School) : The purpose of this exercise is to practice making length or distance conversions in the usual units of measurement.

Exercise example :

Convert to cm, 2 dam.

1122 measurement conversion convert
• N°1123 (Middle School) : The purpose of this exercise is to practice making area or surface area conversions in the usual units of measurement.

Exercise example :

Convert to m^2, 5 dam^2.

1123 measurement conversion
• N°1124 (Middle School) : This exercise corrected of calculation makes it possible to practise on line to transform a decimal number into percentage.

Exercise example :

Express 0.97 as a percentage.

1124 percentage
• N°1125 (Middle School) : This corrected math exercise allows you to practice transforming a fraction into a percentage online.

Exercise example :

Express 24/25 as a percentage.

1125 percentage
• N°1129 (Middle School) : This activity on fractions allows to practice simplifying an integer fraction using the GCD.

Exercise example :

Simplify the following fraction 7/14.

• N°1130 (Middle School) : This corrected exercise on fractions aims to complete a fractional expression so that an equality is verified.

Exercise example :

By what value must the following expression 10/4=.../36 be completed for the equality to be verified?

• N°1131 (Middle School) : The purpose of this corrected fraction exercise is to simplify a fractional expression.

Exercise example :

Write in the form of a fraction or a whole number the following expression: 1/4*14.

• N°1132 (Middle School) : The purpose of this exercise is to give an approximate value to one decimal place of an algebraic.

Exercise example :

Give an approximate value to one decimal place of the following expression: 10/17*19

• N°1211 (Middle School) : The goal of this whole number math exercise is to practice multiplying and adding them.

Exercise example :

What is the result of 87*34+7027.

• N°1212 (Middle School) : The objective of this corrected calculus exercise is to add a fraction with a whole number.

Exercise example :

What is the result of 14+1040/80.

• N°1213 (Middle School) : The objective of this corrected math exercise is to simplify a fraction after calculating its denominator.

Exercise example :

What is the result of 3768/(91+66).

• N°1214 (Middle School) : The objective of this math exercise is to simplify a fraction that has a fraction as the denominator.

Exercise example :

What is the result of 96/(32/4).

• N°1215 (Middle School) : The objective of this corrected math exercise is to calculate a written expression in natural language.

Exercise example :

What is the result of 5 plus 4 plus 2.

• N°1217 (Middle School) : This exercise allows you to apply the techniques of simplification of fractions to calculate the product of two fractions.

Exercise example :

What is the result of the following fraction product: (24/2)*(14/3).

• N°1219 (Middle School) : The purpose of this exercise is to compare two fractions, choosing the appropriate comparison operator from the list provided.

Exercise example :

Compare the following fractions 6/4...5/4.

• N°1220 (Middle School) : This corrected exercise aims to practice addition, subtraction or multiplication of 2 fractions.

Exercise example :

Perform the following calculation 3/5*4/6.

• N°1223 (Middle School) : The purpose of this exercise is to calculate an arithmetic expression composed of addition and subtraction, taking into account the priorities of the operations.

Exercise example :

What is the result of (6-4)+(9+6)+(3-10).

• N°1225 (Middle School) : The purpose of this corrected math exercise is to find the denominator of a fraction from an equality.

Exercise example :

What is the missing number in the following expression 27/?=3.

• N°1226 (Middle School) : The purpose of this exercise is to verify an equality, the goal being to learn about equation solving.

Exercise example :

Is the following equality 4+x-5 = 2 true for x = 2?

• N°1236 (Middle School) : The purpose of this number math exercise is to practice adding relative numbers.

Exercise example :

What is the result of 8+(-10)?

• N°1237 (Middle School) : The purpose of this corrected math exercise is to complete an equality that involves relative numbers.

Exercise example :

What is the missing number in the following expression: 2+...=-4.

• N°1238 (Middle School) : The purpose of this math exercise is to string together a series of additions and subtractions of relative numbers.

Exercise example :

What is the result of 10+6+4-6-7-5.

• N°1239 (Middle School) : This exercise allows to practice developing an algebraic expression by using different techniques of algebraic calculation.

Exercise example :

Expand the following expression 2*(8+x)?

• N°1240 (Middle School) : This exercise allows to practice factoring an algebraic expression by using different techniques of algebraic calculation.

Exercise example :

Factor the following expression 12+4*x.

• N°1241 (Middle School) : The purpose of this exercise is to learn about solving equations using magic squares.

Exercise example :

In a magic square, the sum of the numbers in each row, in each column and on each diagonal is the same.
Complete the following magic square:

1241
• N°1242 (Middle School) : The purpose of this exercise is to calculate the perimeter of a circle knowing its radius.

Exercise example :

The perimeter of a circle is given by the formula P=2*pi*r, where r is the radius of the circle.
Give an approximate value to 2 decimal places of the perimeter of a circle of radius 7.

1242 perimeter_circle
• N°1245 (Middle School) : The purpose of this corrected exercise is to practice calculating the area of a disk.

Exercise example :

The area of a disk is given by the formula A=pi*r^2, where r is the radius of the circle.
Give an approximate value to 2 decimal places of the area of a disk of radius 14.

1245 area_circle
• N°1311 (Middle School) : The objective of this algebraic calculus exercise is to expand an algebraic expression.

Exercise example :

Expand the following expression -10*(-12).

• N°1312 (Middle School) : The objective of this exercise is to put the product of a number by the inverse of another number in fraction form.

Exercise example :

Put in the form a*1/b the following fraction 19/6

• N°1313 (Middle School) : This exercise allows to practice calculations with decimals, the goal is to give the approximate value of a fraction to one decimal place.

Exercise example :

Give a value approximating to 0.1 of the following fraction 19/6.

• N°1314 (Middle School) : The objective of this activity is to simplify a fraction whose numerator and denominator are composed of products of whole numbers.

Exercise example :

Simplify the following fraction (3*3)/(8*3).

• N°1315 (Middle School) : This exercise allows to learn how to simplify a fraction whose numerator and denominator are composed of product of relative numbers.

Exercise example :

Put in the form of an irreducible fraction: -5*8/(9*6).

• N°1316 (Middle School) : The objective of this exercise is to simplify a fraction whose numerator and denominator are fractions, in other words, a fraction of fractions.

Exercise example :

Put in the form of an irreducible fraction: ((2)/(-4))/((6)/(9)).

• N°1317 (Middle School) : The objective of this numerical computation exercise is to write in the form of a power of 10 a product of numbers.

Exercise example :

Write the following product as a power of 10: 10^(-10)*10^(-3).

• N°1318 (Middle School) : The purpose of this exercise is to practice finding the writing in the form of a power of 10, of a number raised to a power.

Exercise example :

Write the following product as a power of 10: (10^(-6))^(-9).

• N°1319 (Middle School) : The purpose of this corrected math exercise is to write a number with scientific notation.

Exercise example :

Write using scientific notation the following number: -0.7539046.

• N°1321 (Middle School) : This exercise allows to practice putting a product of numbers in the form of a power.

Exercise example :

Write in the form of a single power the following expression: 20^(-3)*20^(6).

• N°1322 (Middle School) : The purpose of this math exercise is to complete an equality that involves powers.

Exercise example :

With what value must the question mark be replaced for the following equality to be true? 94^(-3)*94^(?)=94^(-8)

• N°1324 (Middle School) : The objective of this exercise is to give an approximate value of a square root to one decimal place.

Exercise example :

Give a value approximated to 10^-1 of sqrt(91).

• N°1325 (Middle School) : This exercise allows you to practice the techniques of simplifying algebraic expressions that contain a single letter.

Exercise example :

Simplify the following expression 1+5*z+2*z^2+5+4*z+z^2+4+2*z+5*z^2.

• N°1326 (Middle School) : The objective of this algebraic calculus exercise is to expand an algebraic expression.

Exercise example :

Expand the following expression (-4*a-8*b)*(5*a+3*b).

1326 expand_and_simplify
• N°1327 (Middle School) : The objective of this exercise is to calculate an algebraic expression by replacing letters with a given value.

Exercise example :

Compute the following expression 2+x+9+4*y for x=4 ,y=6.

• N°1328 (Middle School) : The objective of this solved exercise is to compare two fractions using the correct operator.

Exercise example :

Compare the following two expressions 90/10 ... 27/10.

• N°1329 (Middle School) : The objective of this math exercise is to frame a fraction using two decimal numbers.

Exercise example :

Give a frame to the nearest 10^-1 of the following fraction 25/4.

• N°1330 (Middle School) : The objective of this math exercise is to equate a simple problem to solve it.

Exercise example :

I have a number, I add 27 to it, I subtract 22 from the result and I get 43, what is this number?

• N°1331 (Middle School) : The purpose of this exercise on proportionality is to check that a table is indeed a proportionality table.

Exercise example :

Does the following table correspond to a proportionality table?

643
604132

1331
• N°1332 (Middle School) : The purpose of this corrected calculus exercise is to find the coefficient of a proportionality table.

Exercise example :

What is the coefficient of proportionality that allows us to go from the first to the second line of the following table?

971
54426

1332
• N°1333 (Middle School) : The purpose of this exercise is to find the missing value of a proportionality table.

Exercise example :

By what value must we replace the ? so that the following table is a proportionality table?

7348
28?1632

1333
• N°1334 (Middle School) : The purpose of this exercise is to complete using the cross product, a simple table so that it is a proportionality table.

Exercise example :

What is the missing value in the following proportionality table?

x80
294560

1334
• N°1335 (Middle School) : The goal of this math exercise is to solve a first degree inequation with one unknown.

Exercise example :

We suppose that 3*x-2<5. Choose the expression that is true from the list below.

• N°1336 (Middle School) : The purpose of this exercise is to solve a linear equation of the first degree with one unknown of the form ax+b=c.

Exercise example :

Solve the following equation: 4*y-4=6.

• N°1337 (Middle School) : The purpose of this corrected exercise is to solve an equation with one unknown of the first degree of the form x+b=c.

Exercise example :

Solve the following equation: 2*x+3=5.

• N°1338 (Middle School) : The purpose of this corrected exercise is to solve an equation with one unknown of the first degree of the form ax+b=cx+d.

Exercise example :

Solve the following equation: 4*z+3=6*z+8.

• N°1339 (Middle School) : The purpose of this corrected math exercise is to solve an equation written in natural language.

Exercise example :

My quadruple is equal to 32. Who am I?

• N°1340 (Middle School) : The purpose of this exercise is to solve a numerical problem by calculating the percentage of a whole number.

Exercise example :

In a class of 10 students 70 % got the average on the last test. What is the number of students who did not get the average?

• N°1341 (Middle School) : The purpose of this math exercise is to calculate a percentage from two numbers.

Exercise example :

In a class of 10 students, 4 got the average in the last math test. What percentage of students got the average?

• N°1342 (Middle School) : The purpose of this math exercise is to determine a percentage from two given integers.

Exercise example :

In a class of 30 students there are 9 boys. What is the percentage of boys in this class?

• N°1412 (Middle School) : The purpose of this exercise is to develop an algebraic expression using the most suitable remarkable identity.

Exercise example :

Using the appropriate special expansion develop the following expression (8*a+5*b)*(8*a-5*b).

• N°1413 (Middle School) : The purpose of this exercise is to calculate the square of a number using a remarkable identity.

Exercise example :

Using the appropriate remarkable identity calculate the following expression 999^2.

• N°1414 (Middle School) : The purpose of this corrected math exercise is to simplify the square root of an integer.

Exercise example :

Calculate the following expression sqrt(939)^2.

• N°1415 (Middle School) : The purpose of this corrected math exercise is to solve an equation of the form x^2=a.

Exercise example :

Find x such that x^2=9.

• N°1416 (Middle School) : The purpose of this corrected math exercise is to simplify a product of square roots.

Exercise example :

Put under the same radical the following expression sqrt(35)*sqrt(31).

• N°1417 (Middle School) : The purpose of this corrected math exercise is to simplify a quotient of square roots.

Exercise example :

Put under the same radical the following expression sqrt(16)/sqrt(25).

• N°1418 (Middle School) : The purpose of this corrected math exercise is to write a square root in a simplified form.

Exercise example :

Write in the form a*sqrt(b), the following expression sqrt(480), where a and b represent two integers.

1418 simplify_surd
• N°1419 (Middle School) : The purpose of this corrected math exercise is to write a quotient of square roots in a simplified form.

Exercise example :

Write in the form a*sqrt(b), the following expression sqrt(140)/sqrt(20), where a and b represent two integers.

• N°1422 (Middle School) : The objective of this corrected math exercise is to solve a first order inequation.

Exercise example :

For what value of x, is the following expression 7*x+6">-"6 true?

1422 solving equations and inequations of the first degree 9th Grade inequality_solver
• N°1423 (Middle School) : The objective of this corrected math exercise is to solve a system of two equations with two unknowns.

Exercise example :

Solve the following system:

-x-2*y = 3

3*x = -2

1423 solve_equations
• N°1427 (Middle School) : The objective of this corrected arithmetic exercise is to calculate the gcd of two integers.

Exercise example :

Calculate the gcd of 225 and 84.

• N°1428 (Middle School) : The objective of this exercise is to use the GCD to check if two integers are prime to each other.

Exercise example :

Are the following numbers 205 and 318 prime to each other ?

• N°1429 (Middle School) : The purpose of this exercise is to put a fraction into its irreducible form.

Exercise example :

Put the following fraction in its irreducible form: 144/210.

• N°1430 (Middle School) : The purpose of this corrected algebraic calculus exercise is to factor an algebraic expression that involves squares.

Exercise example :

Factor the following expression x^2-20*x.

1430 factor
• N°1431 (Middle School) : The purpose of this exercise is to factor an algebraic expression using a remarkable identity of the form a² - b².

Exercise example :

Factor the following expression 9*x^2-49.

1431 factor
• N°1434 (Middle School) : The objective of this corrected calculus exercise is to simplify an expression containing fractions.

Exercise example :

Write D as an irreducible fraction: D = ((9/6+5/7)*2)/8

• N°1435 (Middle School) : The purpose of this corrected math exercise is to calculate the value of a function for a given number.

Exercise example :

Let f be the application of R in R defined by f(x)=2*(3*x+1)^2-6*(2*x+3)^2 :
Compute f(2).

• N°1436 (Middle School) : The objective of this exercise is to reduce a fraction, simplify a square root, and calculate a fraction that contains powers.

Exercise example :

Let A=3/8+10/6-8/4 , B=-8*sqrt(24)-4*sqrt(216)-5*sqrt(54)-1*sqrt(54) and C=(18*10^5*3*10^6)/(6*10^11)
1. Compute A and give the result as an irreducible fraction.
2. Write B in the form a*(sqrt(6)) where a is a relative integer.
3. Write C as an integer.

• N°1437 (Middle School) : The objective of this exercise is to calculate the gcd of two numbers and simplify a fraction.

Exercise example :

1. Compute the GCD of the numbers 5104 and 968.
2. Write the fraction 5104/968 in irreducible form.

• N°1438 (Middle School) : The purpose of this exercise is to practice factoring, expanding, simplifying algebraic expression and solving equation.

Exercise example :

Consider the expression E=(8*x+4)^2-(8*x+4)*(7*x-5).
1. Expand and reduce E.
2. Factor E.
3. Solve the equation (9+x)*(4+8*x)=0.

1438 expand_and_simplify
• N°1439 (Middle School) : The purpose of this exercise is to practice factoring, expanding, simplifying algebraic expression and solving equation.

Exercise example :

Consider the expression E=(2*x+10)^2-(2*x+10)*(5*x-4).
1. Expand and reduce E.
2. Factor E.
3. Solve the equation (14-3*x)*(10+2*x)=0.

1439 expand_and_simplify
• N°1440 (Middle School) : The objective of this exercise is to equate a problem in order to solve it.

Exercise example :

Today Tom is 15 years old and Steve is 37 years old. In how many years the age of Steve will be double that of Tom?

• N°1441 (Middle School) : The purpose of this exercise is to use a system of two equations with two unknowns to solve a problem.

Exercise example :

1. Solve the system
2*x+2*y=30
3*x+10*y=101
2. To organize photos a store offers two types of storage albums or boxes : Tom buys 2 boxes and 2 albums and pays 30. Victoria buys 3 boxes and 10 albums and pays 101.
3. What is the price of a box?
4. What is the price of an album?

• N°2411 (Middle School) : The purpose of this exercise is to find the equation of a line representing a linear function that passes through a given point.

Exercise example :

Determine the equation of the linear function whose graphical representation passes through the point D of coordinates (3/5,2).

• N°2413 (Middle School) : The purpose of this exercise is to find the equation of a line from two points.

Exercise example :

Determine the reduced equation of the line passing through the points A(3;5 )and B(2;4).

2413 equation_straight_line
• N°3300 (Middle School) : The purpose of this exercise is to calculate the hypotenuse of a right triangle using the Pythagorean theorem.

Exercise example :

In the triangle ABC rectangle in A, we give AB=20 and AC=15..
Calculate BC.

• N°3441 (Middle School) : The purpose of this corrected exercise is to calculate the coordinates of a vector from the coordinates of two points.

Exercise example :

Let(O,vec(i),vec(j)) be a reference frame of the plane. Let A and D be two points of coordinates (13,8) and (7,6) respectively in this frame, compute the coordinates of the vector vec(AD).

3441 vector_coordinates
• N°3442 (Middle School) : The purpose of this corrected exercise is to calculate the distance between two points from their coordinates.

Exercise example :

The plane is given an orthonormal reference frame (O,vec(i),vec(j)). Let A and D be two points of coordinates (13,8) and (7,6) respectively in this frame, calculate the distance between A and D .

3442 vector_norm
• N°3443 (Middle School) : The purpose of this corrected analytical geometry exercise is to calculate the coordinates of the midpoint of a segment from coordinates.

Exercise example :

Let(O,vec(i),vec(j)) be a reference frame of the plane. Let D and H be two points of coordinates (2,8) and (2,7) respectively in this frame, compute the coordinates of the middle of the segment [DH].

3443
• N°4401 (Middle School) : The purpose of this corrected statistics exercise is to practice calculating an arithmetic mean.

Exercise example :

In a library open from Tuesday to Saturday inclusive, we counted, day by day, the number of books lent during a week and we obtained the results in the following table:

Tuesday73
Wednesday16
Thursday4
Friday73
Saturday79
1. Calculate the total number of books loaned during the entire week.
2. Calculate the average number of books loaned, per day, during this five-day week.

4401 statistics average
• N°4402 (Middle School) : The purpose of this corrected statistics exercise is to practice calculating the frequency of a series.

Exercise example :

After a test, the marks of 26 students have been grouped in the table below :

grade n0<=n<44<=n<88<=n<1212<=n<1616<=n<=20
Number of students457?7

1. What is the number of students having obtained a mark between 12 and 16 (excluding 16).
2. How many students got less than 12?

4402 statistics
• N°4403 (Middle School) : The purpose of this corrected statistics exercise is to determine from a table the frequency of a series.

Exercise example :

Here are the ages of the employees of a company, give the frequency of employees who are between 25 and 29 years old.

Age20-2425-2930-3940-4949-60
Employees26213

4403 statistics
• N°11171 (Middle School) : This exercise allows you to practice rounding a decimal number to the nearest whole number.

Exercise example :

Rounding to the nearest whole number 71.710931

• N°11172 (Middle School) : To pass this problem on rounding, you just have to round correctly a decimal number to one digit after the decimal point.

Exercise example :

Rounding to one digit after the decimal point 72.597345.

• N°11201 (Middle School) : The purpose of this corrected exercise is to practice calculating the area of a rectangle.

Exercise example :

The area of a rectangle is given by the formula L*l where L is the length and l is the width. Calculate the area of a rectangle where L=9 and l=6.

11201 area_rectangle
• N°11202 (Middle School) : The purpose of this corrected exercise is to practice calculating the area of a square.

Exercise example :

The area of a square is given by the formula l*l where l is the length of a side. Calculate the area of a square where l=9.

11202 area_square
• N°11203 (Middle School) : The objective of this exercise is to calculate the perimeter of a rectangle knowing its length and width.

Exercise example :

The perimeter of a rectangle is given by the formula 2*(L+l), where L is the length and l the width.
Calculate the perimeter of a rectangle of length L=20 and width l=12.

11203 perimeter_rectangle
• N°11204 (Middle School) : The objective of this corrected exercise is training in calculating the perimeter of a square knowing the length of a side.

Exercise example :

The perimeter of a square is given by the formula 4*l, where l is the length of a side. Calculate the perimeter of a square of length l=20.

11204 perimeter_square
• N°11211 (Middle School) : This graphical reading activity consists in reading correctly the coordinates of a point placed in a reference frame.

Exercise example :

What are the coordinates of the following point ?

11211
• N°11212 (Middle School) : To do this exercise of location in the plane, you must place a point in a reference frame from its abscissa and its ordinate.

Exercise example :

The point A has coordinates (7;0). Place it correctly.

11212
• N°14110 (Middle School) : The purpose of this corrected math exercise is to simplify a square root.

Exercise example :

Write in the form sqrt(a)/b, the following expression 1/sqrt(360), where a and b represent two integers.

• N°14111 (Middle School) : The objective of this exercise is to write an expression composed of the sum of an integer and a square root.

Exercise example :

Put 8+sqrt(20) in the form a+b*sqrt(5), where a and b are two natural numbers.

• N°14112 (Middle School) : The objective of this exercise is to simplify an expression composed of several square roots.

Exercise example :

Write C in the form a*sqrt(b) where a is a relative integer and b a natural number: C=1*sqrt(8)-2*sqrt(18)-1*sqrt(32)-2*sqrt(2)

• N°24121 (Middle School) : The purpose of this exercise is to read on a graph the image of a number by a function.

Exercise example :

Let f be a function whose representation is given opposite. What is the image of -3 by f?

24121 linear functions and affine functions
• N°24122 (Middle School) : The purpose of this exercise is to read on a graph the antecedent by a function of a number.

Exercise example :

Let f be a function whose representation is given opposite. What is the antecedent by f of -2 ?

24122 linear functions and affine functions