The least common multiple (LCM) of two numbers is the smallest number that both of them divide into with no remainder. To find it, list the multiples of each number until you find one they share, or use prime factorization. For example, the LCM of 4 and 6 is 12. Before this lesson: You should…
The greatest common factor (GCF) of two numbers is the largest number that divides both of them with no remainder. To find it, list the factors of each number, or use prime factorization. Then pick the biggest factor they share. For example, the GCF of 12 and 18 is 6. Before this lesson: You should…
Prime factorization means writing a number as a product of prime numbers. A prime number has exactly two factors, 1 and itself, like 2, 3, 5 and 7. To find the prime factorization, split the number into factors until every factor is prime. For example, . Before this lesson: You should know your multiplication facts…
Multiplying and dividing integers uses two sign rules. If the two numbers have the same sign, the answer is positive. If they have different signs, the answer is negative. So and . Multiply or divide the numbers as usual, then use the sign rule. Before this lesson: You should know negative numbers and adding and…
Adding and subtracting integers follows three rules. If the signs are the same, add the absolute values and keep the sign. If the signs are different, subtract the smaller absolute value from the larger one and keep the sign of the larger. To subtract, add the opposite: . Before this lesson: You should know how…
A system of two linear equations has one solution, no solution or infinitely many solutions. Lines with different slopes cross once, so there is one solution. Parallel lines never cross, so there is no solution. If both equations make the same line, every point on it is a solution. Before this lesson: You should know…
The substitution method solves a system of equations by replacing one variable with an equal expression. Solve one equation for x or y, then substitute that expression into the other equation and solve. Put that answer back into either equation to find the other variable, and check both. Before this lesson: You should know what…
The elimination method solves a system of equations by adding or subtracting the equations so that one variable cancels out. If nothing cancels right away, first multiply one or both equations so a pair of coefficients become opposites. Solve for the variable that’s left, then substitute to find the other one. Before this lesson: You…
A system of equations is two or more equations that use the same variables. Its solution is the point that makes every equation true at the same time. When you graph a system of two linear equations, the solution is the point where the two lines cross. Before this lesson: You should know how to…
To graph a linear inequality in two variables, graph its boundary line, then shade the side that holds the solutions. Use a solid line for ≤ or ≥ and a dashed line for < or >. To choose a side, test a point such as (0, 0). If it makes the inequality true, shade the…
