UAT EXAM PREP

PREPARED BY KALKIDANE

Here are the basic ideas of LCM, GCF, Ratio, and Percentage:

1. LCM (Least Common Multiple)

Definition: The smallest positive number that is a multiple of two or more numbers.
Use: Finding a common denominator in fractions or determining when events happen together.
Example:Multiples of 4: 4, 8, 12, 16, 20...
Multiples of 8: 8, 16, 24...
LCM(4, 8) = 8 (actually 8 is the first common multiple).

2. GCF (Greatest Common Factor)

Definition: The largest number that divides two or more numbers exactly.
Use: Simplifying fractions and dividing objects into equal groups.
Example:Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
GCF(12, 18) = 6

3. Ratio

Definition: A comparison of two quantities by division.
Written as: or .
Example:If there are 8 boys and 12 girls, the ratio of boys to girls is 8:12 = 2:3.

4. Percentage

Definition: A fraction or ratio expressed out of 100.
Symbol: %
Formula:Percentage = (Part ÷ Whole) × 100%
Example:If 18 out of 20 students pass:
Percentage = (18 ÷ 20) × 100 = 90%

Topic Meaning Example LCM Smallest common multiple LCM(6, 8) = 24 GCF Largest common factor GCF(12, 18) = 6 Ratio Compares two quantities 2:5 Percentage Number out of 100 75% = 75/100

Part 2 Basic Algebra

Algebra is a branch of mathematics that uses letters (variables) and numbers to represent unknown values.

Variable: A letter that represents an unknown number (e.g., ).
Constant: A fixed number (e.g., 5, –2, 10).
Coefficient: The number multiplying a variable (e.g., in , 4 is the coefficient).

Linear Equation

A linear equation is an equation in which the highest power of the variable is 1.

General form:

ax + b = 0

Example

Solve:

2x + 5 = 13

Subtract 5 from 13

2x = 8

Divide both sides by 2:

x = 4

Another Example

Solve:

3x - 9 = 12

Add 9 to both sides:

3x = 21

Divide by 3:

x = 7

Steps to Solve a Linear Equation

Simplify both sides if needed.
Move all variable terms to one side.
Move constants to the other side.
Divide by the coefficient of the variable.
Check your answer by substituting it back into the equation.

Practice 20 questions✨ በወረቀት ስሩ💫 Photo አንስታችሁ ትልኩልናላችሁ🙌

Solve:

   3(2x-5)-4(x+1)=2(x-7)+5

2, Solve

(2x-3)5+(x+4)2=3

3, Solve:

   5(2x-1)-3(x+4)=4(x-2)+7

4. Three consecutive integers have a sum of 96. Find the integers.

5, The sum of twice a number and 15 is equal to three times the number minus 8. Find the number.

6, Solve:

   4(x-3)-2(2x+5)=3(1-x)-8

7, father is three times as old as his son. In 10 years, the father will be twice as old as the son. Find their present ages.

8, Solve:

(x-2)3-(x+1)4=5/6

9,Find the value of :

   2(x-1)+3(x+2)=4(2x-5)+17.

10, Two numbers differ by 8. Their sum is 40. Find the two numbers.

11. The ratio of boys to girls in a class is 5:6 . After 12 girls join the class, the ratio becomes 12:5. How many boys were originally in the class?

12. Find the LCM and HCF of (40, 64)

13. Two numbers are in the ratio 9:4. If their LCM is 280, find the two numbers.

14. A shopkeeper marks an item 40% above cost price and then gives a 20% discount. If the selling price is 672 ETB, find the cost price.

15. A student's score increased from 360 to 450. By what percentage did the score increase?

16. Two numbers have GCF = 18 and LCM = 540. If one number is 90, find the other number.

17. Find the smallest positive number that leaves a remainder of 2 when divided by 6, 8, and 10.

18. How many integers between 100 and 500 are divisible by both 6 and 8 but not divisible by 5?

💡 If , find the value of .

19. Solve the inequality:

3(2x-1)-5<4x+7.

20. Solve and write the solution set:

2x-5 <3x+(72x+3)+15.

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