DEFINITION

A simple equation is a mathematical sentence that shows that two things are equal.

It always has an equal sign (=) and usually contains a letter (like x, y, or n) that we must find. That letter is called the unknown because we do not know its value until we solve the equation.

EXAMPLE OF AN EQUATION

IMPORTANT WORDS TO REMEMBER

• Equation → means two sides are equal.


• Unknown → the letter we are trying to find (like x).


• Solve → means to find the value of the unknown.


• Balance → both sides of the equal sign must remain the same.

WHY WE LEARN SIMPLE EQUATIONS

• It helps us to Find missing numbers in mathematics.


• It helps us to Solve word problems easily.


• It helps us to Learn how to balance quantities.


• It helps us to Prepare for more advanced algebra later.

HOW TO SOLVE SIMPLE EQUATIONS

When solving equations, think of the equal sign as a balance scale. Whatever you do on one side of the equation, you must also do on the other side so that the equation remains balanced.

STEPS TO SOLVE A SIMPLE EQUATION

1. Identify the unknown (the letter).


2. Look for what is done to the unknown (added, subtracted, multiplied, or divided).


3. Do the opposite (reverse) operation to remove that effect.


4. Do the same thing on both sides of the equal sign.


5. Simplify and find the value of the unknown.

REMEMBER

• If something is added, we subtract.


• If something is subtracted, we add.


• If something is multiplied, we divide.


• If something is divided, we multiply.

WORKED EXAMPLES

WORD PROBLEMS ON SIMPLE EQUATIONS

SUMMARY

• A simple equation is a statement showing two equal quantities.


• The unknown is the letter whose value we must find.


• Solve equations by doing the same operation on both sides to keep it balanced.


• Always reverse the operation to isolate the unknown.


• Equations can come from real-life word problems too.

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SIMPLE LINEAR EQUATIONS THAT INCLUDE FRACTIONAL TERMS

DEFINITION

A simple linear equation with fractions is an equation that has fractions in it, and it usually contains a letter (like x or y) that we need to find.

It is called “linear” because the highest power of the letter is 1 (not x², not x³).

Example:

WHY WE LEARN THIS

1. It helps us to Understand how to work with numbers that are shared (fractions).


2. It helps us to Make it easier to solve real-life problems that have parts, like half, one-third, or one-fourth of something.


3. It helps us to Prepare us for algebra in higher classes.

IMPORTANT IDEAS TO REMEMBER

1. Fractions mean “division”. For example, x/3 means x divided by 3.


2. We can remove fractions by multiplying both sides by the denominator (the bottom number).


3. Always do the same thing to both sides so that the equation remains balanced.


4. After removing fractions, the equation becomes easier to solve, just like the normal ones we have learned before.

STEPS TO SOLVE SIMPLE EQUATIONS WITH FRACTIONS

1. Look for all denominators (bottom numbers of fractions).


2. Find the Lowest Common Denominator (L.C.D.).


3. Multiply every term in the equation by that L.C.D. to remove the fractions.


4. Simplify the equation (no more fractions will remain).


5. Solve the new simple equation step by step to find the value of the unknown.

EXAMPLES WITH STEP-BY-STEP SOLUTIONS

QUICK SUMMARY

1. Fractions can be removed by multiplying with their denominators.


2. Always do the same thing on both sides of the equal sign.


3. After removing fractions, the equation becomes easy to solve.


4. Check your answer by putting it back into the equation to see if both sides are equal.

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WORD PROBLEMS THAT LEAD TO SIMPLE EQUATIONS INVOLVING FRACTIONS

DEFINITION

A word problem involving fractions is a story or real-life situation that can be written as an equation containing fractions.

It means we use words to describe a situation, then change those words into a mathematical sentence that includes fractions.

Example:
Half of a number plus three equals seven.
This can be written as: (1/2)x + 3 = 7.
Then we solve to find the unknown number x.

WHY WE LEARN THIS

1. It helps us to Change real-life stories into mathematical equations.


2. It helps us to Understand how fractions are used in daily activities like money, sharing, or measurement.


3. It helps us to Think carefully and solve problems step by step.

IMPORTANT IDEAS TO REMEMBER

1. When you see “half of a number”, it means (1/2)x.


2. When you see “one third of a number”, it means (1/3)x.


3. When you see “one fourth of a number”, it means (1/4)x.


4. “The number” means the unknown, usually written as x.


5. Always form an equation from the words before you solve.

EXAM-STYLE WORD PROBLEMS AND STEP-BY-STEP SOLUTIONS

Question 1

A number added to its half gives 18. Find the number.

Step 1: Let the number be x.

Step 2: Its half means (1/2)x.

Step 3: The equation is: x + (1/2)x = 18.

Step 4: Find a common denominator: (2x + x)/2 = 18.

Step 5: Simplify: (3x)/2 = 18.

Step 6: Multiply both sides by 2: 3x = 36.

Step 7: Divide both sides by 3: x = 12.

Final Answer: The number is 12.

Question 2

Three-fifths of a number is 24. Find the number.

Step 1: Let the number be x.

Step 2: Three-fifths of the number means (3/5)x.

Step 3: (3/5)x = 24.

Step 4: Multiply both sides by 5: 3x = 120.

Step 5: Divide both sides by 3: x = 40.

Final Answer: The number is 40.

Question 3

If half of a number is 8 less than the number itself, find the number.

Step 1: Let the number be x.

Step 2: Half of the number = (1/2)x.

Step 3: Equation: (1/2)x = x - 8.

Step 4: Multiply both sides by 2: x = 2x - 16.

Step 5: Subtract x from both sides: 0 = x - 16.

Step 6: Add 16 to both sides: x = 16.

Final Answer: The number is 16.

Question 4

One-third of a number added to 7 gives 19. Find the number.

Step 1: Let the number be x.

Step 2: Equation: (1/3)x + 7 = 19.

Step 3: Subtract 7 from both sides: (1/3)x = 12.

Step 4: Multiply both sides by 3: x = 36.

Final Answer: The number is 36.

Question 5

A number minus one-fifth of the number equals 48. Find the number.

Step 1: Let the number be x.

Step 2: Equation: x - (1/5)x = 48.

Step 3: Combine like terms: (5x - x)/5 = 48.

Step 4: (4x)/5 = 48.

Step 5: Multiply both sides by 5: 4x = 240.

Step 6: Divide by 4: x = 60.

Final Answer: The number is 60.

Question 6

If two-thirds of a number plus 5 equals 17, find the number.

Step 1: Let the number be x.

Step 2: Equation: (2/3)x + 5 = 17.

Step 3: Subtract 5 from both sides: (2/3)x = 12.

Step 4: Multiply both sides by 3: 2x = 36.

Step 5: Divide by 2: x = 18.

Final Answer: The number is 18.

Question 7

If three-fourths of a number is 6 more than one-half of the number, find the number.

Step 1: Let the number be x.

Step 2: Equation: (3/4)x = (1/2)x + 6.

Step 3: Find L.C.D = 4. Multiply through by 4: 3x = 2x + 24.

Step 4: Subtract 2x from both sides: x = 24.

Final Answer: The number is 24.

Question 8

If half of John’s age plus 3 equals 11, how old is John?

Step 1: Let John’s age be x.

Step 2: Equation: (1/2)x + 3 = 11.

Step 3: Subtract 3 from both sides: (1/2)x = 8.

Step 4: Multiply both sides by 2: x = 16.

Final Answer: John is 16 years old.

Question 9

A trader spent one-fourth of her money and still had ₦900 left. How much did she have at first?

Step 1: Let the money be x.

Step 2: She spent one-fourth, so she has (3/4)x left.

Step 3: (3/4)x = 900.

Step 4: Multiply both sides by 4: 3x = 3600.

Step 5: Divide both sides by 3: x = 1200.

Final Answer: She had ₦1200 at first.

Question 10

Tolu’s father promised him ₦1000. He first gave him one-fifth of the money. How much was left to be given?

Step 1: Let total money = ₦1000.

Step 2: One-fifth given = (1/5) × 1000 = 200.

Step 3: Money left = 1000 - 200 = 800.

Final Answer: ₦800 was left.

SUMMARY

1. Turn the story into a mathematical sentence first.


2. Fractions mean “sharing” or “part of” something.


3. Use × to remove denominators (bottom numbers).


4. Keep the equation balanced by doing the same thing to both sides.


5. Always write your final answer with a clear statement.