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Simple Equations

Numbers · Simple Equations

CBC Grade 5 Mathematics — Simple Equations

Lesson Objectives

By the end of this topic, a learner should be able to:

  • Form a simple equation with one unknown from a real-life situation
  • Solve a simple equation with one unknown, using an inverse operation
  • Appreciate the use of equations in solving everyday problems

Simple Equations

An equation says two things are equal. Solving it means finding the missing number that makes it true.

a) The unknown

We use a letter to stand for the number we do not know yet.

In x + 7 = 12, the letter x is the unknown.

Any letter will do. People often use x or n, but a is just as good.

b) The balance idea

An equation is like a balance with equal weights on both sides.

Whatever you do to one side, you must do to the other. Then it stays balanced.

Take 7 from one side, take 7 from the other. Now both sides are still equal.

c) Inverse operations

To find the unknown, undo what has been done to it.

Adding is undone by subtracting. Subtracting is undone by adding.

Multiplying is undone by dividing. Dividing is undone by multiplying.

These pairs are called inverse operations.

d) Solving

Solving by undoing Solving by undoing x + 7 = 12 the equation undo the +7 = take 7 away the inverse operation x = 12 − 7 do it to both sides x = 5 the answer check → 5 + 7 = 12 it works

Look at what is being done to the letter. Then do the opposite, to both sides.

In x + 7 = 12, the 7 is being added. So take 7 away from both sides.

e) Other examples

For x − 4 = 9, the 4 is taken away. So add 4 to both sides. Then x = 13.

For 3x = 18, the x is multiplied by 3. So divide both sides by 3. Then x = 6.

For x ÷ 2 = 7, the x is divided by 2. So multiply both sides by 2. Then x = 14.

f) Always check

Put your answer back into the original equation.

Take x = 5 in x + 7 = 12. Check that 5 + 7 really is 12. It is, so the answer is right.

Checking takes a moment and catches almost every mistake.

g) From a real situation

From words to an equation From words to an equation let n be = the eggs at first name the unknown the story = n and 6 more is 15 in words as algebra → n + 6 = 15 the equation solve → n = 9 nine eggs

Say what the letter stands for first.

Turn the story into an equation, one part at a time.

Solve it, then say the answer in words. The answer is "nine eggs", not just "9".

h) Where this is used

Working out how many are missing from a set. Finding a price when you know the total. Working out how much more is needed to reach an amount.

:::checkpoint Check yourself

  1. Solve x + 8 = 15.
  2. Solve x − 5 = 11.
  3. Solve 4x = 20.
  4. Sara had some sweets. She got 5 more and now has 12. Form an equation and solve it. :::

Definitions

  • Equation — a statement that two expressions are equal.
  • Unknown — the value not yet found, usually a letter.
  • Inverse operation — an operation that undoes another.

Must Remember

  1. Whatever is done to one side must be done to the other.
  2. To undo addition, subtract; to undo subtraction, add.
  3. Always check by substituting the solution back in.
  4. Read the word problem carefully to decide what the unknown represents.

Conclusion

Forming an equation translates a real situation into a mathematical sentence; solving it undoes what was done to the unknown.

Check yourselfPractise Simple Equations — 10 questions →