How it works
When you see an equation like 0.5 x ___ = 500, it is asking you: 'What number, when multiplied by 0.5, gives 500?' To solve for the missing number, you need to undo the multiplication. You do this using the inverse operation. The inverse of multiplication is division.
Steps:
- Identify what operation is being used with the variable (here, it's multiplication by 0.5).
- Use the opposite operation (division) to isolate the variable. So, divide both sides of the equation by 0.5.
- The answer you get is the value that goes in the blank.
Always check your answer by plugging it back into the original equation to make sure it works!
Worked example
0.25 x ___ = 100
- 1
Set up the equation with a variable.
Let the blank be a variable, like n. So, 0.25 x n = 100.
- 2
Divide both sides by 0.25.
To undo multiplication by 0.25, divide both sides by 0.25: n = 100 ÷ 0.25.
- 3
Calculate the answer.
100 ÷ 0.25 = 400. So, n = 400.
Answer
400
Common mistakes
- 01
Multiplying instead of dividing by the decimal.
Why: Students may mix up which inverse operation to use.
Avoid it: Remember: to undo multiplication, always divide by the same number.
- 02
Dividing the wrong way (e.g., 0.25 ÷ 100)
Why: The order of division is reversed.
Avoid it: The correct way is: total ÷ decimal = answer.
- 03
Forgetting to check the answer.
Why: Some students skip verification.
Avoid it: Always substitute your answer back into the original equation to see if it's correct.
Practice
Answers stay hidden
1.0.2 x ___ = 60
Show hint
What number times 0.2 gives 60? Try dividing 60 by 0.2.
Reveal answer
300
2.0.4 x ___ = 80
Show hint
Divide 80 by 0.4 to find the answer.
Reveal answer
200
3.0.75 x ___ = 150
Show hint
Remember, divide 150 by 0.75.
Reveal answer
200
4.0.6 x ___ = 90
Show hint
Divide 90 by 0.6.
Reveal answer
150