Solve a Multiplicative Equation by Division
Divide both sides by the nonzero supplied coefficient.
About 20 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: Solve 0.6x=9.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
A positive coefficient times an unknown can be undone by dividing both sides by that coefficient. This preserves equality and finds the size of one equal share. Fractions or decimals may be valid solutions, depending on the stated domain. Always check with the original multiplication relationship.
Divide both sides by the nonzero supplied coefficient. Simplify to the unknown and substitute back. Explain the quotient in the story’s unit, such as liters per container or price per unit, rather than reporting an unlabeled number.
Divide by the coefficient, not by the target value. A solution need not be a whole number unless the model restricts it. Write the division beneath both sides before canceling the coefficient.
- Write the division beneath both sides before canceling the coefficient.
- Work through the supplied example and label what each number or attribute represents.
- Divide both sides by the nonzero supplied coefficient.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
Solve 0.6x=9. Dividing both sides by 0.6 gives x=15. Checking 0.6×15=9 confirms the solution. The division can be scaled to 90÷6. A zero coefficient would require separate reasoning, but the supplied coefficient here is nonzero. Divide by the coefficient, not by the target value. A solution need not be a whole number unless the model restricts it. Write the division beneath both sides before canceling the coefficient.
Check your reasoning
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Helpful tips
- Divide by the coefficient, not by the target value.
- A solution need not be a whole number unless the model restricts it.
See the answer and explanation
8
Divide both sides by the same nonzero coefficient and check by multiplication. The result is 8.
Take it further
Solve 4x=30. Expected: x=7.5.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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Check the subject sources
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