Siti had a length of ribbon. She wanted to cut it into 5 equal pieces, but she cut it into 4 equal pieces instead. Each piece was 9 cm longer than it should have been. Find the length of the ribbon.
5 units = 5 × 36 = 180 cm
Ans: 180 cm
How to solve it
Call one planned piece 1 unit. The ribbon cut into 4 and the ribbon cut into 5 are the same ribbon.
Mark the extra 9 centimetres on each of the 4 pieces she cut.
Slide the 4 extras under the piece she never cut. They fill it exactly.
So 1 unit is 4 times 9, which is 36 centimetres.
The ribbon is 5 units: 5 times 36 is 180 centimetres.
She cut 4 pieces, and each one is 9 centimetres too long. Those 4 extras are the fifth piece. The mistake is in the number of pieces, not in the ribbon. So the way back is the extras, gathered into the piece that's missing.
Practice questions with worked solutions
Question 1 is free to try. The other 8 open in the free trial, each with its full working.
How do you solve P5 work backwards word problems with a wrong step?
In these questions someone uses the wrong operation, or a chain of changes ends at a known total, and the starting number has to be recovered.
What your child learns here
In these questions someone uses the wrong operation, or a chain of changes ends at a known total, and the starting number has to be recovered. The page applies the Primary 5 four operations of whole numbers to working backwards.
Undo each step with its inverse: subtraction undoes addition, division undoes multiplication.
Undo the steps in reverse order, last step first.
After undoing the wrong step, carry out the operation that was meant, because that result is the answer asked.
Read words such as 'doubled' or 'gave away half' as operations that must be undone too.
When a length is cut into the wrong number of pieces, use the pieces that were cut to find the size of the planned piece.
Does the answer make sense?
If someone added instead of subtracting, the answer they should have got is smaller than the one they got; if they divided instead of multiplying, it is larger. When a length is cut into more pieces than planned, your child should find each planned piece longer than the pieces that were cut.
How to practise these questions
Basic questions train recovering the starting number when one operation was done the opposite way, then applying the intended one. Intermediate questions add lengths cut into an unplanned number of pieces, shares that each come up short and totals built with the incorrect multiplier. Challenge questions need a common-multiple model, a regrouping after the correction, or a sharing that is partly handed on before the whole can be found. If reversing the steps gets confusing, watch the solution film for that question and come back to it later from Revision.
Questions parents ask
How do I teach my child to work backwards? Ask them to list the steps in order, then undo them from the last to the first, using the opposite operation each time. Writing one undo step per line keeps it clear.
What are inverse operations? They are operations that undo each other: addition and subtraction, and multiplication and division. Working backwards uses them to get back to the start.
Is working backwards in the Primary 5 syllabus? The syllabus lists the four operations of whole numbers; working backwards is a way of using them in word problems. This page practises it with a lesson film and a free question.
