Fadi is learning to simplify fractions.

Question

She writes the following  64/16 = 4/1=4. She crossed out the two 6s.

She asks her dad if 64/16=4 and her day says yes. Fadi believes she has mastered simplifying fractions.

1. Is Fadi's approach reasonable? Explain.

2. Suppose you try to correct Fadi. What could you tell her if she argues that her method produces the correct answer and therefore she must be correct. 

Answer 1

Crossing out digits only worked by random chance for the example where 64/16=4/1=4. However, rules should apply to all cases and not just some. If Fadi would've tried cancelling the 2 from 24/12, the result would be 24/12=4/1=4. This wrong because 24/12 is 2, not 4.

My guess is that Fadi misinterpreted the "multiplication by 1 rule"* as it applies to fractions, which is a subset of the "canceling common factors"* rule.

More specifically: (X*A)/(X*B) = (X/X)*(A/B) = 1*(A/B) = A/B

For Fadi's example 64/16, could be broke down as

64/16 = (2*32)/(2*8)

= 32/8

= (2*16)/(2*4)

= 16/4

= (2*8)/(2*2)

= 8/2

= (2*4)/(2*1)

= 4/1

= 4

You could also do a quicker route:

64/16 = (4*16)/(4*4)

= 16/4

= 4

At each step use whatever numbers you find easiest to break down the fraction.

Sources:

* "multiplication by 1 rule", also known as "Multiplicative Identity Property of One"

See: https://www.splashlearn.com/math-vocabulary/multiplication/multiplicative-identity-property-of-1#:~:text=It%20states%20that%20any%20number,the%20number%20remains%20the%20same.

* "canceling common factors", also known as "Multiplying Fractions By Cancelling Common Factors"

See: https://mathgoodies.com/lessons/multiplying-fractions-with-cancelling/#:~:text=Summary%3A%20To%20multiply%20fractions%20by,any%20numerator%20and%20any%20denominator.