Question

Maria says that 4 2/3 x 7 1/5 = 4 x 7 + 2/3 x 1/5. Explain why Maria has made a good attempt, but her answer is not correct. Explain how to work with what Maria has already written and modify it to get the correct answer. In other words, don’t just start from scratch and show Maria how to do the problem, but rather take what she has already written, use it, and make it mathematically correct. Which property of arithmetic is relevant to correcting Maria’s work? Explain.

Answer 1

Maria has written:

4 2/3 x 7 1/5 = 4 x 7 + 2/3 x 1/5.

Though Maria has made a good attempt, but her answer is not correct.

Explanation:

Property of arithmetic that is relevant to correcting Maria's work is as follows:

For multiplying 2 numbers each containing an integer part and fractional part, it is incorrect to multiply the integral parts with fractional parts.

The correct method is first convert each of the 2 numbers containing an integer part and fractional part as improper fractions, then multiplying the resultant improper fractions and finally converting the resultant improper fraction into integer with a fraction form.

Step 1:

Take what she has already written:

4 2/3 x 7 1/5

Step 2:

Convert 4 2/3 as improper fraction as follows:

4 2/3 = 14/3

Sep 3:

Convert 7 1/5 as improper fraction as follows:

7 1/5 = 36/5

Step 4:
Multiply the resulting improper fractions as follows:

14/3 X 36/5 = (14 X 36)/(3 X 5) = 504/15

Step 5:
Convert the resultant improper fraction into integer with a fraction form.as follows:

504/15 = 33 9/15 = 33 3/5

So,

Answer is:

33 3/5