A student’s work to solve 2 6/7÷ 2/7 is shown below. Which of the following statements do you agree with?
2 6/7÷ 2/7 =
19/7 ÷2/7 =
7/19 • 2/7 =
Cross Out 7 with 1/19 2/Cross Out 7 with 1=
2 /19
Myriah: “The only mistake is in changing the mixed number to an improper fraction.”
Thomas: “There’s a mistake with the multiplicative inverse of two-sevenths.”
Gabriel: “The problem looks fine to me.”
Siri: “There’s a mistake with changing the mixed number to an improper fraction as well as in changing the division problem to multiplication.”****
thank u bob very cool
I agree with Siri's statement. There are two mistakes in the student's work. The first mistake is in changing the mixed number 2 6/7 to an improper fraction. It should be written as 20/7 instead of 19/7.
The second mistake is in changing the division problem to multiplication. Instead of multiplying by the multiplicative inverse of 2/7, the student should actually divide by 2/7.
I agree with Siri's statement. There are two mistakes in the student's work.
First, the student correctly changes the mixed number 2 6/7 to an improper fraction 20/7. However, they mistakenly write it as 19/7.
Secondly, when dividing fractions, we need to find the multiplicative inverse (reciprocal) of the second fraction and multiply it with the first fraction. In this case, the student wrongly multiplies 20/7 by 2/7, instead of dividing it.
To solve the problem correctly:
Step 1: Convert the mixed number 2 6/7 to an improper fraction:
2 6/7 = (2 * 7 + 6)/7 = 20/7
Step 2: Find the multiplicative inverse of the second fraction:
2/7 becomes 7/2 when we flip the numerator and denominator.
Step 3: Multiply the first fraction by the reciprical of the second fraction:
20/7 * 7/2 = (20 * 7)/(7 * 2) = 140/14 = 10
Therefore, the correct answer is 10, and the student's work is incorrect in two places.