Explain how the answers for 20 divided by 1/7 (140), 20 divided by 2/7 (70) and 20 divided 6/7 (23 1/3) are related. Show why this makes sense. Please answer my question
dividing by a fraction is the same as multiplying by its reciprocal.
WHAT IS NTH
To understand how the answers for the divisions you mentioned are related, we first need to understand the concept of dividing fractions.
When dividing fractions, we can use the reciprocal (also known as the multiplicative inverse) of the second fraction and then multiply it by the first fraction. So, if we have the expression a divided by b (a ÷ b), we can rewrite it as a multiplied by 1/b (a × 1/b) or a × b^(-1).
Now, let's analyze each division case:
1. 20 divided by 1/7:
When dividing 20 by 1/7, we can rewrite it as 20 multiplied by 7/1 (20 × 7/1 = 140). Here, the reciprocal of 1/7 is 7/1, which is just the whole number 7. So, 20 divided by 1/7 equals 20 multiplied by 7, which gives us 140.
2. 20 divided by 2/7:
Similarly, for 20 divided by 2/7, we can rewrite it as 20 multiplied by 7/2 (20 × 7/2 = 140/2 = 70). In this case, the reciprocal of 2/7 is 7/2. So, 20 divided by 2/7 equals 20 multiplied by 7/2, which simplifies to 70.
3. 20 divided by 6/7:
Lastly, for 20 divided by 6/7, we can rewrite it as 20 multiplied by 7/6 (20 × 7/6 = 140/6 = 23 1/3). Again, the reciprocal of 6/7 is 7/6. So, 20 divided by 6/7 equals 20 multiplied by 7/6, which gives us 23 1/3.
Therefore, we can see that all three divisions have a similar relationship. The reciprocal of the denominator fraction (1/7, 2/7, and 6/7) is multiplied by the numerator (20) to find the result. This approach helps in dividing fractions by converting them into multiplication problems and simplifies the calculations.
So, it makes sense that the answers for 20 divided by 1/7, 20 divided by 2/7, and 20 divided by 6/7 are related because they follow the same concept of dividing fractions and applying the reciprocal of the denominator.