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.
When dividing by a fraction, it is the same as multiplying by the inverse of the fraction.
20 divided by 1/7 = 20 * 7/1 = 140
Check with the other problems.
9.20
9.26
To understand how the answers for dividing 20 by different fractions are related, let's break it down step by step and see if we can find a pattern.
1. 20 divided by 1/7:
To divide by a fraction, we can multiply the dividend (20) by the reciprocal of the divisor (1/7). The reciprocal of a fraction is obtained by swapping the numerator and the denominator. So, the reciprocal of 1/7 is 7/1.
Calculation: 20 x (7/1) = 140.
The result is 140.
2. 20 divided by 2/7:
Again, we multiply the dividend (20) by the reciprocal of the divisor (2/7). The reciprocal of 2/7 is 7/2.
Calculation: 20 x (7/2) = 70.
The result is 70.
3. 20 divided by 6/7:
Once again, we multiply the dividend (20) by the reciprocal of the divisor (6/7). The reciprocal of 6/7 is 7/6.
Calculation: 20 x (7/6) = 23.33 (rounded to two decimal places).
The result is 23 1/3 or 23.33.
Now let's analyze the results and see if we can identify the relationship:
- When we divide 20 by smaller fractions (like 1/7 and 2/7), the resulting quotient is larger. In other words, the answer is bigger.
- Conversely, when we divide 20 by larger fractions (like 6/7), the resulting quotient is smaller. The answer is reduced.
This relationship makes sense because dividing by a smaller fraction is equivalent to dividing by a larger whole number. So, when we divide by a smaller fraction, we get a larger answer. Conversely, dividing by a larger fraction is equivalent to dividing by a smaller whole number, resulting in a smaller answer.
Therefore, the answers for 20 divided by 1/7, 20 divided by 2/7, and 20 divided by 6/7 are related in such a way that the quotients are inversely proportional to the size of the divisor/fraction being divided by.