Jamar helped in the community garden for 21/10 hours this week. That was 2 4/5 equal-length shifts, because Jamar stopped early one day when it started to rain. What does 21/10 divided by 2 4/5 represent in this situation

Answer 1

To solve this problem, we need to convert the mixed number, 2 4/5, into an improper fraction.

To do this, we multiply the whole number, 2, by the denominator of the fraction, 5, and add the numerator of the fraction, 4, to get 2 * 5 + 4 = 14 as the new numerator.

The denominator remains the same, so the improper fraction is 14/5.

Now, we need to divide 21/10 by 14/5.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

Reciprocal of 14/5 = 5/14

Therefore, 21/10 divided by 14/5 is: (21/10) * (5/14).

Multiplying the numerators together, 21 * 5 = 105, and multiplying the denominators together, 10 * 14 = 140.

So, (21/10) * (5/14) = 105/140.

We can simplify this fraction by dividing the numerator and denominator by their greatest common divisor, which is 35.

105/35 = (105/35) / (35/35) = 3/1.

Therefore, 21/10 divided by 2 4/5 equals 3/1 or simply 3.