First estimate answer then divide to find exact answer. Simplify all answers.
2 2/3 divided by 10 2/3
I don't understand how to estimate the answer.
2 2 / 3 = 2 + 2 / 3 = 6 / 3 + 2 / 3 = 8 / 3
10 2 / 3 = 10 + 2 / 3 = 30 / 3 + 2 / 3 = 32 / 3
2 2 / 3 / 10 2 / 3 =
( 8 / 3 ) / ( 32 / 3 ) =
3 * 8 / ( 3 * 32 ) =
8 / 32 =
8 / ( 4 * 8 ) = 1 / 4
is that how you estimate the answer?
To estimate the answer of a division problem, you can round the numbers involved to the nearest whole number and then perform the division. Here's how to estimate the answer for the division problem "2 2/3 divided by 10 2/3":
1. Round the dividend (the number being divided) to the nearest whole number. In this case, rounding 2 2/3 (or 8/3) to the nearest whole number gives us 3.
2. Round the divisor (the number by which the dividend is divided) to the nearest whole number. In this case, rounding 10 2/3 (or 32/3) to the nearest whole number gives us 11.
3. Perform the division using the rounded numbers. 3 divided by 11 is approximately 0.27.
Now let's move on to finding the exact answer using division:
To divide fractions, follow these steps:
1. Convert mixed numbers to improper fractions (if necessary).
2 2/3 can be converted to an improper fraction as follows:
2 * 3 = 6
6 + 2 = 8
So, 2 2/3 as an improper fraction is 8/3.
10 2/3 can be converted to an improper fraction as follows:
10 * 3 = 30
30 + 2 = 32
So, 10 2/3 as an improper fraction is 32/3.
2. Invert the divisor (the second fraction) and multiply.
When you divide fractions, you actually multiply the first fraction by the reciprocal of the second fraction.
Therefore, the division problem 2 2/3 divided by 10 2/3 can be rewritten as:
8/3 ÷ 32/3.
To find the exact answer, we need to divide 8/3 by 32/3:
8/3 ÷ 32/3 = 8/3 * 3/32.
3. Simplify the resulting fraction (if possible).
Multiplying the numerators and denominators gives:
(8 * 3) / (3 * 32) = 24 / 96.
Finally, simplify the fraction by canceling out any common factors:
24 and 96 can both be divided by 24:
24 ÷ 24 = 1
96 ÷ 24 = 4.
So, the exact answer is 1/4 or 0.25.
To summarize:
- The estimated answer is approximately 0.27.
- The exact answer is 1/4 or 0.25.