I checked the problem but I didn't understand the answer how could you do?, because what happened with the fractions?
Estimate the result of the following problem as a whole number:
4 1/43+2 15/16 -1 24/26+ 5 11/12 -3 3/61
Can you explain me, please....?
It will be close to 4 + 3 -2 + 6 -3 = 8, because all of the numbers added are close to integers.
The exact answer is 7.905165.
Remember they only asked for an estimate that was the closest whole number
The ability to make accurate estimates quickly is often useful.
Certainly! Let's break down the process step by step:
Step 1: Convert mixed numbers to improper fractions.
To do this, multiply the whole number by the denominator of the fraction, and then add the numerator. For example, to convert the mixed number 4 1/43:
4 1/43 = (4 * 43) + 1/43 = 172/43 + 1/43 = 173/43
Similarly, converting all the other mixed numbers to improper fractions, we get:
2 15/16 = 47/16
1 24/26 = 50/26
5 11/12 = 71/12
3 3/61 = 184/61
Step 2: Add and subtract the fractions.
Now that we have converted all the numbers to improper fractions, we can perform the arithmetic operations.
(173/43) + (47/16) - (50/26) + (71/12) - (184/61)
To add or subtract fractions, we need to find a common denominator. The common denominator for the given fractions is the least common multiple (LCM) of 43, 16, 26, 12, and 61.
LCM(43, 16, 26, 12, 61) = 23,408
Now, each fraction needs to be expressed with the common denominator:
((173/43) * (544/544)) + ((47/16) * (1463/1463)) - ((50/26) * (904/904)) + ((71/12) * (1950/1950)) - ((184/61) * (384/384))
Simplifying:
(8,226,512/23,408) + (70,961/23,408) - (45,200/23,408) + (137,850/23,408) - (70,656/23,408)
Step 3: Combine the fractions.
Now that all the fractions have the same denominator, we can add or subtract them:
(8,226,512 + 70,961 - 45,200 + 137,850 - 70,656) / 23,408
Simplifying the numerator:
8,226,512 + 70,961 - 45,200 + 137,850 - 70,656 = 8,319,467
Finally:
8,319,467 / 23,408
Step 4: Estimate the result as a whole number.
To estimate the result as a whole number, divide the numerator (8,319,467) by the denominator (23,408):
8,319,467 ÷ 23,408 = 355.375
Since the estimate is to be a whole number, we round the result:
355
Therefore, the estimated result of the given problem as a whole number is 355.