How can we find # 3 9/10# of #15/16?# How could we check by estimating?
Switch to an incorrect fraction.
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To find ( \frac{3 \frac{9}{10}}{15/16} ), first convert the mixed number to an improper fraction:
( 3 \frac{9}{10} = \frac{(3 \times 10) + 9}{10} = \frac{39}{10} )
Now, multiply this fraction by ( \frac{15}{16} ):
( \frac{39}{10} \times \frac{15}{16} = \frac{39 \times 15}{10 \times 16} = \frac{585}{160} )
To estimate, you can round the fractions to simpler numbers:
( \frac{39}{10} \approx \frac{40}{10} = 4 )
( \frac{15}{16} \approx \frac{16}{16} = 1 )
So, estimating ( 4 \times 1 = 4 ) would be a close approximation to the actual value.
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To find (3 \frac{9}{10}) of (\frac{15}{16}), you multiply the whole number part and the fraction part separately, and then add the results.

Multiply the whole number part: [3 \times \frac{15}{16} = \frac{45}{16}]

Multiply the fraction part: [\frac{9}{10} \times \frac{15}{16} = \frac{135}{160}]

Add the results: [\frac{45}{16} + \frac{135}{160} = \frac{180}{160} + \frac{135}{160} = \frac{315}{160}]
To check by estimation, you can round the fraction (\frac{15}{16}) to the nearest whole number, which is approximately (1). Then you can calculate (3 \frac{9}{10}) of (1) which is approximately (3), since (9/10) of (1) is close to (1). This estimation suggests that the result of the calculation should be close to (3), confirming the accuracy of the calculation.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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