How can we find # 3 9/10# of #15/16?#
How could we check by estimating?

Question

Ethan Adkins · Accepted Answer

#=3 21/32#

"Of" is the same as #xx#

#3 9/10 xx 15/16#

Switch to an incorrect fraction.

#= 39/10 xx15/16" "larr# cancel where possible

#= 39/cancel10^2 xxcancel15^3/16#

#=117/32#

#=3 21/32#

If we estimate the answer we see that we are multiplying a number a little less than #4# by a number just less than #1#. We expect an answer a bit less than #4#.

#3 21/32# is reasonable.

Eli Assouline · Answer

undefined 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.

Ethan Adkins · Answer

undefined 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.

1. Multiply the whole number part:
$$3 \times \frac{15}{16} = \frac{45}{16}$$

2. Multiply the fraction part:
$$\frac{9}{10} \times \frac{15}{16} = \frac{135}{160}$$

3. 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.

How can we find # 3 9/10# of #15/16?# How could we check by estimating?