How do you evaluate #\frac { 1} { 3} ( 2\frac { 1} { 4} \cdot 1\frac { 1} { 5} - \frac { 17} { 20} )#?

Question

Autumn Arnold · Accepted Answer

#1/3(2 1/4*1 1/5-17/20)=37/60#

To evaluate #1/3(2 1/4*1 1/5-17/20)#

we should follow the order of operations PEMDAS i.e. first parentheses, then exponents, multiplication, division, addition and subtraction. Here we do not have exponents, but have parentheses and within the parentheses, we should first solve multiplication.

Most importantly we should convert mixed fractions to improper fractions. As #2 1/4=(2xx4+1)/4=9/4# and #1 1/5=(1xx5+1)/5=6/5#, the above expression becomes

#1/3(9/4*6/5-17/20)# and performing multiplication first, we get

#1/3(54/20-17/20)#

= #1/3xx(54-17)/20#

= #1/3xx37/20# - parentheses has been simplified and now carrying out multiplication we get

#1/3(2 1/4*1 1/5-17/20)=37/60#

Gabriel Agustin · Answer

#color(magenta)(37/60# #1/3(2 1/4*1 1/5-17/20)# #:.=1/3(9/4*6/5-17/20)# #:.=1/3(54/20-17/20)# #:.=1/3(37/20)# #:.=1/3 xx 37/20# #:.color(magenta)(=37/60#

Emery Allen · Answer

undefined To evaluate $ \frac {1} {3} \left( 2\frac {1} {4} \cdot 1\frac {1} {5} - \frac {17} {20} \right) $, we follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

First, we simplify the expression inside the parentheses:

$ 2\frac {1} {4} \cdot 1\frac {1} {5} $

To multiply mixed numbers, we first convert them into improper fractions:

$ 2\frac {1} {4} = \frac {9} {4} $
$ 1\frac {1} {5} = \frac {6} {5} $

Then, we multiply:

$ \frac {9} {4} \cdot \frac {6} {5} = \frac {9 \times 6} {4 \times 5} = \frac {54} {20} $

Next, we subtract $ \frac {17} {20} $ from $ \frac {54} {20} $:

$ \frac {54} {20} - \frac {17} {20} = \frac {54 - 17} {20} = \frac {37} {20} $

Now, we multiply the result by $ \frac {1} {3} $:

$ \frac {1} {3} \cdot \frac {37} {20} = \frac {37} {60} $

Therefore, $ \frac {1} {3} \left( 2\frac {1} {4} \cdot 1\frac {1} {5} - \frac {17} {20} \right) $ evaluates to $ \frac {37} {60} $.

Noah Archer · Answer

undefined To evaluate the expression $\frac{1}{3} \left(2\frac{1}{4} \cdot 1\frac{1}{5} - \frac{17}{20}\right)$, follow these steps:

1. Convert the mixed numbers to improper fractions:
$$ 2\frac{1}{4} = \frac{9}{4} $$
$$ 1\frac{1}{5} = \frac{6}{5} $$

2. Multiply the mixed numbers:
$$ \frac{9}{4} \cdot \frac{6}{5} = \frac{54}{20} = \frac{27}{10} $$

3. Substitute the results back into the original expression:
$$ \frac{1}{3} \left(\frac{27}{10} - \frac{17}{20}\right) $$

4. Subtract the fractions inside the parentheses:
$$ \frac{1}{3} \left(\frac{27}{10} - \frac{17}{20}\right) = \frac{1}{3} \left(\frac{27}{10} - \frac{17}{20} \cdot \frac{2}{2}\right) $$
$$ = \frac{1}{3} \left(\frac{27}{10} - \frac{34}{20}\right) $$
$$ = \frac{1}{3} \left(\frac{27}{10} - \frac{17}{10}\right) $$
$$ = \frac{1}{3} \cdot \frac{10}{10} = \frac{10}{30} = \frac{1}{3} $$

So, $\frac{1}{3} \left(2\frac{1}{4} \cdot 1\frac{1}{5} - \frac{17}{20}\right) = \frac{1}{3}$.