How do you simplify $7 \frac{1}{2} - (\frac{1}{9} + \frac{2}{3}) \div \frac{3}{2}$ $7 1/2 - (1/9 + 2/3) div 3/2$ ?

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How do you simplify $7 \frac{1}{2} - (\frac{1}{9} + \frac{2}{3}) \div \frac{3}{2}$ $7 1/2 - (1/9 + 2/3) div 3/2$ ?

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Answer 1 · 2018-05-19T03:07:35

$7 \frac{1}{2} - (\frac{1}{9} + \frac{2}{3}) \div \frac{3}{2} = \frac{377}{54}$ $7 1/2-(1/9+2/3)-:3/2=377/54$

Explanation:

Simplify:

$7 \frac{1}{2} - (\frac{1}{9} + \frac{2}{3}) \div \frac{3}{2}$ $7 1/2-(1/9+2/3)-:3/2$

Follow the order of operations as indicated by the acronym PEMDAS:

Parentheses/brackets
Exponents/radicals
Multiplication and Division in order from left to right.
Addition and Subtraction in order from left to right.

Simplify the parentheses.

$(\frac{1}{9} + \frac{2}{3})$ $(1/9+2/3)$

In order to add or subtract fractions, they must have the same denominator, called the least common denominator (LCD).

The LCD is $9$ $9$ . Multiply $\frac{2}{3}$ $2/3$ by $\frac{3}{3}$ $3/3$ to get an equivalent fraction with a denominator of $9$ $9$ . Since $\frac{3}{3} = 1$ $3/3=1$ , the numbers will change, but the value remains the same.

$\frac{1}{9} + \frac{2}{3} \times \frac{3}{3} =$ $1/9+2/3xx3/3=$

$\frac{1}{9} + \frac{6}{9} =$ $1/9+6/9=$

$\frac{7}{9}$ $7/9$

Rewrite the expression.

$7 \frac{1}{2} - \frac{7}{9} \div \frac{3}{2}$ $7 1/2-7/9-:3/2$

Carry out the division next. Since we are dividing by a fraction, we invert it and multiply.

$7 \frac{1}{2} - \frac{7}{9} \times \frac{2}{3}$ $7 1/2-7/9xx2/3$

$7 \frac{1}{2} - \frac{7 \times 2}{9 \times 3}$ $7 1/2-(7xx2)/(9xx3)$

$7 \frac{1}{2} - \frac{14}{27}$ $7 1/2-14/27$

Convert $7 \frac{1}{2}$ $7 1/2$ to an improper fraction by multiplying the denominator by the whole number and adding the numerator. Place the result over the denominator of $2$ $2$ .

$\frac{(2 \times 7 + 1)}{2} - \frac{14}{27}$ $((2xx7+1))/2-14/27$

Simplify.

$\frac{15}{2} - \frac{14}{27}$ $15/2-14/27$

The denominators $2$ $2$ and $27$ $27$ do not have a common multiple, so to get the LCD, we multiply the denominators.

LCD $=$ $=$ $2 \times 27 = 54$ $2xx27=54$

Multiply $\frac{15}{2}$ $15/2$ by $\frac{27}{27}$ $27/27$ , and multiply $\frac{14}{27}$ $14/27$ by $\frac{2}{2}$ $2/2$ to get equivalent fractions with $54$ $54$ as the denominator.

$\frac{15}{2} \times \frac{27}{27} - \frac{14}{27} \times \frac{2}{2}$ $15/2xx27/27-14/27xx2/2$

$\frac{15 \times 27}{2 \times 27} - \frac{14 \times 2}{27 \times 2}$ $(15xx27)/(2xx27)-(14xx2)/(27xx2)$

Simplify.

$\frac{405}{54} - \frac{28}{54} = \frac{377}{54}$ $405/54-28/54=377/54$

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How do you simplify $7 \frac{1}{2} - (\frac{1}{9} + \frac{2}{3}) \div \frac{3}{2}$ $7 1/2 - (1/9 + 2/3) div 3/2$ ?

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Explanation:

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How do you simplify $7 \frac{1}{2} - (\frac{1}{9} + \frac{2}{3}) \div \frac{3}{2}$ $7 1/2 - (1/9 + 2/3) div 3/2$ ?