How do you insert a pair of brackets to make each statement true $\frac{1}{2} + \frac{2}{3} - \frac{1}{4} \cdot \frac{2}{5} \div \frac{1}{6} = 6 \frac{2}{5}$ $1/2+ 2/3 - 1/4 * 2/5 ÷ 1/6 = 6 2/5$ ?

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How do you insert a pair of brackets to make each statement true $\frac{1}{2} + \frac{2}{3} - \frac{1}{4} \cdot \frac{2}{5} \div \frac{1}{6} = 6 \frac{2}{5}$ $1/2+ 2/3 - 1/4 * 2/5 ÷ 1/6 = 6 2/5$ ?

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Answer 1 · 2015-07-04T20:25:41

$(\frac{1}{2} + \frac{2}{3} - \frac{1}{4} \cdot \frac{2}{5}) \div \frac{1}{6} = 6 \frac{2}{5}$ $(1/2+ 2/3 - 1/4 * 2/5) ÷ 1/6 = 6 2/5$

Explanation:

$\frac{1}{2} + \frac{2}{3} - \frac{1}{4} \cdot \frac{2}{5} \div \frac{1}{6} = 6 \frac{2}{5}$ $1/2+ 2/3 - 1/4 * 2/5 ÷ 1/6 = 6 2/5$

I first rewrote $\div \frac{1}{6}$ $-:1/6$ as $\cdot \frac{6}{1}$ $*6/1$

$\frac{1}{2} + \frac{2}{3} - \frac{1}{4} \cdot \frac{2}{5} \cdot \frac{6}{1} = 6 \frac{2}{5}$ $1/2+ 2/3 - 1/4 * 2/5 * 6/1 = 6 2/5$

Now that mixed number on the right confuses me, so write:

$\frac{1}{2} + \frac{2}{3} - \frac{1}{4} \cdot \frac{2}{5} \cdot \frac{6}{1} = \frac{32}{5}$ $1/2+ 2/3 - 1/4 * 2/5 * 6/1 = 32/5$

That looks better but there are too many denominators especially in the addition and subtraction. So let's write:

$\frac{30}{60} + \frac{40}{60} - \frac{15}{60} \cdot \frac{2}{5} \cdot 6 = \frac{384}{60}$ $30/60 + 40/60 - 15/60 * 2/5 *6 = 384/60$

Keeping the factors $\frac{15}{60} \cdot \frac{2}{5} \cdot 6$ $15/60 * 2/5 *6$ together means we'll need to do something with
$- \frac{15}{60} \cdot \frac{2}{5} \cdot 6 = - \frac{3}{60} \cdot \frac{2}{3} \cdot 6 = - \frac{36}{60}$ $-15/60*2/5*6 = -3/60 * 2/3*6 = -36/60$

But the first two only sum to $\frac{70}{60}$ $70/60$ , so that won't work.

Next, I divided $384$ $384$ by $6$ $6$ to see what we'd need $\frac{1}{2} + \frac{2}{3} - \frac{1}{4} \cdot \frac{2}{5}$ $1/2+ 2/3 - 1/4 * 2/5$ to be, if multiply by $6$ $6$ was the last step.

$384 \div 6 = 64$ $384 -: 6 = 64$

And, (Bonus)

$\frac{30}{60} + \frac{40}{60} - \frac{15}{60} \cdot \frac{2}{5} = \frac{30}{60} + \frac{40}{60} - (\frac{3}{60} \cdot \frac{2}{1})$ $30/60 + 40/60 - 15/60 * 2/5 = 30/60 + 40/60 - (3/60 * 2/1)$

$= \frac{30}{60} + \frac{40}{60} - \frac{6}{60} = \frac{64}{60}$ $= 30/60 + 40/60 - 6/60 = 64/60$

Last check:

$(\frac{1}{2} + \frac{2}{3} - \frac{1}{4} \cdot \frac{2}{5}) \div \frac{1}{6}$ $(1/2+ 2/3 - 1/4 * 2/5) ÷ 1/6$

$= (\frac{1}{2} + \frac{2}{3} - (\frac{1}{4} \cdot \frac{2}{5})) \div \frac{1}{6}$ $= (1/2 + 2/3 -(1/4*2/5)) -: 1/6$

$= (\frac{1}{2} + \frac{2}{3} - \frac{1}{10}) \div \frac{1}{6}$ $= (1/2 + 2/3 -1/10) -: 1/6$

$= (\frac{15}{30} + \frac{20}{30} - \frac{3}{30}) \div \frac{1}{6}$ $= (15/30 + 20/30 -3/30) -: 1/6$

$= (\frac{35}{30} - \frac{3}{30}) \div \frac{1}{6}$ $= (35/30 - 3/30)-: 1/6$

$= \frac{32}{30} \div \frac{1}{6}$ $= 32/30 -: 1/6$

$= \frac{32}{30} \cdot \frac{6}{1} = \frac{32}{5} = 6 \frac{2}{5}$ $= 32/30 * 6/1 = 32/5 = 6 2/5$

It works!

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How do you insert a pair of brackets to make each statement true $\frac{1}{2} + \frac{2}{3} - \frac{1}{4} \cdot \frac{2}{5} \div \frac{1}{6} = 6 \frac{2}{5}$ $1/2+ 2/3 - 1/4 * 2/5 ÷ 1/6 = 6 2/5$ ?

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How do you insert a pair of brackets to make each statement true $\frac{1}{2} + \frac{2}{3} - \frac{1}{4} \cdot \frac{2}{5} \div \frac{1}{6} = 6 \frac{2}{5}$ $1/2+ 2/3 - 1/4 * 2/5 ÷ 1/6 = 6 2/5$ ?