What fraction lies between 2/3 and 6/7 on the number line?
a. 3/5
b. 4/8
c. 3/7
d. 5/6

  D.  5/6

Step-by-step explanation:

The given fractions have decimal values of ...

  2/3 ≈ 0.67

  6/7 ≈ 0.86

The answer choices are approximately 0.60, 0.50, 0.43, and 0.83.

The last choice (5/6) is between 2/3 and 6/7.

Using a common denominator of 42, these three fractions are ...

  2/3 = 28/42

  5/6 = 35/42

  6/7 = 36/42

The fraction 5/6 lies between 2/3 and 6/7.

It is useful to memorize the decimal equivalents of fractions with denominators of 10 or less. There are some patterns involved that make it easier.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

30 feet

step-by-step explanation:

that would be 2 1/2 * 12

= 24 + 6

= 30 feet   (answer)