Plug in a value for x: If x = 20, then the expression \(\frac{\frac{20}{5}+\frac{20}{5}+\frac{20}{5}+\frac{20}{5}}{4}\) becomes \(\frac{4+4+4+4}{4}=\frac{16}{4}=4\). Now Plug in 20 for x in the answer choices; only choice (E) hits your target answer of 4. Alternatively, you could factor the expression: \(\frac{\frac{x}{5}+\frac{x}{5}+\frac{x}{5}+\frac{x}{5}}{4}=\frac{4\times \left ( \frac{x}{5} \right )}{4}=\frac{x}{5}\)

Solve each equation by translating into algebra.The first is a=\(\frac{40}{100}\times 45\).Reduce and multiply to find a = 18.The second is \(\frac{40}{100}\times 45\). Multiply both sides by 100 then divide by 90 to find b = 20. Quantity B is greater.

To calculate this expression, break it into pieces: \(\frac{3}{\left ( \frac{3}{4} \right )}-\frac{\left ( \frac{3}{2} \right )}{3}=3\div \frac{3}{4}-\frac{3}{2}\div 3=3\times \frac{4}{3}-\frac{3}{2}\times \frac{1}{3}=4-\frac{1}{2}=\frac{7}{2}\)

This question is really asking about place value. Start with the greatest place: the thousands. So, 6 × 1,000 means a 6 in the thousands place.Eliminate choices (A), (B), and (C). Next, 4 × 100 means the next digit should be 4.Eliminate choice (D), and select choice (E).

Try Plugging In a possible value for ¹⁄_k. If ¹⁄_k= ³⁄₄, then ⁴⁄₃, which is closest to coordinate D

Twenty cigars bought individually would cost $40, so apply the percent change formula—\(\frac{difference}{original}\times 100\)—to determine Quantity A. In this case, the difference is $10, and the original, because it’s a percent decrease, is $40: \(\frac{10}{40}\) × 100 = 25, so Quantity A is 25%. Quantity B is greater.

There are two ways to go about this problem. One is to use the Bowtie method to compare fractions.²⁄₃ versus ⁵⁄₈ yields a 16 versus 15. Pretty close.³⁄₄ versus ⁵⁄₈ yields 24 versus 20. Not as close, so eliminate it \(\frac{7}{11}\) versus ⁵⁄₈ yields 56 versus 55, that’s really close on a percentage basis because the number are bigger.Eliminate choice (A).\(\frac{19}{25}\) versus ⁵⁄₈ yields 152 versus 115. Get rid of it.Choice (E) yields 18 versus 50. Get rid of it. Alternatively, you could also use long division, but if you do, there is no need to finish out the math for each answer. 5 divided by 8 = 0.625.²⁄₃ = 0.66.Keep it. When you start to divide 3 by four, the first number you see is a 7. Don’t continue to divide, just eliminate it because 0.7 is farther from 0.625 than 0.66.Choice (C) yields 0.63, so keep it and eliminate choice (A).The answer is 19 divided by 23 begins with 0.8, so get rid of it.The answer to 23 divided by 30 begins with 0.7 so get rid of that too.

Convert 0.0025 to a percent by sliding the decimal point two places to the right: 0.25%.Then convert 0.25 to a fraction to get ¹⁄₄%.

The question asks for a percent increase from the original price; be careful not to find 20% of $18,000, and reduce the higher total ($18,000) by that amount. Instead, you’ll need to find the amount that yields the higher total, when increased by 20%, though, it’s much easier to just increase the price in Quantity B and compare it to the total in the problem: 10% of $14,400 is $1,440, so 20% must be $2,880; adding this to the base price of $14,400 yields a total of $17,280.That’s smaller than what you were looking for, so Quantity A is greater.

Plug In for the variables. Let m = 3 and n = 5, and \(\frac{2+3}{3\times 5}=\frac{5}{15}=\frac{1}{3}\). Only choice (E) works. Alternatively, you could manipulate the fractions \(\frac{2+m}{mn}=\frac{2}{mn}+\frac{2}{mn}+\frac{m}{mn}=\frac{2}{mn}+\frac{1}{n}\).