Estimation - SSAT Upper Level Quantitative (Math)

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Question

Estimate the result $8 \frac{2}{7}\times 9\frac{4}{5}+ 3\frac{4}{5} \times 6\frac{2}{5}$ by first rounding each number to the nearest unit.

Answer

$8 \frac{2}{7} < 8\frac{1}{2}$ , so $8 \frac{2}{7}$ rounded to the nearest unit is 8.

$9\frac{4}{5} \ge 9\frac{1}{2}$ , so $9\frac{4}{5}$ rounded to the nearest unit is 10.

$3\frac{4}{5} \ge 3\frac{1}{2}$ , so $3\frac{4}{5}$ rounded to the nearest unit is 4.

$6\frac{2}{5} < 6\frac{1}{2}$ , so $6\frac{2}{5}$ rounded to the nearest unit is 6.

The desired estimate can be found as follows:

$8 \frac{2}{7}\times 9\frac{4}{5}+ 3\frac{4}{5} \times 6\frac{2}{5}$

$\approx 8 \times 10 + 4 \times 6$

$= 80 + 4 \times 6$

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Question

Evan wants to tip approximately on a restaurant tab. Which of the following comes closest to what he should leave?

Answer

The tab can be rounded to . is equal to .

$=\frac{20}{100}=0.20$

Now we can multiply the percent by the total amount.

is the most reasonable estimate of the recommended tip.

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Question

If the number is rounded to the nearest hundredth, which of the following expressions would be equal to that value?

Answer

If is rounded to the nearest hundredth, the result will be .

Given that $505\cdot100=50,500$ , the correct answer is $505\cdot100$

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Question

Estimate the product $437 \times 877 \times 551$ by rounding each factor to the nearest hundred, then multiplying.

Answer

437 rounded to the nearest hundred is 400.

877 rounded to the nearest hundred is 900.

551 rounded to the nearest hundred is 600.

Multiply the three whole multiples of 100 to get the desired estimate:

$437 \times 877 \times 551 \approx 400 \times 900 \times 600 = 216,000,000$

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Question

Estimate the product $5 \frac{3}{7}\times 9\frac{3}{5} \times 4\frac{4}{5}$ by rounding each factor to the nearest unit, then multiplying.

Answer

$5 \frac{3}{7} < 5\frac{1}{2}$ , so $5 \frac{3}{7}$ rounded to the nearest unit is 5.

$9\frac{3}{5} \geq 9\frac{1}{2}$ , so $9\frac{3}{5}$ rounded to the nearest unit is 10.

$4\frac{4}{5} \geq 4\frac{1}{2}$ , so $4\frac{4}{5}$ rounded to the nearest unit is 5.

Multiply the three whole numbers to get the desired estimate:

$5 \frac{3}{7}\times 9\frac{3}{5} \times 4\frac{4}{5} \approx 5 \times 10 \times 5 = 250$

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Question

Melissa is trying to come up with a reasonable estimate of the amount she spent on groceries over the last six months. She notices that the six checks she wrote out to the local grocery store are in the following amounts: $187.54, $218.89, $174.74, $104.76, $189.75, and $228.64. By estimating each of the amounts of the checks to the nearest ten dollars, come up with a reasonable estimate for Melissa's total expenditure for groceries.

Answer

Round each of the amounts to the nearest ten dollars as follows:

$187.54 rounds to $190.

$218.89 rounds to $220.

$174.74 rounds to $170.

$104.76 rounds to $100.

$189.75 rounds to $190.

$228.64 rounds to $230.

Add the rounded figures:

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Question

Estimate the product $8.39 \times 7.34 \times 3.52$ by rounding each factor to the nearest unit, then multiplying.

Answer

8.39 rounded to the nearest unit is 8 because 0.39 is less than 0.5.

7.34 rounded to the nearest unit is 7 because 0.34 is less than 0.5.

3.52 rounded to the nearest unit is 4 because 0.52 is greater than 0.5.

Multiply the three whole numbers to get the desired estimate:

$8.39 \times 7.34 \times 3.52 \approx 8 \times 7 \times 4 = 56 \times 4 = 224$

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Question

Estimate the result $8.19 \times 4.87 + 3.27 \times 7.42$ by first rounding each number to the nearest unit.

Answer

8.19 rounded to the nearest unit is 8.

4.87 rounded to the nearest unit is 5

3.27 rounded to the nearest unit is 3.

7.42 rounded to the nearest unit is 7.

The desired estimate can be found as follows:

$8.19 \times 4.87 + 3.27 \times 7.42$

$\approx 8 \times 5 + 3 \times 7$

$=40 + 3 \times 7$

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