Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : Number Concepts and Operations

Study concepts, example questions & explanations for SSAT Upper Level Math

Create An Account

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : How To Divide Square Roots

Simplify by rationalizing the denominator:

$\frac{3\sqrt{2}+2\sqrt{3}}{\sqrt{6}}$

Possible Answers:

$\sqrt{3}+ \sqrt{2}$

$\frac{\sqrt{3}+ \sqrt{2}}{2}$

$\frac{9\sqrt{3}+4 \sqrt{2} }{6}$

$\frac{9\sqrt{3}+4 \sqrt{2} }{4}$

$\frac{9\sqrt{3}+4 \sqrt{2} }{9}$

Correct answer:

$\sqrt{3}+ \sqrt{2}$

Explanation:

Multiply both numerator and denominator by $\sqrt{6}$ :

$\frac{3\sqrt{2}+2\sqrt{3}}{\sqrt{6}}$

$= \frac{(3\sqrt{2}+2\sqrt{3})\cdot \sqrt{6}}{\sqrt{6}\cdot \sqrt{6}}$

$= \frac{3\sqrt{2}\cdot \sqrt{6}+2\sqrt{3}\cdot \sqrt{6}}{6}$

$= \frac{3\sqrt{12} +2\sqrt{18} }{6}$

$= \frac{3\cdot \sqrt{4} \cdot \sqrt{3}+2\cdot \sqrt{9}\cdot \sqrt{2} }{6}$

$= \frac{3\cdot 2 \cdot \sqrt{3}+2\cdot3 \cdot \sqrt{2} }{6}$

$= \frac{6 \cdot \sqrt{3}+6 \cdot \sqrt{2} }{6}$

$= \sqrt{3}+ \sqrt{2}$

Report an Error

Example Question #4 : How To Divide Square Roots

Divide: $\frac{\sqrt{64}}{\sqrt{8}}$

Possible Answers:

$2\sqrt2$

$\frac{\sqrt2}{4}$

$\frac{1}{8}$

Correct answer:

$2\sqrt2$

Explanation:

The values are of the same power. Divide the terms.

$\frac{\sqrt{64}}{\sqrt{8}}= \sqrt{\frac{64}{8}}= \sqrt{8} = \sqrt{4}\times \sqrt{2}= 2\sqrt2$

The correct answer is: $2\sqrt2$

Report an Error

Example Question #1 : How To Estimate

Evan wants to tip approximately on a $\$78.45$ restaurant tab. Which of the following comes closest to what he should leave?

Possible Answers:

$\$14$

$\$16$

$\$18$

$\$22$

$\$20$

Correct answer:

$\$16$

Explanation:

The tab can be rounded to $\$80$ . is equal to 0.20 .

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

Now we can multiply the percent by the total amount.

0.20 * 80 = 16

$\$16$ is the most reasonable estimate of the recommended tip.

Report an Error

Example Question #2 : How To Estimate

If the number 50,467 is rounded to the nearest hundredth, which of the following expressions would be equal to that value?

Possible Answers:

$505\cdot100$

$504\cdot100$

$505\cdot1,000$

$505\cdot10$

$504.7\cdot100$

Correct answer:

$505\cdot100$

Explanation:

If 50,467 is rounded to the nearest hundredth, the result will be 50,500 .

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

Report an Error

Example Question #1 : Estimation

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

Possible Answers:

211,000,000

270,000,000

180,000,000

216,000,000

192,000,000

Correct answer:

216,000,000

Explanation:

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:

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

Report an Error

Example Question #2 : How To Estimate

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.

Possible Answers:

180

250

240

300

225

Correct answer:

250

Explanation:

$5 \frac{3}{7} < 5\frac{1}{2}$ , 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:

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

Report an Error

Example Question #1 : How To Estimate

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

Possible Answers:

Correct answer:

Explanation:

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:

$8.19 \times 4.87 + 3.27 \times 7.42$

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

$=40 + 3 \times 7$

=40 + 21 = 61

Report an Error

Example Question #4 : How To Estimate

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.

Possible Answers:

104

106

544

504

Correct answer:

104

Explanation:

$8 \frac{2}{7} < 8\frac{1}{2}$ , 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:

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

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

$= 80 + 4 \times 6$

= 80 + 24 = 104

Report an Error

Example Question #2 : How To Estimate

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.

Possible Answers:

$\$ 1\textup{,}130$

$\$ 1\textup{,\textup{}}120$

$\$ 1\textup{,}110$

$\$ 1\textup{,}090$

$\$ 1\textup{,}100$

Correct answer:

$\$ 1\textup{,}100$

Explanation:

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:

190+220+170+100+190+230 = 1,100

Report an Error

Example Question #6 : How To Estimate

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

Possible Answers:

224

288

217

168

196

Correct answer:

224

Explanation:

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:

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

Report an Error

View SSAT- Upper Level Tutors

Brooke
Certified Tutor

New York University, Bachelor in Arts, Drama and Dance Teacher Education. Georgia State University, Master of Arts, Communica...

View SSAT- Upper Level Tutors

Carneta
Certified Tutor

Langston University, Bachelor in Arts, Theater Arts.

View SSAT- Upper Level Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Math Tutors in Philadelphia, Math Tutors in Boston, LSAT Tutors in Miami, Math Tutors in Seattle, Biology Tutors in New York City, Math Tutors in San Francisco-Bay Area, ISEE Tutors in Dallas Fort Worth, SAT Tutors in Miami, Algebra Tutors in Seattle, ISEE Tutors in Atlanta

Popular Courses & Classes

ACT Courses & Classes in Phoenix, GMAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in San Diego, MCAT Courses & Classes in Chicago, ACT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Atlanta, SAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Seattle, Spanish Courses & Classes in Atlanta

Popular Test Prep

SSAT Test Prep in Washington DC, GMAT Test Prep in Philadelphia, ACT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Chicago, GMAT Test Prep in Seattle, SAT Test Prep in Miami, GRE Test Prep in Washington DC, GRE Test Prep in Los Angeles, MCAT Test Prep in San Diego, ACT Test Prep in Phoenix

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

SSAT Upper Level Math : Number Concepts and Operations

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #4 : How To Divide Square Roots

Example Question #4 : How To Divide Square Roots

Example Question #1 : How To Estimate

Example Question #2 : How To Estimate

Example Question #1 : Estimation

Example Question #2 : How To Estimate

Example Question #1 : How To Estimate

Example Question #4 : How To Estimate

Example Question #2 : How To Estimate

Example Question #6 : How To Estimate

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: