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SSAT Middle Level Math : Numbers and Operations

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

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All SSAT Middle Level Math Resources

10 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #9 : Grade 6

If candidate A receives votes for every votes that candidate B receives. At the end of the election candidate B has votes. How many votes did candidate A get?

Possible Answers:

$66\tfrac{1}{2}$

125

Correct answer:

$66\tfrac{1}{2}$

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every votes cast for candidate A, candidate B got votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$7:4\rightarrow \frac{7}{4}$

We know that candidate B received votes. Write a new ratio.

$A:38\rightarrow\frac{A}{38}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{7}{4}=\frac{A}{38}$

Cross multiply and solve for .

4(A)=38(7)

Simplify.

4A=266

Divide both sides of the equation by .

$\frac{4A}{4}=\frac{266}{4}$

Solve.

$A=66\tfrac{1}{2}$

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Example Question #4 : Grade 6

If candidate A receives votes for every votes that candidate B receives. At the end of the election candidate B has votes. How many votes did candidate A get?

Possible Answers:

129

219

169

$162\tfrac{5}{9}$

216

Correct answer:

$162\tfrac{5}{9}$

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every votes cast for candidate A, candidate B got votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$19:9\rightarrow \frac{19}{9}$

We know that candidate B received votes. Write a new ratio.

$A:77\rightarrow\frac{A}{77}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{19}{9}=\frac{A}{77}$

Cross multiply and solve for .

9(A)=77(19)

Simplify.

9A=1463

Divide both sides of the equation by .

$\frac{9A}{9}=\frac{1463}{9}$

Solve.

$A=162\tfrac{5}{9}$

Report an Error

Example Question #5 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

A motorcycle travels $60\textup{ miles}$ in $1\textup{ hour}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$20\textup{ mph}$

$120\textup{ mph}$

$60\textup{ mph}$

$30\textup{ mph}$

$25\textup{ mph}$

Correct answer:

$60\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$60\ miles: 1\ hour=\frac{60\ miles}{1\ hour}$

Reduce and solve.

60mph

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Example Question #6 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

A motorcycle travels $723\textup{ miles}$ in $3\textup{ hours}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$241\textup{ mph}$

$421\textup{ mph}$

$142\textup{ mph}$

$211\textup{ mph}$

$124\textup{ mph}$

Correct answer:

$241\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$723\ miles: 3\ hours=\frac{723\ miles}{3\ hours}$

Reduce and solve.

241mph

Report an Error

Example Question #32 : Numbers And Operations

A motorcycle travels $750\textup{ miles}$ in $10\textup{ hours}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$60\textup{ mph}$

$100\textup{ mph}$

$75\textup{ mph}$

$750\textup{ mph}$

$57\textup{ mph}$

Correct answer:

$75\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$750\ miles: 10\ hours=\frac{750\ miles}{10\ hours}$

Reduce and solve.

75mph

Report an Error

Example Question #7 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

A motorcycle travels $3828\textup{ miles}$ in $58\textup{ hours}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$55\textup{ mph}$

$72\textup{ mph}$

$76\textup{ mph}$

$68\textup{ mph}$

$66\textup{ mph}$

Correct answer:

$66\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$3828\ miles: 58\ hours=\frac{3828\ miles}{58\ hours}$

Reduce and solve.

66mph

Report an Error

Example Question #31 : Numbers And Operations

A motorcycle travels $567\textup{ miles}$ in $9\textup{ hours}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$36\textup{ mph}$

$72\textup{ mph}$

$69\textup{ mph}$

$63\textup{ mph}$

$66\textup{ mph}$

Correct answer:

$63\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$567\ miles: 9\ hours=\frac{567\ miles}{9\ hours}$

Reduce and solve.

63mph

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Example Question #32 : Numbers And Operations

A motorcycle travels $1296\textup{ miles}$ in $18\textup{ hours}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$75\textup{ mph}$

$66\textup{ mph}$

$80\textup{ mph}$

$72\textup{ mph}$

$77\textup{ mph}$

Correct answer:

$72\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$1296\ miles: 18\ hours=\frac{1296\ miles}{18\ hours}$

Reduce and solve.

72mph

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Example Question #35 : Numbers And Operations

A motorcycle travels $195\ miles$ in $5\ hours$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

35mph

39mph

24mph

43mph

42mph

Correct answer:

39mph

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$195\ miles: 5\ hours=\frac{195\ miles}{5\ hours}$

Reduce and solve.

39mph

Report an Error

Example Question #1 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

A motorcycle travels $2035\ miles$ in $37\ hours$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

47mph

57mph

53mph

45mph

55mph

Correct answer:

55mph

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$2035\ miles: 37\ hours=\frac{2035\ miles}{37\ hours}$

Reduce and solve.

55mph

Report an Error

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All SSAT Middle Level Math Resources

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SSAT Middle Level Math : Numbers and Operations

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #9 : Grade 6

Example Question #4 : Grade 6

Example Question #5 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

Example Question #6 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

Example Question #32 : Numbers And Operations

Example Question #7 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

Example Question #31 : Numbers And Operations

Example Question #32 : Numbers And Operations

Example Question #35 : Numbers And Operations

Example Question #1 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

All SSAT Middle Level Math Resources

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