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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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Example Questions

Example Question #1522 : Common Core Math: Grade 5

How many $\textup{meters}$ are in $4\textup{ centimeters?}$

Possible Answers:

$4\textup{ meters}$

$40\textup{ meters}$

$.004\textup{ meters}$

$400\textup{ meters}$

$.04\textup{ meters}$

Correct answer:

$.04\textup{ meters}$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ and we can use as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{4\ centimeters}{x\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times x\ meters=.01\ meter\times 4\ centimeters$

$x\ meters=\frac{.01\ meter\times 4\ centimeters}{1\ centimeter}$

The centimeters will cancel and we are left with $.04\ meters$

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Example Question #31 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

How many $\textup{ meters}$ are in $7\textup{ centimeters?}$

Possible Answers:

$.07\textup{ meters}$

$.007\textup{ meters}$

$7\textup{ meters}$

$70\textup{ meters}$

$700\textup{ meters}$

Correct answer:

$.07\textup{ meters}$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ and we can use as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{7\ centimeters}{x\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times x\ meters=.01\ meter\times 7\ centimeters$

$x\ meters=\frac{.01\ meter\times 7\ centimeters}{1\ centimeter}$

The centimeters will cancel and we are left with $.07\ meters$

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Example Question #181 : Numbers And Operations

$\frac{C}{D} = \frac{11}{14}$

11D = ?

Possible Answers:

$\frac{14}{C}$

$\frac{C}{14}$

14C

C+ 14

Correct answer:

14C

Explanation:

The cross-products (the product of a numerator and the other denominator) of a proportion are equal, so, if

$\frac{C}{D} = \frac{11}{14}$ ,

it follows that

11D = 14C .

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Example Question #181 : Numbers And Operations

$\frac{F}{G} = \frac{17}{19}$

$\frac{F}{17} = ?$

Possible Answers:

19G

G + 19

$\frac{19}{G}$

$\frac{G}{19}$

Correct answer:

$\frac{G}{19}$

Explanation:

A property of proportions states that if two ratios are equivalent, then the ratio of numerators and the ratio of denominators are as well. Therefore, since

$\frac{F}{G} = \frac{17}{19}$ ,

it follows that

$\frac{F}{17} = \frac{G}{19}$

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Example Question #182 : Numbers And Operations

$\frac{A}{B} = \frac{7}{12}$

$\frac{B}{A} =?$

Possible Answers:

$\frac{12}{7}$

$\frac{7}{19}$

$\frac{5}{19}$

Correct answer:

$\frac{12}{7}$

Explanation:

A property of proportions states that if two ratios are equivalent, so are their reciprocals. Therefore, since

$\frac{A}{B} = \frac{7}{12}$ ,

it follows that

$\frac{B} {A}= \frac{12}{7}$ .

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Example Question #81 : Solve Problems Involving Measurement And Conversion Of Measurements

Hannah has a 4lb bag of peanuts that she is going to divide evenly between her four friends. How many ounces of peanuts does she give to each friend?

Possible Answers:

12oz

16oz

6oz

8oz

1oz

Correct answer:

16oz

Explanation:

The first thing we need to do is put our pounds into ounces because our final answer is asking for ounces. We know that 1lb=16oz . We can set up a proportion and cross multiply to solve.

$\frac{1lb}{16oz}=\frac{4lb}{x}$

1lb(x)=16oz(4lb)

Then we can divide to isolate the .

$\frac{1lb(x)}{1lb}=\frac{16oz(4lb)}{1lb}$

x=64oz

Now we need to divide our 64oz by because we are splitting the peanuts up equally between people.

$64oz\div4=16oz$

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Example Question #82 : Solve Problems Involving Measurement And Conversion Of Measurements

Molly has a 6lb bag of peanuts that she is going to divide evenly between her three friends. How many ounces of peanuts does she give to each friend?

Possible Answers:

2oz

24oz

32oz

23oz

Correct answer:

32oz

Explanation:

The first thing we need to do is put our pounds into ounces because our final answer is asking for ounces. We know that 1lb=16oz . We can set up a proportion and cross multiply to solve.

$\frac{1lb}{16oz}=\frac{6lb}{x}$

1lb(x)=16oz(6lb)

Then we can divide to isolate the .

$\frac{1lb(x)}{1lb}=\frac{16oz(6lb)}{1lb}$

x=96oz

Now we need to divide our 96oz by because we are splitting the peanuts up equally between people.

$96oz\div3=32oz$

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Example Question #31 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

How many $\textup yards$ are in $720\textup{ inches?}$

Possible Answers:

$18\textup { yards}$

$14\textup { yards}$

$16\textup { yards}$

$12\textup { yards}$

$20\textup { yards}$

Correct answer:

$20\textup { yards}$

Explanation:

To solve this problem we can make proportions.

We know that $1\ yard=36\ inches$ , and we can use as our unknown.

$\frac{1\ yard}{36\ inches}=\frac{x\ yards}{720\ inches}$

Next, we want to cross multiply and divide to isolate the on one side.

$36\ inches\times x\ yards= 1\ yard \times 720\ inches$

$20\ yards= \frac{1\ yard \times 720\ inches}{36\ inches}$

The $\yards$ $\ inches$ will cancel and we are left with $20\ yards$

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Example Question #32 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

How many $\textup{centimeters}$ are in $13\textup { meters?}$

Possible Answers:

$.0013\textup { centimeters}$

$1\textup,300\textup { centimeters}$

$13\textup,000\textup { centimeters}$

$1.3\textup{ centimeters}$

$130\textup { centimeters}$

Correct answer:

$1\textup,300\textup { centimeters}$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ and we can use as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{13\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 13\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 13\ meters}{.01\ meter}= x\ centimeters$

The meters will cancel and we are left with $1,300\ centimeters$

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Example Question #63 : How To Find A Proportion

$\frac{A}{B} = \frac{9}{7}$

$\frac{A +B}{B} = ?$

Possible Answers:

$\frac{9}{16}$

$\frac{7}{16}$

$\frac{16}{9}$

$\frac{16}{7}$

Correct answer:

$\frac{16}{7}$

Explanation:

By a proportion property, if $\frac{A}{B} = \frac{C}{D}$ , it follows that $\frac{A+B}{B} = \frac{C+ D}{D}$ .

Setting C= 9, D = 7 ,

if $\frac{A}{B} = \frac{9}{7}$ , then $\frac{A +B}{B} = \frac{9+7 }{7} = \frac{16}{7}$ .

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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 #1522 : Common Core Math: Grade 5

Example Question #31 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

Example Question #181 : Numbers And Operations

Example Question #181 : Numbers And Operations

Example Question #182 : Numbers And Operations

Example Question #81 : Solve Problems Involving Measurement And Conversion Of Measurements

Example Question #82 : Solve Problems Involving Measurement And Conversion Of Measurements

Example Question #31 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

Example Question #32 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

Example Question #63 : How To Find A Proportion

All SSAT Middle Level Math Resources

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