SSAT Middle Level Math : Numbers and Operations

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

varsity tutors app store varsity tutors android store

Example Questions

Example Question #37 : Whole And Part

What is \displaystyle 79.25 in expanded form? 

 

 

Possible Answers:

\displaystyle 7\times10+9\times1+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{1000}\right)

\displaystyle 7\times10+9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

\displaystyle 7\times100+9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

\displaystyle 7\times10+9\times10+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

\displaystyle 7\times100+9\times10+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

Correct answer:

\displaystyle 7\times10+9\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

Explanation:

When we write a number in expanded form, we multiply each digit by its place value. 

\displaystyle 7 is in the tens place, so we multiply by \displaystyle 10.

\displaystyle 7\times10=70

 

\displaystyle 9 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 9\times1=9

\displaystyle 2 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 2\times\frac{1}{10}=.2

\displaystyle 5 is in the hundredths place, so we multiply by \displaystyle \frac{1}{100}.

\displaystyle 5\times\frac{1}{100}=.05

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}70.00\\9.00\\ +\ .20\\ .05 \end{array}}{ \ \ \space79.25}

Example Question #31 : How To Find The Whole From The Part

What is \displaystyle 36.73 in expanded form? 

 

 

Possible Answers:

\displaystyle 3\times100+6\times10+7\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)

\displaystyle 3\times10+6\times1+7\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)

\displaystyle 3\times100+6\times1+7\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{10}\right)

\displaystyle 3\times10+6\times1+7\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{10}\right)

\displaystyle 3\times10+6\times10+7\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)

Correct answer:

\displaystyle 3\times10+6\times1+7\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)

Explanation:

When we write a number in expanded form, we multiply each digit by its place value. 

\displaystyle 3 is in the tens place, so we multiply by \displaystyle 10.

\displaystyle 3\times10=30

 

\displaystyle 6 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 6\times1=6

\displaystyle 7 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 7\times\frac{1}{10}=.7

\displaystyle 3 is in the hundredths place, so we multiply by \displaystyle \frac{1}{100}.

\displaystyle 3\times\frac{1}{100}=.03

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}30.00\\6.00\\ +\ .70\\ .03 \end{array}}{ \ \ \space36.73}

Example Question #202 : Number & Operations In Base Ten

What is \displaystyle 49.28 in expanded form? 

 

 

Possible Answers:

\displaystyle 4\times10+9\times1+2\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{100}\right)

\displaystyle 4\times10+9\times10+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)

\displaystyle 4\times10+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{10}\right)

\displaystyle 4\times100+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)

\displaystyle 4\times10+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)

Correct answer:

\displaystyle 4\times10+9\times1+2\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)

Explanation:

When we write a number in expanded form, we multiply each digit by its place value. 

\displaystyle 4 is in the tens place, so we multiply by \displaystyle 10.

\displaystyle 4\times10=40

 

\displaystyle 9 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 9\times1=9

\displaystyle 2 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 2\times\frac{1}{10}=.2

\displaystyle 8 is in the hundredths place, so we multiply by \displaystyle \frac{1}{100}.

\displaystyle 8\times\frac{1}{100}=.08

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}40.00\\9.00\\ +\ .20\\ .08 \end{array}}{ \ \ \space49.28}

Example Question #211 : Number & Operations In Base Ten

What is \displaystyle 53.26 in expanded form? 

 

 

Possible Answers:

\displaystyle 5\times100+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)

\displaystyle 5\times10+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{10}\right)

\displaystyle 5\times1+3\times10+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)

\displaystyle 5\times10+3\times1+2\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{100}\right)

\displaystyle 5\times10+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)

Correct answer:

\displaystyle 5\times10+3\times1+2\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{100}\right)

Explanation:

When we write a number in expanded form, we multiply each digit by its place value. 

\displaystyle 5 is in the tens place, so we multiply by \displaystyle 10.

\displaystyle 5\times10=50

 

\displaystyle 3 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 3\times1=3

\displaystyle 2 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 2\times\frac{1}{10}=.2

\displaystyle 6 is in the hundredths place, so we multiply by \displaystyle \frac{1}{100}.

\displaystyle 6\times\frac{1}{100}=.06

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}50.00\\3.00\\ +\ .20\\ .06 \end{array}}{ \ \ \space53.26}

Example Question #41 : Whole And Part

What is \displaystyle 69.62 in expanded form? 

 

 

Possible Answers:

\displaystyle 6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{10}\right)

\displaystyle 6\times10+9\times10+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)

\displaystyle 6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)

\displaystyle 6\times100+9\times10+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)

\displaystyle 6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{1000}\right)

Correct answer:

\displaystyle 6\times10+9\times1+6\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)

Explanation:

When we write a number in expanded form, we multiply each digit by its place value. 

\displaystyle 6 is in the tens place, so we multiply by \displaystyle 10.

\displaystyle 6\times10=60

 

\displaystyle 9 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 9\times1=9

\displaystyle 6 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 6\times\frac{1}{10}=.6

\displaystyle 2 is in the hundredths place, so we multiply by \displaystyle \frac{1}{100}.

\displaystyle 2\times\frac{1}{100}=.02

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}60.00\\9.00\\ +\ .60\\ .02 \end{array}}{ \ \ \space69.62}

Example Question #41 : Whole And Part

What is \displaystyle 79.14 in expanded form? 

 

 

Possible Answers:

\displaystyle 7\times10+9\times10+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)

\displaystyle 7\times10+9\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)

\displaystyle 7\times10+9\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)

\displaystyle 7\times100+9\times10+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)

\displaystyle 7\times10+9\times1+1\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{100}\right)

Correct answer:

\displaystyle 7\times10+9\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)

Explanation:

When we write a number in expanded form, we multiply each digit by its place value. 

\displaystyle 7 is in the tens place, so we multiply by \displaystyle 10.

\displaystyle 7\times10=70

 

\displaystyle 9 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 9\times1=9

\displaystyle 1 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 1\times\frac{1}{10}=.1

\displaystyle 4 is in the hundredths place, so we multiply by \displaystyle \frac{1}{100}.

\displaystyle 4\times\frac{1}{100}=.04

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}70.00\\9.00\\ +\ .10\\ .04 \end{array}}{ \ \ \space79.14}

Example Question #43 : How To Find The Whole From The Part

What is \displaystyle 87.53 in expanded form? 

 

 

Possible Answers:

\displaystyle 8\times100+7\times1+5\times\left(\frac{1}{100}\right)+3\times\left(\frac{1}{100}\right)

\displaystyle 8\times10+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{10}\right)

\displaystyle 8\times10+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)

\displaystyle 8\times10+7\times10+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)

\displaystyle 8\times100+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{1000}\right)

Correct answer:

\displaystyle 8\times10+7\times1+5\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)

Explanation:

When we write a number in expanded form, we multiply each digit by its place value. 

\displaystyle 8 is in the tens place, so we multiply by \displaystyle 10.

\displaystyle 8\times10=80

 

\displaystyle 7 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 7\times1=7

\displaystyle 5 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 5\times\frac{1}{10}=.5

\displaystyle 3 is in the hundredths place, so we multiply by \displaystyle \frac{1}{100}.

\displaystyle 3\times\frac{1}{100}=.03

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}80.00\\7.00\\ +\ .50\\ .03 \end{array}}{ \ \ \space87.53}

Example Question #44 : How To Find The Whole From The Part

What is \displaystyle 94.25 in expanded form? 

 

 

Possible Answers:

\displaystyle 9\times10+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{10}\right)

\displaystyle 9\times100+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)

\displaystyle 9\times100+4\times10+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{10}\right)

\displaystyle 9\times100+4\times10+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

\displaystyle 9\times10+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

Correct answer:

\displaystyle 9\times10+4\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

Explanation:

When we write a number in expanded form, we multiply each digit by its place value. 

\displaystyle 9 is in the tens place, so we multiply by \displaystyle 10.

\displaystyle 9\times10=90

 

\displaystyle 4 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 4\times1=4

\displaystyle 2 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 2\times\frac{1}{10}=.2

\displaystyle 5 is in the hundredths place, so we multiply by \displaystyle \frac{1}{100}.

\displaystyle 5\times\frac{1}{100}=.05

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}90.00\\4.00\\ +\ .20\\ .05 \end{array}}{ \ \ \space94.25}

Example Question #45 : How To Find The Whole From The Part

What is \displaystyle 23.65 in expanded form? 

 

 

Possible Answers:

\displaystyle 2\times10+3\times1+6\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

\displaystyle 2\times100+3\times1+6\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

\displaystyle 2\times1+3\times10+6\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

\displaystyle 2\times10+3\times1+6\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)

\displaystyle 2\times10+3\times1+6\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{1000}\right)

Correct answer:

\displaystyle 2\times10+3\times1+6\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)

Explanation:

When we write a number in expanded form, we multiply each digit by its place value. 

\displaystyle 2 is in the tens place, so we multiply by \displaystyle 10.

\displaystyle 2\times10=20

 

\displaystyle 3 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 3\times1=3

\displaystyle 6 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 6\times\frac{1}{10}=.6

\displaystyle 5 is in the hundredths place, so we multiply by \displaystyle \frac{1}{100}.

\displaystyle 5\times\frac{1}{100}=.05

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}20.00\\3.00\\ +\ .60\\ .05 \end{array}}{ \ \ \space23.65}

Example Question #46 : How To Find The Whole From The Part

What is \displaystyle 14.57 in expanded form? 

 

 

Possible Answers:

\displaystyle 1\times10+4\times10+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)

\displaystyle 1\times100+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)

\displaystyle 1\times10+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{10}\right)

\displaystyle 1\times10+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)

\displaystyle 1\times10+4\times10+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)

Correct answer:

\displaystyle 1\times10+4\times1+5\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)

Explanation:

When we write a number in expanded form, we multiply each digit by its place value. 

\displaystyle 1 is in the tens place, so we multiply by \displaystyle 10.

\displaystyle 1\times10=10

 

\displaystyle 4 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 4\times1=4

\displaystyle 5 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 5\times\frac{1}{10}=.5

\displaystyle 5 is in the hundredths place, so we multiply by \displaystyle \frac{1}{100}.

\displaystyle 7\times\frac{1}{100}=.07

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}10.00\\4.00\\ +\ .50\\ .07 \end{array}}{ \ \ \space14.57}

Learning Tools by Varsity Tutors