SSAT Middle Level Math : How to find the whole from the part

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

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Example Questions

Example Question #7 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is \displaystyle 9.16 in expanded form? 

 

 

Possible Answers:

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

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

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

\displaystyle 9\times1+1\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)

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

Correct answer:

\displaystyle 9\times1+1\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 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 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. 

 

Example Question #8 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is \displaystyle 8.63 in expanded form? 

 

 

Possible Answers:

\displaystyle 8\times1+6\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{10}\right)

\displaystyle 8\times1+6\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{1000}\right)

\displaystyle 8\times1+6\times\left(\frac{1}{100}\right)+3\times\left(\frac{1}{100}\right)

\displaystyle 8\times1+6\times\left(\frac{1}{100}\right)+3\times\left(\frac{1}{10}\right)

\displaystyle 8\times1+6\times\left(\frac{1}{10}\right)+3\times\left(\frac{1}{100}\right)

Correct answer:

\displaystyle 8\times1+6\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 ones place, so we multiply by \displaystyle 1

\displaystyle 8\times1=8

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

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

\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}8.00\\ +\ .60\\ .03 \end{array}}{ \ \ \space8.63}

Example Question #10 : Read And Write Decimals To Thousandths Using Base Ten Numerals, Number Names, And Expanded Form: Ccss.Math.Content.5.Nbt.A.3a

What is \displaystyle 2.34 in expanded form? 

 

 

Possible Answers:

\displaystyle 2\times1+3\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{10}\right)

\displaystyle 2\times1+3\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)

\displaystyle 2\times1+3\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{100}\right)

\displaystyle 2\times1+3\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)

\displaystyle 2\times1+3\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{10}\right)

Correct answer:

\displaystyle 2\times1+3\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 2 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 2\times1=2

\displaystyle 3 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 3\times\frac{1}{10}=.3

\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}2.00\\ +\ .30\\ .04 \end{array}}{ \ \ \space2.34}

Example Question #211 : Numbers And Operations

What is \displaystyle 3.74 in expanded form? 

 

 

Possible Answers:

\displaystyle 3\times1+7\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{100}\right)

\displaystyle 3\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{10}\right)

\displaystyle 3\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)

\displaystyle 3\times1+7\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{10}\right)

\displaystyle 3\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)

Correct answer:

\displaystyle 3\times1+7\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 3 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 3\times1=3

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

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

\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}3.00\\ +\ .70\\ .04 \end{array}}{ \ \ \space3.74}

Example Question #212 : Numbers And Operations

What is \displaystyle 1.33 in expanded form? 

 

 

Possible Answers:

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

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

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

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

\displaystyle 1\times1+3\times\left(\frac{1}{100}\right)+3\times\left(\frac{1}{100}\right)

Correct answer:

\displaystyle 1\times1+3\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 1 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 1\times1=1

\displaystyle 3 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 3\times\frac{1}{10}=.3

\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}1.00\\ +\ .30\\ .03 \end{array}}{ \ \ \space1.33}

Example Question #213 : Numbers And Operations

What is \displaystyle 2.58 in expanded form? 

 

 

Possible Answers:

\displaystyle 2\times1+5\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)

\displaystyle 2\times1+5\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{1000}\right)

\displaystyle 2\times1+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10}\right)

\displaystyle 2\times1+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{100}\right)

\displaystyle 2\times1+5\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{10}\right)

Correct answer:

\displaystyle 2\times1+5\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 2 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 2\times1=2

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

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

\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}2.00\\ +\ .50\\ .08 \end{array}}{ \ \ \space2.58}

Example Question #21 : Whole And Part

What is \displaystyle 3.82 in expanded form? 

 

 

Possible Answers:

\displaystyle 3\times1+8\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{100}\right)

\displaystyle 3\times1+8\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{100}\right)

\displaystyle 3\times1+8\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{10}\right)

\displaystyle 3\times1+8\times\left(\frac{1}{10}\right)+2\times\left(\frac{1}{1000}\right)

\displaystyle 3\times1+8\times\left(\frac{1}{100}\right)+2\times\left(\frac{1}{10}\right)

Correct answer:

\displaystyle 3\times1+8\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 3 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 3\times1=3

\displaystyle 8 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

\displaystyle 8\times\frac{1}{10}=.8

\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}3.00\\ +\ .80\\ .02 \end{array}}{ \ \ \space3.82}

Example Question #22 : Whole And Part

What is \displaystyle 4.25 in expanded form? 

 

 

Possible Answers:

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

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

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

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

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

Correct answer:

\displaystyle 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 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}4.00\\ +\ .20\\ .05 \end{array}}{ \ \ \space4.25}

Example Question #23 : Whole And Part

What is \displaystyle 5.55 in expanded form? 

 

 

Possible Answers:

\displaystyle 5\times1+5\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{100}\right)

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

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

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

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

Correct answer:

\displaystyle 5\times1+5\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 5 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 5\times1=5

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

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}5.00\\ +\ .50\\ .05 \end{array}}{ \ \ \space5.55}

Example Question #24 : Whole And Part

What is \displaystyle 6.27 in expanded form? 

 

 

Possible Answers:

\displaystyle 6\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)

\displaystyle 6\times1+2\times\left(\frac{1}{100}\right)+7\times\left(\frac{1}{10}\right)

\displaystyle 6\times1+2\times\left(\frac{1}{100}\right)+7\times\left(\frac{1}{100}\right)

\displaystyle 6\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{10}\right)

\displaystyle 6\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)

Correct answer:

\displaystyle 6\times1+2\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 6 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 6\times1=6

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

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

\displaystyle 7 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}6.00\\ +\ .20\\ .07 \end{array}}{ \ \ \space6.27}

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