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 #431 : Common Core Math: Grade 5

What is \displaystyle 28.278 in expanded form? 

 

 

Possible Answers:

\displaystyle 2\times10+8\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)

\displaystyle 2\times10+8\times100+2\times\left(\frac{1}{100}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)

\displaystyle 2\times10+8\times100+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)

\displaystyle 2\times1+8\times10+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)

\displaystyle 2\times10+8\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)

Correct answer:

\displaystyle 2\times10+8\times1+2\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\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 8 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 8\times1=8

\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

\displaystyle 8 is in the thousandths place, so we will multiply by \displaystyle \frac{1}{1000}.

\displaystyle 8\times\frac{1}{1000}=.008

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}20.000\\8.000\\ +\ .200\\ .070\\.008 \end{array}}{ \ \ \space28.278}

Example Question #432 : Common Core Math: Grade 5

What is \displaystyle 49.754 in expanded form? 

 

 

Possible Answers:

\displaystyle 4\times10+9\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{10000}\right)

\displaystyle 4\times10+9\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)

\displaystyle 4\times10+9\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)+4\times\left(\frac{1}{1000}\right)

\displaystyle 4\times10+9\times100+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)

\displaystyle 4\times1+9\times10+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)

Correct answer:

\displaystyle 4\times10+9\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\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 7 is in the tenths place, so we multiply by \displaystyle \frac{1}{10}

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

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

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

\displaystyle 4 is in the thousandths place, so we will multiply by \displaystyle \frac{1}{1000}.

\displaystyle 4\times\frac{1}{1000}=.004

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}40.000\\9.000\\ +\ .700\\ .050\\.004 \end{array}}{ \ \ \space49.754}

Example Question #81 : Whole And Part

What is \displaystyle 76.148 in expanded form? 

 

 

Possible Answers:

\displaystyle 7\times10+6\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)

\displaystyle 7\times10+6\times10+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)

\displaystyle 7\times10+6\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)

\displaystyle 7\times10+6\times1+10\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)

\displaystyle 7\times10+6\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)

Correct answer:

\displaystyle 7\times10+6\times1+1\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\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 6 is in the ones place, so we multiply by \displaystyle 1

\displaystyle 6\times1=6

\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

\displaystyle 8 is in the thousandths place, so we will multiply by \displaystyle \frac{1}{1000}.

\displaystyle 8\times\frac{1}{1000}=.008

Then we add the products together. 

\displaystyle \frac{\begin{array}[b]{r}70.000\\6.000\\ +\ .100\\ .040\\.008 \end{array}}{ \ \ \space76.148}

Example Question #81 : Whole And Part

What number is two hundred fifty-three and eighty-six hundredths?

Possible Answers:

\displaystyle 253.086

\displaystyle 253.86

\displaystyle 25\textup,384

\displaystyle 253.084

\displaystyle 25\textup,386

Correct answer:

\displaystyle 253.86

Explanation:

In number form, two hundred fifty-three and eighty-six hundredths is \displaystyle 253.86. The "and" signifies the decimal, and "hundredths" signifies the place value of the last decimal number. 

Example Question #82 : Whole And Part

What number is seven hundred forty-two and sixty-six hundredths?

 

Possible Answers:

\displaystyle 742.066

\displaystyle 7.4266

\displaystyle 742.66

\displaystyle 74\textup,266

\displaystyle 74.266

Correct answer:

\displaystyle 742.66

Explanation:

In number form, seven hundred forty-two and sixty-six hundredths is \displaystyle 742.66. The "and" signifies the decimal, and "hundredths" signifies the place value of the last decimal number. 

Example Question #83 : Whole And Part

What number is three hundred twenty-four and thirty-seven hundredths?

 

Possible Answers:

\displaystyle 32\textup,437

\displaystyle 324.37

\displaystyle 324.037

\displaystyle 3204.37

\displaystyle 32.437

Correct answer:

\displaystyle 324.37

Explanation:

In number form, three hundred twenty-four and thirty-seven hundredths is \displaystyle 324.37. The "and" signifies the decimal, and "hundredths" signifies the place value of the last decimal number. 

Example Question #84 : Whole And Part

What number is four hundred seventy-two and thirty-four hundredths?

 

Possible Answers:

\displaystyle 472.34

\displaystyle 472.034

\displaystyle 47.234

\displaystyle 4723.4

\displaystyle 47\textup,234

Correct answer:

\displaystyle 472.34

Explanation:

In number form, four hundred seventy-two and thirty-four hundredths is \displaystyle 472.34. The "and" signifies the decimal, and "hundredths" signifies the place value of the last decimal number. 

Example Question #85 : Whole And Part

What number is five hundred fifty-one and forty-two hundredths?

 

Possible Answers:

\displaystyle 5.5142

\displaystyle 55.142

\displaystyle 551.042

\displaystyle 551.42

\displaystyle 5514.2

Correct answer:

\displaystyle 551.42

Explanation:

In number form, five hundred fifty-one and forty-two hundredths is \displaystyle 551.42. The "and" signifies the decimal, and "hundredths" signifies the place value of the last decimal number. 

Example Question #86 : Whole And Part

What number is six hundred ninety-seven and eighty-six hundredths?

 

Possible Answers:

\displaystyle 6970.86

\displaystyle 6.9786

\displaystyle 697.86

\displaystyle 697.086

\displaystyle 69708.6

Correct answer:

\displaystyle 697.86

Explanation:

In number form, six hundred ninety-seven and eighty-six hundredths is \displaystyle 697.86. The "and" signifies the decimal, and "hundredths" signifies the place value of the last decimal number. 

Example Question #87 : Whole And Part

What number is seven hundred fifty-nine and seventeen hundredths?

 

Possible Answers:

\displaystyle 75.917

\displaystyle 75901.7

\displaystyle 759.017

\displaystyle 7591.7

\displaystyle 759.17

Correct answer:

\displaystyle 759.17

Explanation:

In number form, seven hundred fifty-nine and seventeen hundredths is \displaystyle 759.17. The "and" signifies the decimal, and "hundredths" signifies the place value of the last decimal number. 

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