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Common Core: 5th Grade Math : Common Core Math: Grade 5

Study concepts, example questions & explanations for Common Core: 5th Grade Math

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All Common Core: 5th Grade Math Resources

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

Example Questions

Example Question #67 : Whole And Part

What is 87.376 in expanded form?

Possible Answers:

$8\times1+7\times100+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$

$8\times10+7\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$

$8\times10+7\times100+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$

$8\times10+7\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{1000}\right)+6\times\left(\frac{1}{1000}\right)$

$8\times10+7\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{10}\right)+6\times\left(\frac{1}{1000}\right)$

Correct answer:

$8\times10+7\times1+3\times\left(\frac{1}{10}\right)+7\times\left(\frac{1}{100}\right)+6\times\left(\frac{1}{1000}\right)$

Explanation:

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

is in the tens place, so we multiply by .

$8\times10=80$

is in the ones place, so we multiply by .

$7\times1=7$

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

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

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

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

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

$6\times\frac{1}{1000}=.006$

Then we add the products together.

$\frac{\begin{array}[b]{r}80.000\\7.000\\ +\ .300\\ .070\\.006 \end{array}}{ \ \ \space87.376}$

Report an Error

Example Question #68 : Whole And Part

What is 94.218 in expanded form?

Possible Answers:

$9\times10+4\times100+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)$

$9\times10+4\times1+2\times\left(\frac{1}{100}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$9\times10+4\times100+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$9\times10+4\times1+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$

$9\times10+4\times1+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Correct answer:

$9\times10+4\times1+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Explanation:

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

is in the tens place, so we multiply by .

$9\times10=90$

is in the ones place, so we multiply by .

$4\times1=4$

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

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

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

$1\times\frac{1}{100}=.01$

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

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

Then we add the products together.

$\frac{\begin{array}[b]{r}90.000\\4.000\\ +\ .200\\ .010\\.008 \end{array}}{ \ \ \space94.218}$

Report an Error

Example Question #62 : How To Find The Whole From The Part

What is 67.458 in expanded form?

Possible Answers:

$6\times10+7\times100+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$6\times10+7\times1+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)$

$6\times10+7\times1+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$6\times10+7\times100+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)$

$6\times1+7\times10+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Correct answer:

$6\times10+7\times1+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Explanation:

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

is in the tens place, so we multiply by .

$6\times10=60$

is in the ones place, so we multiply by .

$7\times1=7$

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

$4\times\frac{1}{10}=.4$

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

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

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

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

Then we add the products together.

$\frac{\begin{array}[b]{r}60.000\\7.000\\ +\ .400\\ .050\\.008 \end{array}}{ \ \ \space67.458}$

Report an Error

Example Question #422 : Common Core Math: Grade 5

What is 73.254 in expanded form?

Possible Answers:

$7\times10+3\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)+4\times\left(\frac{1}{1000}\right)$

$7\times1+3\times100+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$7\times10+3\times100+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$7\times10+3\times1+2\times\left(\frac{1}{100}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$7\times10+3\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

Correct answer:

$7\times10+3\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

Explanation:

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

is in the tens place, so we multiply by .

$7\times10=70$

is in the ones place, so we multiply by .

$3\times1=3$

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

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

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

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

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

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

Then we add the products together.

$\frac{\begin{array}[b]{r}70.000\\3.000\\ +\ .200\\ .050\\.004 \end{array}}{ \ \ \space73.254}$

Report an Error

Example Question #241 : Number & Operations In Base Ten

What is 58.458 in expanded form?

Possible Answers:

$5\times1+8\times10+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$

$5\times1+8\times10+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)$

$5\times10+8\times1+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$5\times1+8\times100+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$5\times1+8\times10+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Correct answer:

$5\times10+8\times1+4\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Explanation:

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

is in the tens place, so we multiply by .

$5\times10=50$

is in the ones place, so we multiply by .

$8\times1=8$

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

$4\times\frac{1}{10}=.4$

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

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

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

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

Then we add the products together.

$\frac{\begin{array}[b]{r}50.000\\8.000\\ +\ .400\\ .050\\.008 \end{array}}{ \ \ \space58.458}$

Report an Error

Example Question #71 : Whole And Part

What is 12.258 in expanded form?

Possible Answers:

$1\times10+2\times100+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$

$1\times10+2\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)$

$1\times10+2\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{1000}\right)$

$1\times10+2\times100+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$1\times10+2\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Correct answer:

$1\times10+2\times1+2\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Explanation:

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

is in the tens place, so we multiply by .

$1\times10=10$

is in the ones place, so we multiply by .

$2\times1=2$

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

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

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

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

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

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

Then we add the products together.

$\frac{\begin{array}[b]{r}10.000\\2.000\\ +\ .200\\ .050\\.008 \end{array}}{ \ \ \space12.258}$

Report an Error

Example Question #72 : Whole And Part

What is 29.748 in expanded form?

Possible Answers:

$2\times10+9\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{1000}\right)$

$2\times10+9\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)$

$2\times1+9\times10+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$2\times10+9\times100+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$2\times10+9\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Correct answer:

$2\times10+9\times1+7\times\left(\frac{1}{10}\right)+4\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Explanation:

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

is in the tens place, so we multiply by .

$2\times10=20$

is in the ones place, so we multiply by .

$9\times1=9$

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

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

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

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

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

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

Then we add the products together.

$\frac{\begin{array}[b]{r}20.000\\9.000\\ +\ .700\\ .040\\.008 \end{array}}{ \ \ \space29.748}$

Report an Error

Example Question #71 : Whole And Part

What is 31.784 in expanded form?

Possible Answers:

$3\times10+1\times1+7\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{10000}\right)$

$3\times10+1\times1+7\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$3\times10+1\times100+7\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$3\times10+1\times1+7\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

$3\times1+1\times10+7\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

Correct answer:

$3\times10+1\times1+7\times\left(\frac{1}{10}\right)+8\times\left(\frac{1}{100}\right)+4\times\left(\frac{1}{1000}\right)$

Explanation:

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

is in the tens place, so we multiply by .

$3\times10=30$

is in the ones place, so we multiply by .

$1\times1=1$

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

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

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

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

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

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

Then we add the products together.

$\frac{\begin{array}[b]{r}30.000\\1.000\\ +\ .700\\ .080\\.004 \end{array}}{ \ \ \space31.784}$

Report an Error

Example Question #74 : Whole And Part

What is 45.218 in expanded form?

$4\times10+5\times1+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Possible Answers:

$4\times1+5\times10+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$4\times1+5\times10+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$

$4\times10+5\times1+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$4\times10+5\times100+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$4\times10+5\times1+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$

Correct answer:

$4\times10+5\times1+2\times\left(\frac{1}{10}\right)+1\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Explanation:

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

is in the tens place, so we multiply by .

$4\times10=40$

is in the ones place, so we multiply by .

$5\times1=5$

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

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

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

$1\times\frac{1}{100}=.01$

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

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

Then we add the products together.

$\frac{\begin{array}[b]{r}40.000\\5.000\\ +\ .200\\ .010\\.008 \end{array}}{ \ \ \space45.218}$

Report an Error

Example Question #75 : Whole And Part

What is 54.758 in expanded form?

Possible Answers:

$5\times10+4\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$

$5\times10+4\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{10000}\right)$

$5\times1+4\times10+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{1000}\right)+8\times\left(\frac{1}{1000}\right)$

$5\times1+4\times10+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

$5\times10+4\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Correct answer:

$5\times10+4\times1+7\times\left(\frac{1}{10}\right)+5\times\left(\frac{1}{100}\right)+8\times\left(\frac{1}{1000}\right)$

Explanation:

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

is in the tens place, so we multiply by .

$5\times10=50$

is in the ones place, so we multiply by .

$4\times1=4$

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

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

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

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

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

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

Then we add the products together.

$\frac{\begin{array}[b]{r}50.000\\4.000\\ +\ .700\\ .050\\.008 \end{array}}{ \ \ \space54.758}$

Report an Error

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Common Core: 5th Grade Math : Common Core Math: Grade 5

Study concepts, example questions & explanations for Common Core: 5th Grade Math

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #67 : Whole And Part

Example Question #68 : Whole And Part

Example Question #62 : How To Find The Whole From The Part

Example Question #422 : Common Core Math: Grade 5

Example Question #241 : Number & Operations In Base Ten

Example Question #71 : Whole And Part

Example Question #72 : Whole And Part

Example Question #71 : Whole And Part

Example Question #74 : Whole And Part

Example Question #75 : Whole And Part

All Common Core: 5th Grade Math Resources

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