The Best Free 8th Grade Math Resources: Complete List! — Mashup Math - Free Printable

The image shows two 8th-grade math worksheets from the New York State Common Core Mathematics Curriculum. Below is an explanation of the tasks presented in the worksheets and how to solve them:

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Worksheet 1: Expressing Numbers

#### Problem Set 5-1
This worksheet focuses on expressing numbers in decimal form, writing values in words, and using place value charts.

#### Task 1: Express as Decimal Numerals
The task involves converting fractions or mixed numbers into decimal form.

Example Problem:
- Given: Four thousandths
- Solution:
Four thousandths means \( \frac{4}{1000} \).
Converting this to a decimal:
\( \frac{4}{1000} = 0.004 \)

Steps for Other Problems:
1. Twenty-four thousandths:
\( \frac{24}{1000} = 0.024 \)
2. One and three hundred twenty-four thousandths:
\( 1 + \frac{324}{1000} = 1.324 \)
3. Six hundred eight thousandths:
\( \frac{608}{1000} = 0.608 \)
4. Six hundred and eight thousandths:
\( 600 + \frac{8}{1000} = 600.008 \)
5. \( \frac{46}{1000} \):
\( 0.046 \)
6. \( 3 \frac{946}{1000} \):
\( 3 + \frac{946}{1000} = 3.946 \)
7. \( 200 \frac{904}{1000} \):
\( 200 + \frac{904}{1000} = 200.904 \)

#### Task 2: Express Each Value in Words
The task involves converting decimal numbers into their word forms.

Example Problem:
- Given: \( 0.005 \)
- Solution:
\( 0.005 \) is "five thousandths."

Steps for Other Problems:
1. \( 11.037 \):
Eleven and thirty-seven thousandths.
2. \( 403.608 \):
Four hundred three and six hundred eight thousandths.

#### Task 3: Write the Number on a Place Value Chart
The task involves breaking down a number into its place value components.

Example Problem:
- Given: \( 35.827 \)
- Solution:
- Tens: 3
- Ones: 5
- Tenths: 8
- Hundredths: 2
- Thousandths: 7

Expanded form:
\[ 35.827 = 3 \times 10 + 5 \times 1 + 8 \times \frac{1}{10} + 2 \times \frac{1}{100} + 7 \times \frac{1}{1000} \]

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Worksheet 2: Subtracting Fractions from a Whole Number

#### Lesson 5 Sprint 5-3
This worksheet focuses on subtracting fractions from whole numbers.

#### General Steps for Subtracting Fractions from Whole Numbers:
1. Convert the whole number into a fraction with the same denominator as the fraction being subtracted.
2. Perform the subtraction.

Example Problem:
- Given: \( 4 - \frac{1}{2} \)
- Solution:
Convert 4 into a fraction with a denominator of 2:
\( 4 = \frac{8}{2} \)
Now subtract:
\( \frac{8}{2} - \frac{1}{2} = \frac{7}{2} \)
Simplify if necessary (here, it is already simplified).

Steps for Other Problems:
1. \( 3 - \frac{1}{2} \):
\( 3 = \frac{6}{2} \)
\( \frac{6}{2} - \frac{1}{2} = \frac{5}{2} \)
2. \( 2 - \frac{1}{2} \):
\( 2 = \frac{4}{2} \)
\( \frac{4}{2} - \frac{1}{2} = \frac{3}{2} \)
3. \( 1 - \frac{1}{2} \):
\( 1 = \frac{2}{2} \)
\( \frac{2}{2} - \frac{1}{2} = \frac{1}{2} \)
4. \( 2 - \frac{1}{3} \):
\( 2 = \frac{6}{3} \)
\( \frac{6}{3} - \frac{1}{3} = \frac{5}{3} \)
5. \( 4 - \frac{1}{3} \):
\( 4 = \frac{12}{3} \)
\( \frac{12}{3} - \frac{1}{3} = \frac{11}{3} \)
6. \( 3 - \frac{2}{3} \):
\( 3 = \frac{9}{3} \)
\( \frac{9}{3} - \frac{2}{3} = \frac{7}{3} \)

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Summary of Solutions

1. Worksheet 1:
- Task 1: Convert fractions/mixed numbers to decimals.
- Task 2: Write decimal numbers in words.
- Task 3: Use place value charts and expanded forms.

2. Worksheet 2:
- Subtract fractions from whole numbers by converting the whole number to a fraction with the same denominator.

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Final Answer

\[
\boxed{\text{See detailed solutions above.}}
\]