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Grade 8:  The Learning Equation Math

11.02 Compare and Order Numbers

Number Concepts

Refresher pp 4-5

Learning Outcomes:

The student will:

Review Rules for Ordering Integers

Directions Example(s)

3458 and 3472

If  both numbers are positive:

Line up the ones digit for the numbers.
Compare the place value for each digit starting from the left.  When you find the first difference, the number with the largest digit is the largest number.

 

3458
3472

The ones digits are lined up.  Starting from the left, the first difference is in the tens column.

Since 7 > 5, then 3472 > 3458

 

If one number is positive and the other is negative, then the positive number has the greatest value

34 > -3458

-3458 and -3472

If both numbers are negative:

Line up the ones digit for the numbers.
Compare the place value for each digit starting from the left.  When you find the first difference, the number with the largest digit is the smallest number.

-3458
-3472

The ones digits are lined up.  Starting from the left, the first difference is in the tens column.

Since -7 < -5, then -3472 < -3458

 

Fun with integers

Source:  http://cs.georgefox.edu/~ewheeler/310hw/1.20/

 

Review Rules for Ordering Decimals

Directions Example(s)
If  both numbers are positive:

3458.32 and 3458.318

Line up the ones digit for the numbers.   Add zeros if necessary to give both numbers the same number of decimal places.

Compare the place value for each digit starting from the left.  When you find the first difference, the number with the largest digit is the largest number.

 

3458.320
3458.318

The ones digits are lined up and there are the same number of decimal places.   Starting from the left, the first difference is in the tenths column.

Since 2 > 1, then 3458.320 > 3458.318

 If one number is positive and the other is negative, then the positive number has the greatest value

 

34.23 > -345.8

If  both numbers are negative:

-3458.32 and -3458.318

Line up the ones digit for the numbers.   Add zeros if necessary to give both numbers the same number of decimal places.
Compare the place value for each digit starting from the left.  When you find the first difference, the number with the largest digit is the smallest number.

-3458.320
-3458.318

The ones digits are lined up and there are the same number of decimal places.   Starting from the left, the first difference is in the tenths column.

Since -2 < -1, then -3458.320 < -3458.318

Comparing Decimals

 

Review Rules for Ordering Proper/Improper Fractions

Directions Example(s)
If both fractions are positive:

When proper/improper fractions have different numerators and denominators, they can be converted to equivalent fractions with the same denominators.

1/2 = 3/6     1/3 = 2/6

Since 3/6 > 2/6, then 1/2 > 1/3

If one fraction is positive and the other is negative, then the positive fraction has the largest value.

2/3 > -55/2

If both fractions are negative:

When proper/improper fractions have different numerators and denominators, they can be converted to equivalent fractions with the same denominators.

-1/2 = -3/6     -1/3 = -2/6

Since -3/6 < -2/6, then -1/2 < -1/3

Compare Fractions

Comparing Fractions

Integer Bars (Cusenaire Rods): Learning Fractions

Pattern Blocks: Exploring Fractions with Shapes

 

Review Rules for Ordering Mixed Number Fractions

Directions Example(s)
If both mixed numbers are positive:

When the whole numbers are different, you will not need to compare the fractions.

13 5/6 and 14 4/5

Line up the ones digit for the whole numbers.
Compare the place value for each digit starting from the left.  When you find the first difference, the number with the largest digit is the largest number.

When the whole numbers are the same, then the mixed number with the largest fraction has the greatest value.  Use the same rules as you did in:

 

13 5/6
14 4/5

The ones digits are lined up.  Starting from the left, the first difference is in the tens column.

Since 4 > 3, then 14 4/5 > 13 5/6

 

9/7 > 9/8
9/8 > 9/9
9/9 > 9/10

If one mixed number is positive and the other is negative, then the positive mixed number has the largest value.

 

1 2/3 > -23 4/5

If both mixed numbers are negative:

When the whole numbers are different, you will not need to compare the fractions.

-13 5/6 and -14 4/5

Line up the ones digit for the whole numbers.
Compare the place value for each digit starting from the left.  When you find the first difference, the number with the largest digit is the smallest number.

When the whole numbers are the same, then the mixed number with the largest fraction has the smallest value.  Use the same rules as you did in:

 
-13 5/6
-14 4/5

The ones digits are lined up.  Starting from the left, the first difference is in the tens column.

Since -4 < -3, then -14 4/5 < -13 5/6

 

-9/7 < -9/8
-9/8 < -9/9
-9/9 < -9/10

 

Fun with Fractions and Decimals

The following 100 square grid can be used to compare fractions and/or decimals.  Click on a square to shade/unshade it.

Sample: If 47/100 = 0.47 and 53/100 = .0.53  The shaded region will show 0.53 is bigger.

 

 

Review:

Fraction Inequalities - A+ Math

Whole Number Inequality Flashcards - A+ Math

 

Enrichment:

 

Key Terms:

natural number, whole number, least common denominator, integer

Wordsearch 1101-1105

Pre- requisite Skills:

Rules for Ordering Whole Numbers

Directions Example(s)
Whole numbers:

3458 and 3472

Line up the ones digit for the numbers.
Compare the place value for each digit starting from the left.  When you find the first difference, the number with the largest digit is the largest number.

 

3458
3472

The ones digits are lined up.  Starting from the left, the first difference is in the tens column.

Since 7 > 5, then 3472 > 3458

Comparing Whole Numbers

Compare It? - whole numbers

Inequality Flashcards

Fractions and Decimals Calculator

Conversion of Fractions:  Grade 7 Lesson 11.05 - improper fractions

Conversion of Fractions:  Grade 7 Lesson 11.05 - mixed numbers

Ordering Numbers:   Grade 7 Lesson 11.07

Decimal Conversions:   Grade 7 Lesson 11.06

Introduction to Integers:  Grade 7 Lesson 11.09

 

 

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