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Number Sense
Lesson 1		 Number and Numeration
 Objectives/Vocab/Tips > Examples 1 | 2 | 3 | 4 > Practice: 1 | 2 | 3 | 4 > Reflection

ALPObjective:

Number and Numeration

In this lesson you will demonstrate your knowledge of place values in decimals, reducing fractions to lowest terms, compare integers or whole numbers, fractions, and decimals, and more on understanding numbers.

Vocabulary:

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  • Integer
  • Fraction
  • Equivalent Fractions
  • Denominator
  • Numerator
  • Least Common Multiple (Least Common Denominator)
  • Mixed Numbers
  • Improper Fraction
  • Place Value
  • Decimal

Tips to Remember:

  • Place Values of a number from the hundred millions place to the thousandths place.
    123, 456, 789.876

  • Converting improper fractions to a mixed number.
To convert 14/3 into a mixed number follow these steps:

Step 1: Divide the denominator into the numerator.

  • 14 divided by 3
  • We get 4 with a remainder of 2.

Step 2: Take the answer from dividing and present it as a mixed number.

  • 4 is the whole number
  • With our remainder of 2, we write this as a fraction keeping our denominator the same, 3, and place the remainder as the numerator. Our fraction of our mixed number is 2/3.
  • Together our mixed number is 4 2/3.
  • Converting a mixed number to an improper fraction.

To convert a mixed number, 5 3/7, to an improper fraction follow these steps:

Step 1: Multiply the denominator by the whole number in front of the fraction.

7 * 5 = 35

Step 2: To the above product, 35, add the numerator. This number is now the numerator of our improper fraction.

35 + 3 = 38

Step 3: The denominator is the same as the denominator in the original fraction, which is 7. So the final answer is:

38/7
  • Reducing fractions to lowest terms.

To reduce a fraction, 24/68, to lowest terms follow these steps:

Step 1: Find the greatest common factor, GCF, of the numerator and denominator.

  • 24 - 1, 2, 3, 4, 6, 8, 12, 24
  • 68 - 1, 2, 4, 17, 34, 68

    The greatest factor common to both is 4.

Step 2: Divide the greatest common factor into both the numerator and denominator.

  • 24 divided by 4 = 6
  • 68 divided by 4 = 17

Step 3: Our reduced fraction is 6/17. Since we divided by the greatest common factor of both numbers we know our fraction is reduced to the lowest possible terms. Just be sure to find the greatest common factor.
  • When comparing fractions, make sure that your fractions have like denominators.
For example: to compare 3/4 and 5/8 we need to make the fractions so that they have common denominators. So we find the common denominator to be 8 by finding the least common multiple (LCM) of 4 and 8. Our two fractions now become 6/8 and 5/8 stays the same. We can now see that 6/8 or 3/4 is larger than 5/8.
  • Comparing fractions with mixed numbers, you will want to be sure to make your mixed numbers improper fractions and then rewrite them with common denominators.

  • When comparing decimals, it may be helpful to add zeros at the end of the number so that each decimal has the same number of place values.
For example: to compare .508 and .58 you notice that the first decimal has three decimal places while the other has only two. If we add a 0 at the end of .58 so that it reads .580 we didn't change the value of our decimal, but made it easier to compare. You can now compare .508 and .580 with .580 being larger than .508.
  • When comparing a list of whole numbers, fractions, and decimals, you will need to rewrite each into a common form whether it is all whole numbers if possible, all fractions with common denominators, or all decimals.

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