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- Slide 1
- Rational Numbers ~ Comparing Rational Numbers Rational Numbers ~ Comparing Rational Numbers
- Slide 2
- Rational Numbers
- Slide 3
- RATIONAL NUMBERS? WHAT ARE THEY?
- Slide 4
- RATIONAL NUMBERS ARE NATURAL NUMBERS 1, 2, 3, 4, 5,... 1, 2, 3, 4, 5,... The use of three dots at the end of the list is a common mathematical notation to indicate that the list keeps going forever. The use of three dots at the end of the list is a common mathematical notation to indicate that the list keeps going forever.
- Slide 5
- RATIONAL NUMBERS WHOLE NUMBERS Natural Numbers together with zero Natural Numbers together with zero 0, 1, 2, 3, 4, 5,... 0, 1, 2, 3, 4, 5,... At some point, the idea of zero came to be considered as a number. If the farmer does not have any sheep, then the number of sheep that the farmer owns is zero. We call the set of natural numbers plus the number zero the whole numbers. At some point, the idea of zero came to be considered as a number. If the farmer does not have any sheep, then the number of sheep that the farmer owns is zero. We call the set of natural numbers plus the number zero the whole numbers.
- Slide 6
- RATIONAL NUMBERS ARE INTEGERS Whole numbers plus negatives Whole numbers plus negatives... 4, 3, 2, 1, 0, 1, 2, 3, 4,...... 4, 3, 2, 1, 0, 1, 2, 3, 4,...
- Slide 7
- RATIONAL NUMBERS ARE All numbers of the form a/b (a divided by b), where a and b are integers (but b is not equal to zero). All numbers of the form a/b (a divided by b), where a and b are integers (but b is not equal to zero). Rational numbers include what we usually call fractions. Rational numbers include what we usually call fractions. Notice that the word rational contains the word ratio, which should remind you of fractions. Notice that the word rational contains the word ratio, which should remind you of fractions.
- Slide 8
- THEN THERE ARE THE IRRATIONAL NUMBERS Irrational numbers cannot be expressed as a ratio of integers. Irrational numbers cannot be expressed as a ratio of integers. As decimals, Irrational Numbers never repeat or terminate. (Rational numbers always do one or the other.) As decimals, Irrational Numbers never repeat or terminate. (Rational numbers always do one or the other.)
- Slide 9
- Diagram: This diagram illustrates the relationships of the sets that make up the real numbers.
- Slide 10
- Lets be even more specific.
- Slide 11
- Rational Numbers are. Positive Positive numbers numbers greater than zero. 0123456
- Slide 12
- Negative Negative numbers numbers less than zero. 0123456-2-3-4-5-6 Rational Numbers are.
- Slide 13
- Opposite Opposite Numbers numbers that are the same distance from zero in the opposite direction 0123456-2-3-4-5-6 Rational Numbers are.
- Slide 14
- Integers Integers Integers are all the whole numbers and all of their opposites on the negative number line including zero. 7 opposite -7 Rational Numbers are.
- Slide 15
- Use a number line To compare integers, plot the points on the number line. The number farther to the right is the larger number Compare 1 and -3 ___________ *_______*_______________ -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 Since 1 is to the right of -3, 1 > -3or Since -3 is to the left of 1,-3 < 1
- Slide 16
- To order integers from least to greatest, draw a number line and plot the points. Order the integers -4, 7, 3, -2, and 1 from least to greatest. _________*____*_____*___*_________*_ -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 Order the integers by reading from left to right. -4, -2, 1, 3, 7
- Slide 17
- Identifying Positive and Negative Integers on a Number Line Numbers to the right are greater than zero. Numbers to the right are greater than zero. Numbers less than zero are to the left of zero. Numbers less than zero are to the left of zero. -5 is five points to the left of zero. -5 is five points to the left of zero. +9 is nine points to the right of zero. +9 is nine points to the right of zero.
- Slide 18
- Comparing and Ordering Integers Order from least to greatest: 4, -6, 2, 9 Order from least to greatest: 4, -6, 2, 9 -6, 2, 4, 9 -6, 2, 4, 9 Order from greatest to least: 5, -9, 9, -5 Order from greatest to least: 5, -9, 9, -5 9, 5, -5, -9 9, 5, -5, -9
- Slide 19
- Comparing Integers < is less than < is less than > is greater than > is greater than = has same value = has same value 6 8 - 4 7 10 5 -3 4 6 12 2 2 9 < < < > < < =