You would want to put numbers in order when
- comparing grades
- placing events in date order
- comparing the cost of two or more objects
How do we actually compare two numbers to each other? Line up the numbers being compared. Then compare the place value for each digit starting from the left. Find the first difference. The number with the largest digit is the largest number.
Example: Order the numbers:
9,568
9,471
9,568
9,471
The hundreds digit is the first difference. Since 5 is larger than 4, the number 9,568 is larger than the number 9,471
Ordering decimal Numbers
Align the ones digit for the numbers. Compare the place value for each digit starting from the left. Find the difference, the number with the largest digits is the largest number.
Example:
Which of the following numbers is larger?
357,2153 and 357.241
357.2153
357.241
The hundredths digit is the first difference. Since 4 is larger than 1, the number 357.241 is larger than 357.2153.
Order Fractions with a Common Denominator.
When the denominators are the same, then the proper/improper fraction with the largest numerator is the largest fraction.
Example:
Order the numbers 7/13 and 11/13.
The fractions have a common denominator of 13. Thus, compare the numerators. Since 7<11,
7/13 <>
Ordering Fractions with Different Denominators
When the denominators are different rewrite the fractions using a common denominator. The proper/improper fraction with the largest numerator with the largest numerator is the largest fraction.
Example:
Order the numbers 3/5 and 4/9.
The fractions have different denominators. Since 45 is the least common multiple of 5 and 9, rewrite the fractions using a denominator of 45.
3/5=27/45
4/9 = 20/45
Now that the fractions are written with a common denominator, compare the numerators. SInce 27>20
3/5 = 27/45 > 20/45 = 4/9
Alternatively, when the fractions have different denominators, find the equivalent of each fraction by dividing the numerator by the denominator, compare the equivalents
