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Example |
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Problem |
Which number is greater, `8` or `14`? |
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`14` is to the right of `8`, so `14` is greater than `8`.
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Answer |
`14` is greater than `8`. |
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Comparing Whole Numbers
There will be times when it’s helpful to compare two numbers and determine which number is greater, and which one is less. This is a useful way to compare quantities such as travel time, income, or expenses. The symbols `<` and `>` are used to indicate which number is greater, and which is less than the other.
When comparing the values of two numbers, you can use a number line to determine which number is greater. The number on the right is always greater than the number on the left. In the example below, you can tell that `14` is greater than `8` because `14` is to the right of `8` on the number line.
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Example |
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Problem |
Which number is greater, `8` or `14`? |
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`14` is to the right of `8`, so `14` is greater than `8`.
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Answer |
`14` is greater than `8`. |
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In the example below, you can determine which number is greater by comparing the digits in the ones place value.
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Example |
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Problem |
Which number is greater, `33` or `38`? |
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In both `33` and `38`, the digit in the tens place is `3`.
Because they have the same number in the tens place, you can determine which one is greater by comparing the digits in the ones place.
In the number `38`, the digit in the ones place is `8`.
In the number `33`, the digit in the ones place is `3`.
Because `8` is greater than `3`, `38` is greater than `33`.
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Answer |
`38` is greater than `33`. This answer was obtained from comparing their digits in the ones place value, which are `8` and `3`, respectively. |
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Which number is greater, `17` or `11`?
A) `17`
B) `11`
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If one number is significantly greater than another number, it may be difficult to compare the numbers effectively with a number line. In general, whole numbersAny of the numbers `0`, `1`, `2`, `3`, and so on. with more digits are greater than whole numbers with fewer digits. For example, `542` is greater than `84` because `542` has the digit `5` in the hundreds place. There are no hundreds in `84`.
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Which number is greater, `71` or `710`?
A) `71`
B) `710`
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An inequalityA mathematical sentence that compares two numbers that are not equal. is a mathematical sentence that compares two numbers that aren’t equal. Instead of an equal sign (`=`), inequalities use greater than (`>`) or less than (`<`) symbols. The important thing to remember about these symbols is that the small end points towards the lesser number, and the larger (open) end is always on the side of the greater number.
There are other ways to remember this. For example, the wider part of the symbol represents the jaws of an alligator, which “gobbles up” the greater number. So “`35` is greater than `28`” can be written as `35>28`, and “`52` is less than `109`” can be written as `52<109`.
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Example |
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Problem
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Replace the question mark with `<` or `>` to make a true sentence: `180` `?` `220`. |
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`180` is to the left of `220`, so `180<220`. The symbol points at `180`, which is the lesser number. |
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Answer |
`180<220` |
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Which expression correctly compares the numbers `85` and `19`?
A) `85<19`
B) `19 = 85`
C) `85>19`
D) `19>85`
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Many times, an answer needs to be a range of values rather than just a single value. For example, you want to make more than `$22` an hour. This can be expressed as all numbers greater than `22`. See the example below.
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Example |
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Problem
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`?>22`. What whole number(s) will make this statement true? |
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The symbol points at `22`, so the numbers you want to replace the question mark with are greater than `22`. There are many numbers that work.
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Answer |
`23, 24, 25, 26`, and any additional whole numbers that are greater than `26` make this statement true. |
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A farmer has produced `230` pumpkins for the autumn harvest. Last year, he produced `198`. Write an expression that compares these two numbers.
A) `230>198`
B) `230<198`
C) `198 = 230`
D) `198>230`
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To compare two values that are not the same, you can write an inequality. You can use a number line or place value to determine which number is greater than another number. Inequalities can be expressed using greater than (`>`) or less than (`<`) symbols.
