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Another method for remembering if the sign is" greater than" or "less than" is to look at the symbol, and remember that the larger side of the symbol always faces the larger number.    

  • Larger side of symbol > Smaller side of the symbol
  • 7>6 seven is larger than 6   6<7 six is less than 7

Hi welcome to MooMooMath. Today we are going to talk about comparing integers, which include positive and negative numbers. So let’s look at our first example. You have 4 comparing to negative 6 and the 4 is greater than the negative 6. Next up is negative two compared to negative 8. Negative 8 is greater than negative 2 so we will use the less that symbol. ( < ) Finally let’s look at negative 6 and absolute value of negative 6. The value of negative 6 is greater so we will use the greater than symbol (>) Now let’s look at the rules of comparing integers. The first symbol is the less than symbol (<) the way I remember this is it actually looks like the letter L. The symbol switched around (<) is greater than and notice it does not look like the letter L so it can’t be less than and the last one is equal to. Now that is how the symbols. Now let’s go to a number line. Anything to the left is smaller than anything to the right. You can look at your number line and make some comparisons in order to determine which one is greater than or less than. The first one is four compared to negative 6. I will use the number line for this and negative 6 are to the left of 4 so 4 are greater than negative 6. 4 are greater than negative 6. You want to use the symbol that the smaller end of the symbol is pointing towards the smaller number. Next up is negative 12 and negative 8. These are both negative numbers. Many times students will say that -12 is greater than -8 because it is larger but in negatives it is the opposites. On the number line the 12 is over here on the left so it is less than -8. So the -8 is larger so we will use a less than sign. Now let’s look at the absolute value. You will always take the positive, because the definition of absolute value is the distance from zero. So negative 6 is 6 units from 0 and we will compare that to the negative of absolute value and that actually is positive 6 so you are actually comparing positive 6 to -6 and positives are always greater so we will use the smaller end towards the smaller number which becomes 6 > -6 Hope this helps.

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On a number line with integers any number to the left of another is less than the number on the right.    

​Let's look at an example problem related to this standard.

​How much money is left on my $ 20.00 Starbucks gift card if I purchase 3 tall coffees at $3.00 each?

Step 1. 3*3 =9 

Step 2. 20 -9 ( cost of 3 coffees) = $11 amount left on the card

What is my elevation if I start hiking at 10,000 feet, climb 1000 feet, then descend 2000 feet, climb again for 2000 feet, and then descend 500 feet.

Step 1 10,000 + 1000 =11,000 feet

Step 2. 11,000-2000=9000 feet

Step 3  9000 +2000= 11,000

Step 4 11,000 -500 = 10,500 feet
Common Core Standard  6.G.1 , 7.G.6  6th Grade Math    7th Grade Math

An easy method for comparing fractions and integers is to convert the fraction into a decimal and then compare this to the integer.

For example, compare 7/8, 11/16, 6, -1,
Convert the fractions to decimals    7/8 = .875 11/16 = .6875 

Now place from least to greatest.
-1 < .6875 <.875 < 6

Finally you can convert back to the original fraction and list them from least to greatest.
-1 < 11/16 <7/8  < 6

A rational number is a number that can be expressed as a fraction.
Follow these steps when comparing integers and rational numbers.

Convert the rational number into a decimal. 
Make sure the decimals are lined up correctly.

For example compare 7/14, .6, 1, -5
Convert 7/14 =.5 

Now you can compare .5,.6, 1, -5 by placing them from least to greatest
-5 < .5 <  .6 < 1

Finally you can place them in their original form
-5< 7/14 < .6 < 1

Comparing integers word problems

Comparing integers and fractions

Comparing integers and rational numbers

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You can easily compare integers when you order the integers on a number line.

Comparing Integers

Left < Right
The smaller end of the symbol should face towards the smaller number. For example: 6<10    -8> -10     1<2
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Integers on a number line

The following symbols are used when comparing integers:

1. < equals less than, I remember this because it looks like a L for less
2. > Doesn't look like a L so it is greater than
3. = equals  
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more white dogs used to compare integers
white dog used to compare integers
There are less cats than dogs, therefore 2<3
2 men 1 women
There are more men than women, therefore  2>1
family of four
family of four
Each family has the same number of members (4) therefore 4=4

Comparing and Ordering Integers

Whenever you have two numbers in Math you can compare these two numbers. Integers are positive or negative counting numbers, which means they are not fractions or decimals. For example, 2,35,-56 34, and 0 are all integers. 5.4,61/2, and 3/4 are not integers. When comparing integers the number is either greater than, less than, or equal to the other number.