COMPARING AND ORDERING INTEGERS
We use number line to compare and order integers.
That is, if we want to compare two integers, first we have to locate the integers on the number line and mark them.
The integer which comes to the right of the other integer is greater. The integer which comes to the left of the other integer is smaller.
To order the integers, we have to locate the given integers on the number line and mark them. Then, write the integers from left to right to list them in order from least to greatest.
Comparing Integers
Example 1 :
Compare the integers -4 and 4
Solution :
Let us locate the two integers -4 and 4 on a number line and mark them.
Here, the positive integer 4 comes to the right of -4.
Therefore "4" is greater than "-4"
And -4 comes to the left of 4.
Therefore "-4" is smaller than "4"
Example 2 :
Compare the integers -1 and 1
Solution :
Let us locate the two integers -1 and 1 on a number line and mark them.
Here, the positive integer 1 comes to the right of -1.
Therefore "1" is greater than "-1"
And -1 comes to the left of 1.
Therefore "-1" is smaller than "1".
Ordering integers
Question :
Order the integers -2, -5, 4, 0, -3, -1, 3 from least to greatest.
Answer :
Let us locate the integers -2, -5, 4, 0, -3, -1, 3 on a number line and mark them.
From the above number line, write the integers from left to right to list them in order from least to greatest.
Thus, we get
-5, -3, -2, -1, 0, 3, 4
Real World Problems
Problem 1 :
In 2010, Sacramento, California, received 23 inches in annual precipitation. In 2011, the city received 17 inches in annual precipitation. In which year was there more precipitation ?
Solution :
Locate the two integers 23 and 17 on a number line and mark them.
23 is to the right of 17 on the number line.
This means that 23 is greater than 17.
We can write the above situation in terms of inequality as 23 > 17.
17 is to the left of 23 on the number line.
This means that 17 is less than 23.
We can write the above situation in terms of inequality as 17 < 23.
There was more precipitation in 2010.
Problem 2 :
John recorded the following golf scores during his first week at a golf academy. Negative numbers represent scores below par, a standard score. In golf, a lower score beats a higher score.
Graph John’s scores on the number line, and then list the numbers in order from least to greatest.
Solution :
Step 1 :
Graph the scores on the number line.
Step 2 :
Read from left to right to list the scores in order from least to greatest.
The scores listed from least to greatest are
–5, –3, –2, –1, 0, 3, 4.
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WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
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Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
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Sum of all three four digit numbers formed with non zero digits
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