This document contains 12 math word problems involving properties of numbers and operations. Each problem provides numeric relationships and asks the reader to find unknown values. The document then shows step-by-step work to solve each problem algebraically. Overall, the document demonstrates different types of math word problems and their solutions through algebraic expressions and equations.

1. teacher Yodhathai Reesrikom

3. 1, 2, 3, …
Whole Number
Real
Numbers
Irrational
Number
0.5254578
Rational Number
IntegerNegative (less than 0)
ZeroDivide all number is no
answer
Plus all number is all number
Minus all number is all number
Multiply all number is 0
Number divide 0 is 0
Positive (more than 0)
Natural Number
0, 1, 2, 3, …

6. No. Number Property of equality
1 8 = 8 Reflexive Property
2 9 = 9
3 100 = 100
4 If 6 = 5 + 1 then 5 + 1 = 6 Symmetric Property
5 If 8 = 3 + 5 then 3 + 5 = 8
6 If 10 = 7 + 3 then 7 + 3 = 10
7 If 42
= 16 then 16 = 7 + 9 42
= 7 +
9
Transitive Property
8 If 52
= 25 then 25 = 20 + 5 52
=
20 + 5
9 If 72
= 49 then 49 = 40 + 9 72
=
40 + 9
Reflexive Property
Reflexive Property
Symmetric Property
Symmetric Property
Transitive Property
Transitive Property

7. 10 If 45 = 20 then (45) +3 = 20+3 AdditionProperty
11 If (26) = 12 then (26)+2 = 12+2
12 If 32 = 6 then (32)+5 = 6+5
13 If (43) = 12 then (43)5 = 12
5
MultiplicationProperty
14 If (52) = 10 then (52)6 = 106
15 If 2
8
= 4 then 2
8
4 = 46
Addition Property
Addition Property
Multiplication Property
Multiplication Property

8. EX.
7 = 7
5 = 5
10 = 10
4 = 4
9 = 9
Reflexive Property
Reflexive Property is A = A
when A is Real number.
If 9 = 6+ 3 then 6+ 3 = 9
If 6 = 4 + 2 then 4 + 2 = 6
If 7 = 4 + 3 then 4 + 3 = 7
If 12 = 10 + 2 then 10 + 2 = 12
Symmetric Property
Symmetric Property is if A = B, then
A = B when A and B is Real number.
Property of Equality

9. If 32 = 9 and 9 = 6 + 3 then 32 = 6 + 3
If 52 = 25 and 25 = 21 + 4 then 52 = 21 + 4
If 42 = 16 and 16 = 6 + 10 then 62 = 6 + 10
If 132 = 169 and 169 = M + 3 then 32 = M + 3
Transitive Property
Transitive Property is if A = B and B = C, then A = C when
A ,B and C are Real number.

10. If 4  3 = 12 and c = 2 then (4  3) + 2 = 12 + 2
If 5  2 = 10 and c = 5 then (5  2 ) + 5 = 10 + 5
If 7  8 = 56 and c = 9 then (8  7) + 9 = 56 + 9
If 8  4 = 32 and c = 3 then (8  4) + 3 = 32 + 3
Addition Property is if A = B, then A + C = B + C when
A ,B and C is Real number.
Addition Property

11. If 4 x 8 = 32 and c = 5 then (4 x 8 )x 5 = 32 x 5
If 9 x 6 = 54 and c = 8 then (9 x 6 )x 8 = 54 x 8
If 12 x 8 = 96 and c = 9 then (12 x 8 )x 9 = 96 x 9
Multiplication Property
Multiplication Property is if A = B, then A × C = B ×C
when A ,B and C is Real number.

20. 1. When the square of a certain number is diminished by 9
times the number the result is 36. Find the number.
square of a certain number =
2
x
9 times the number = x9
3692
 xx
03692
 xx
0)3)(12(  xx
312  orx

21. 2. A certain number added to its square is 30. Find the
number.
A certain number = x
its square =
2
x
302
 xx
0302
 xx
0)5)(6(  xx
5)6( orx 

22. 3. The square of a number exceeds the number by 72.
Find the number.
a number = x
square of a number =
2
x
722
 xx
0722
 xx
0)8)(9(  xx
89 orx 

23. 4. Find two positive numbers whose ratio is 2:3 and whose
product is 600.
numbers whose ratio is 2:3 = 2x:3x
First numbers = x
xx
2
3
:
product is 600 = 600)
2
3
( xx
600
2
3 2

x
12003 2
x
3
12002
x
4002
x
04002
x
02022
x

24. 0)20)(20(  xx
2020  orx
20xpositive numbers
two positive numbers 30:20)20(
2
3
:20
2
3
: xx

25. 5. The product of two consecutive odd integers is 99. Find
the integers.
odd integers = x
consecutive odd integers = 2x
99)2( xx
9922
 xx
09922
 xx
0)11)(9(  xx
119  orx
If x = 9
consecutive odd integers
= 9+2=11
If x = -11
consecutive odd integers
= -11+2=-9

26. 6. Find two consecutive positive integers such that the
square of the first is decreased by 17 equals 4 times the
second.
First number = x
Second number = 1x
)1(4172
 xx
0)1(4172
 xx
044172
 xx
02142
 xx
0)3)(7(  xx
37  orx
7x
First number = 7
Second number = 7+1=8

27. 7. The ages of three family children can be expressed as consecutive integers. The
square of the age of the youngest child is 4 more than eight times the age of the
oldest child. Find the ages of the three children.
youngest child = x
oldest child = 2x
)2(842
 xx
16842
 xx
02082
 xx
0)10)(2(  xx
102orx 
10x
The ages of three family children = 10,11,12 year old

28. 8. Find three consecutive odd integers such that the square
of the first increased the product of the other two is 224.
224)4)(2(2
 xxx
2248622
 xxx
021662 2
 xx
010832
 xx
0)9)(12(  xx
912orx 
9x
three consecutive odd integers = 9,10,11

29. 9. The sum of the squares of two consecutive integers is 113.
Find the integers.
113)1( 22
 xx
1131222
 xxx
011222 2
 xx
0562
 xx
0)8)(7(  xx
87  orx
If x= 7 two consecutive integers is 7 and 8
If x= -8 two consecutive integers is -8 and -7

30. 10. The sum of the squares of three consecutive integers is 302.
Find the integers.
302)2()1( 222
 xxx
302)44()12( 222
 xxxxx
029763 2
 xx
09922
 xx
0)9)(11(  xx
911orx 
If x= -11 three consecutive integers is -11,-10,-9
If x= 9 three consecutive integers is 9,10,11

31. 11. Two integers differ by 8 and the sum of their squares
is 130.
130)8( 22
 xx
130641622
 xxx
066162 2
 xx
03382
 xx
0)11)(3(  xx
113 orx 
If integers is -3 two integers is -3 and -11
If integers is 11 two integers is 11 and 3

32. 12. rectangle is 4 m longer than it is wide, its area is 192 m2. Find the
dimensions of the rectangle.
192)4( xx
19242
 xx
019242
 xx
0)12)(16(  xx
1216 orx 
12x
12
412 
Dimensions of the rectangle
= 12 x 16 = 192