Basic Number Properties (LMU)
There are three basic properties of numbers, and every math problem you have ever
worked has obeyed these properties. Although these properties may seem simple and of
no importance, the ISEE requires you to be familiar with them to be successful.
Exercise 1
Can you describe the three basic properties of numbers?
1. Associative Property
2. Commutative Property
3. Distributive Property
176 Math Skills
Basic Number Properties Activity
In the following activity, select the response that best illustrates numbers and
operations.
1.
Which of the following expressions is an example of the distributive
property?
(A)
(B)
(C)
(D)
2.
Associative Property
Commutative Property
Distributive Property
Identity Property
Which expression represents the associative property?
(A)
(B)
(C)
(D)
6.
(10 + 4) × 6 = 6 × (10 + 4)
(10 + 6) × 4 = (10 + 4) × 6
(6 × 10) + (6 × 4) = 6 × (10 + 4)
(6 × 10) × (6 × 4) = (6 × 10) + 4
The expression 10 × (12 + 15) = 10 × (15 + 12) is an example of which of the
following properties?
(A)
(B)
(C)
(D)
5.
Associative Property
Commutative Property
Distributive Property
Identity Property
Which expression represents the commutative property?
(A)
(B)
(C)
(D)
4.
If you are having trouble
with fractions and decimals,
try estimating.
The expression 4 × 36 = 36 × 4 demonstrates which of the following
properties?
(A)
(B)
(C)
(D)
3.
(32 × 4) + 7 = (32 + 7) × (4 + 7)
(32 + 7) × 4 = 4 × (32 + 7)
(4 × 32) + (4 × 7) = 4 × (32 + 7)
(4 × 32) × (4 × 7) = 4 × 32 × 7
(18 + 2) + 15 = 18 + (15 + 2)
(15 + 2) + 18 = (2 + 15) +18
(18 × 15) + (18 × 2) = 18 × (15 + 2)
(18 + 15) + (18 + 2) = (18 + 2) + (18 + 15)
The expression 2(4y + 3) = 8y + 6 is an example of which of the following
properties?
(A)
(B)
(C)
(D)
Associative Property
Commutative Property
Distributive Property
Identity Property
Math Skills
177
Fractions & Decimals (LMU)
Operations with fractions and decimals can be troublesome on the ISEE
because it is easy to make mistakes, especially if you are in a hurry. Being
familiar with common fraction and decimal equivalents will go a long way
Exercise 2
Can you give the decimal equivalent to the following fractions?
1.
1
2
5.
1
6
2.
1
3
6.
1
8
3.
1
4
7.
1
9
4.
1
5
8.
1
10
Exercise 3
Can you give the decimal equivalent to the following fractions?
1. 0.2
5. 0.6
2. 0.3
6. 0.7
3. 0.375
7. 0.75
4. 0.4
8. 0.8
Exercise 4
Can you describe the steps for the following operations?
1. Adding two fractions
2. Subtracting two fractions
3. Multiplying two fractions
4. Dividing two fractions
5. Adding with decimals
6. Subtracting with decimals
7. Multiplying with decimals
8. Dividing with decimals
178 Math Skills
Fractions & Decimals Activity
In the following activity, select the response that best illustrates the correct
operation with fractions and decimals.
1.
Which of the following is equivalent
1
2
to 2 + 3 ?
(A)
(B)
(C)
(D)
2.
3.
What is the value of the
3
3
7
expression 8 + 4 – 8 +
(B)
(C)
(D)
4.
1
3
3
5
7
6
8
5
Shelly has
2
3
of a container of
1
3
bake a cake, what portion of the
(A)
(B)
Which of the following is equivalent
to 0.75 × 0.5?
(A) 0.375
(B) 0.600
(C) 0.850
(D) 1.200
(A)
5.
1
2
?
1
8
3
8
1
4
3
4
(C)
(D)
6.
Steven is performing in the
Paper Olympics Paper Cutting
Extravaganza. He begins by
1
cutting off 3 of his standard sheet
of notebook paper. Then, he cuts
1
off 5 of the remaining portion.
After the second cut, what fraction
of his paper remains?
(A)
(B)
3
5
A soda bottle is currently full. If
Bill drinks half of this amount, what
4
9
1
2
2
3
5
6
(C)
(D)
1
15
7
15
8
15
2
3
with soda?
(A)
(B)
(C)
(D)
1
5
3
10
2
5
7
10
Math Skills
179
Mixed Numbers (LMU)
Mixed numbers appear in many problems. These numbers contain an integer
followed by a proper fraction. Before trying to solve problems that contain
mixed numbers, it is best to convert the mixed numbers into improper
fractions.
Exercise 5
Can you convert the following mixed numbers into improper fractions?
1.
1 23
4.
5 61
2.
3 45
5.
6 37
3.
4 29
6.
2 121
Exercise 6
Can you convert the following improper fractions into mixed numbers.
1.
2.
3.
180 Math Skills
5
2
10
3
9
4
4.
5.
6.
17
5
23
6
19
7
Mixed Numbers Activity
In the following activity, select the response that best illustrates the correct
operation with fractions and decimals.
1.
Which of the following is equivalent to the sum of
(A)
(B)
(C)
(D)
2.
(B)
(C)
(D)
3.
5 56
6
6
Remember:
Operations with mixed
numbers can be tough.
When you are strapped
for time, ESTIMATE!
1
6
5
6
3 45 # 2 13 ?
5 12
6 152
8 13
15
10 38
1
1
Sean has 5 2 slices of pizza. A day later, he only has 3 of his pizza
remaining. How many slices of pizza does he have left?
(A)
(B)
(C)
(D)
4.
5 15
Which of the following is equivalent to
(A)
2 13 and 3 12 ?
1 56
2 13
3 23
4 16
Which of the following is equivalent to
(A)
(B)
(C)
(D)
1
2
_ 4 13 + 2 14 i ?
3 247
4 125
5 11
24
6 127
Math Skills
181
5.
Which of the following is equivalent to
(A)
(B)
(C)
(D)
182 Math Skills
1 12
2 185
4 121
5 16
5 18 ' 2 14 ?