SKILLS TEST – STUDY GUIDE
Example:
4889 + 651 =
1 1 1
4889
+ 651
5540
7030 – 582 =
6 9 12 10
7030
- 582
6448
356 x 148 =
How to:
Add Whole Numbers:
Your turn:
1) 3097 + 809
Estimate first.
Arrange addends in vertical columns,
being careful with place values.
Find the sum and check your estimate.
Subtract Whole Numbers:
Estimate first.
Arrange vertically by place values.
2) 8306 - 597
Start subtracting in the ones column
and move left.
If you can’t subtract from the column
you’re in, borrow one from the
column to the left.
Check your estimate.
Multiply Whole Numbers:
3) 187 x 79
Write vertically and line up place
356
X 148
2848
14240
35600
52,688
9856 ÷ 27 =
365
27) 9856
81
175
162
136
135
1
Multiply 356 by 40 (write a 0 and then
Multiply 356 by 100 (write two 0s and
multiply 356 by 1.)
Remember to keep all digits in columns
and add carefully.
Divide Whole Numbers:
Write with dividend inside and divisor
outside.
Follow steps: D, M, S, B, and finally R.
(Divide, multiply, subtract, bring
down, and work with remainder.)
Each time you “bring down” you must
divide, even if you bring down a 0.
If you have a remainder you need to
change it to a decimal or a fraction.
4) 1944 ÷ 48
SKILLS TEST – STUDY GUIDE
Example:
62,391 +27,587 =
62,391
+ 11.890
670.235
70.33 – 16.684 =
2 2 10
70.330
- 16.684
53.646
3.192 x 25 =
3.198
x 25
15960
63840
79.800
Your turn:
5) 112.576 + 867
Arrange numbers vertically and line
up the decimal points.
1 1 1
6 9
How to:
Add decimals:
(3 decimal places) +
(0 decimal places)
(3 decimal places total)
8.91 ÷ 3.3 =
3.3)8.91
2.7
33)89.1
66
23 1
23 1
0
You may add a 0 to have the same
number of decimal places.
Add numbers and place decimal point
in your answer.
Subtract decimals:
6) 143.8 – 7.822
Arrange numbers vertically and line
up the decimal points.
Place a 0 to make decimals the same
length (see arrow).
Subtract normally and place the
decimal point in the answer.
Multiply decimals:
7) 5.9 x 0.03
Write the number with more digits on
top, and fewer digits underneath. Do
not line up decimal points.
Multiply normally ignoring the
decimal point.
Put in the decimal point; it will have
the same number of places as the two
factors combined.
Divide decimals:
If divisor is not a whole number move
decimal to the right to make it whole;
move decimal in dividend the same
number of places to the right.
Rewrite the problem (for neatness).
Write decimal point in the quotient,
then divide normally.
(Add additional 0s to the end of the
dividend if necessary and divide until
there is no remainder.)
Note: If the original divisor is a whole
number do not move the decimal, just
write decimal in the quotient.
8) 193.2 ÷ 4.2
SKILLS TEST – STUDY GUIDE
Example:
How to:
Add fractions:
15 + 22 =
+ 22 = 22
Add numerators and write over the
common denominator.
37
or 37 + 1
Add any whole numbers.
Simplify fraction if necessary.
38
Subtract fractions:
26 - 16 =
26 = 26 = 25 + = 25
- 16
9) 12 + 9
Make sure denominators are the
same (rename with common
denominators if necessary).
15 = 15
=
Your turn:
- 16
- 16
9
10) 32 - 19
Make sure denominators are the
same (rename if necessary).
Subtract numerators and rewrite the
denominator. (If not possible, borrow
from the ones place and rename the
fraction first – see example.)
Subtract any whole numbers.
Simplify fraction if necessary.
Multiply fractions:
3 x2 =
11) 4 x 2
Keep problem written horizontally.
If there is a mixed number write it as
an improper fraction.
6
x =
= 9
1
Simplify any one numerator with any
one denominator. Simplify as much as
possible.
Multiply numerators then
denominators. Simplify (make a
mixed number if necessary).
Divide fractions:
7 ÷ 2 =
=
5
4
x
1
=
7
= 2
Keep problem written horizontally.
Change mixed numbers to improper
fractions.
Multiply first fraction by the reciprocal
of the second.(Keep the first fraction,
Change to multiplication, Flip the
second fraction). KCF
Follow steps for multiplication.
12) 8 ÷ 2
SKILLS TEST – STUDY GUIDE
Example:
12.5% of 70
Rewrite as: .125 x 70
.125
x 70
8750
8.750 or 8.75
How to:
Percent of a number:
Percent means parts of 100 (divided by 100).
To divide by 100 move the decimal two
places to the left.
“of” often means times, so multiply the new
decimal times your number.
Remember: Percent of a number is a
number, not a percent.
65
13
(5)(13)
=
=
100 (2)(2)(5)(5) 20
2.
3.
4.
Write the prime factorization of both the
numerator and denominator.
Rewrite the fraction so that the numerator
and denominator are written as the
product of their prime factors.
Cancel out any common prime factors.
Multiply together any remaining factors in
the numerator and denominator
Volume of a Rectangular Prism:
6 in
Use formula V = bwh
(Same as V = lwh or V = Bh)
8 in
13 in
V = bwh
= (13)(6)(8)
= 624 in3
= 2(13)(8)+2(13)(6)+2(8)(6)
= 208 + 156 + 96
2
= 460in
14)
V=
12 cm
12 cm
Tip: Always write a formula.
3cm
Remember to write units.
2 cm
Surface Area of Rectangular Prism:
(using figure above) Find
S.A.= 2bh + 2bw + 2hw
13) 6% of 20
Simplifying Fractions
1.
Write 65% as a lowest term fraction.
Your turn:
the total of all surfaces. S.A. =
2bh + 2bw + 2hw
Short cut - Multiply:
Base
Width
Height
Total x 2
Remember to write units.
or
15)
(Use figure above.)
S.A. =_
SKILLS TEST – STUDY GUIDE
Example:
How to:
Perimeter and Area of a Triangle:
15cm
9cm
12cm
P = 9 + 12 + 15
= 36cm
A= bh
= (12)(9)
= 54cm2
16a)P =_
17a)A=
To find the perimeter add the lengths
of the sides.
To find the area use the following
formula: A = bh or A =
23in
23in
Tip (for Area): Always copy the
formula first, then substitute numbers
for variables.
22in
Remember to write units.
Perimeter and Area of a Rectangle:
10in
To find the perimeter add the lengths
of the sides.
9cm
12cm
P = 9 + 12 + 9 +12
= 42 cm
A = lw
= (12)(9)
= 108 cm2
To find the area use the following
formula: A = lw
Perimeter and Area of a Parallelogram
5ft
Your turn:
6ft
P=8+8+6+6
= 28ft
A =bh
=(8)(5)
= 40ft2
To find the perimeter add the lengths
of the four sides.
To find the area use the following
formula: A = bh
Reminder: Do not confuse the height
with the slant length.
Remember to write units.
16b)P=
9cm
4cm
17b) A=_
8cm
SKILLS TEST – STUDY GUIDE
Example:
7m
6m
P = 7+6+7+8
= 28m
8m
6m
7m
How to:
Perimeter and Area of a Trapezoid:
To find the perimeter add the lengths
of the four sides.
Your turn:
16c) P=
8m
8m
= ( )(6)(8 + 6)
=
42m2
formula:
9m
11m
To find the area use the following
A = h (b1 + b2)
17c) A=_
A = h (b1 + b2)
(The bases are the parallel lines and
the height is the distance between the
bases.)
fy a fraction, you should follow
Remember to write units.
Circumference of a Circle:
14 ft
C = πd
= (3.14)(14)
43.96ft
=
Use formula:
C = πd (or C = 2πr)
Use 3.14 for π. Substitute numbers
for variables and multiply.
Remember to copy and use the
circumference formula.
Remember to write units.
Concept of Pi
Given:
c = 43.96 ft
d = 14 ft
Pi =
43.96
14
= 3.14
Pi is the ratio of the circumference
of a circle to its diameter.
18)
C=
8cm
SKILLS TEST – STUDY GUIDE
Example:
Use formula:
11m
A = πr2
A = πr2
= (3.14)(11)(11)
= 379.94m
How to:
Area of a Circle:
Your turn:
19)
A=
16yd
Use 3.14 for π. Substitute numbers
for variables and multiply.
2
Remember to copy and use the area
formula.
Remember to write units.
42 + 35
=4 x 4 + 3 x 3 x 3 x 3 x 3
= 16 + 9 x 9 x 3
= 16 +
81 x
3
= 16 +
243
=
259
Exponents:
20) 52 + 26
Write the exponent problem as a
product of the factors.
Perform the necessary operations and
calculate the total.
Tips and Reminders:
NEATNESS COUNTS.
Show work in two columns
and do calculations neatly
next to each problem.
NO CALCULATORS
ALLOWED.
Always try to estimate first
and check final answer with
your estimate.
Remember to write units:
P
1
A
2
V
3
Whenever you have a
geometry problem start by
writing the formula.
For Circles:
Cherry pie is delicious!
Apple pies are, too!
Box your final answers.
SKILLS TEST – STUDY GUIDE
Example:
10cm
How to:
Volume of a Cylinder:
Your turn:
Bonus 1:
6in
Use formula:
V = πr2h or V=Bh
12cm
Substitute numbers for variables and
multiply.
2in
V=_
Remember to write units.
2
V=πr h
=(3.14)(5)(5)(12)
= 942cm3
(Use figure above.)
S.A.= 2πrh + 2πr
2
=(2)(3.14)(5)(12) +(2)(3.14)(5)(5)
= (3.14)(120) + (3.14)(50)
= 376.8 + 157
=
533.8cm2
Surface Area of a Cylinder:
Bonus 2: (Use figure above.)
Use formula:
S.A.=
S.A. = 2πrh + 2πr
2
Substitute numbers for variables.
Multiply both parts and then add
(remember the order of operations.)
Remember to write units.