Download Basic Math Review - Riverland Community College

Basic Math Review
Courtesy of the
Student Success Center
Revised 2016
Sharon Stiehm
Computation/Arithmetic
Natural Numbers
These are the numbers used for counting, sometimes called “Counting
Numbers.” They are …
1, 2, 3, 4, 5, 6, 7, 8, 9, 10…
There is no largest natural number and the smallest natural number is one (1).
Whole Numbers
To answer questions such as, “How many” and “How much,” we generally use
whole numbers. The set or collection of whole numbers is
0, 1, 2, 3, 4, 5, 6, 7, …
There is no largest whole number, and the smallest whole number is zero (0).
Integers
Consist of all Natural Numbers, Whole Numbers, and Negative Numbers. These
numbers can best be illustrated on a “number line.” For each Natural Number, 1, 2,
3, 4, 5, …, there is an opposite number to the left of zero, -1, -2,
-3, -4, -5, and so on. Negative numbers are considered to be the “opposites” of
positive numbers.
Rational Numbers
This is a larger number system, which includes the number systems mentioned above
and “quotients of integers with nonzero divisors.” Quotients of integers are
commonly expressed as “Fractions and Decimals.”
Examples of these are…
2/3, -2/3, 7/1, -0.17, 0/8, -8.75, .3334
Every rational number has a point on the number line. However, there are some
points on the line for which there is no rational number. These points correspond to
what is called “irrational numbers.”
Fractions
Fractions are a portion of a whole number and they consist of a numerator,
denominator, and fraction bar. In the fraction ½, the
(1) one is the numerator
(2) two is the denominator
(/ or --) is the fraction bar that separates the numerator and denominator.
Fractions are another way of showing division. One-half (1/2) can be expressed as 1
÷ 2. When evaluating this expression we get the decimal five-tenths (.5).
Revised 2016
Sharon Stiehm
Decimals
Decimals are fractions whose denominators are powers of ten (10). The number of
decimal places equals the number of zeros in the denominator:
1/4 or 25/100 in decimal form is .25
¾ or 75/100 in decimal form is .75
When adding or subtracting decimal numbers, place the numbers in a column with
the decimal points lined up vertically.
Percentage
“Of all wood harvested, 35% is used for paper production.” This means for every 100
tons of wood harvested, 35 tons is used to produce paper. 35% is also considered a
ratio of 35 to 100, or 35:100. Using a percentage is a more convenient way of
showing this relationship. A percentage is changed to a decimal number by
dropping the percent sign and moving the decimal two places to the left. (Example:
37.5% = .375 and 45% = .45)
Irrational Numbers
As mentioned before, irrational numbers represent points on the number line for
which there is no rational number. Examples of irrational numbers are…
π (read as “pi”) and √2 (square root of “2”).
π is used in finding the area and circumference of a circle, the approximate
number for π is 3.141592654…
√2 is the length of the diagonal of a square with sides of length one (1). There is
no rational number that can be multiplied by itself to get 2.
 1.4 is an approximation of √2 because (1.4)2 = 1.96
 1.4142 is an even better approximation because (1.4142)2 = 1.99996164
Real Numbers
Real Numbers are the set of all numbers corresponding to points on the number line
and include…
 Natural Numbers
 Whole Numbers
 Integers
 Rational Numbers
 Irrational Numbers
Applications
An application is one of the main uses of mathematics. It is how we use our math
skills in everyday life.
(The previous explanation for percentage is a good example).
Problem Solving
Problem solving is the other main use of mathematics. Look at a situation and try to
translate the problem into mathematical terms.
Revised 2016
Sharon Stiehm
Five Steps for Problem Solving
1. Familiarize yourself with the situation. If the problem is described in words,
read it carefully. Draw a picture whenever possible. Choose a letter like a, b,
c, n, x, y, z, etc. to represent the unknown quantity. In math, we call this letter
the “variable.”
2. Translate the problem into an equation.
3. Solve for the variable.
4. Check the answer in the original word problem.
5. State the answer to the problem with appropriate units.
Order of Operations
Rules for “Order
of Operations”:
1. Begin with the innermost expression, do all calculations within parentheses ( ),
brackets [ ], and braces { } before doing expressions outside these symbols.
2. Evaluate all exponential expressions.
3. Do all multiplications and divisions in order from left to right.
4. Do all additions and subtractions in order from left to right.
Revised 2016
Sharon Stiehm
Whole Number Problems
1. True or False: -1, 2, 4, -3, 0, and 12 are all whole numbers.
2. True or False: 3, 4, 7, 78, and 1,000,000 are all whole numbers.
3. What digit is in the ones place?
2356
4. What digit is in the tens place?
2356
5. Write a sentence in which the number 250,000,000 is used.
6. Connor is 6’4” tall and weighs 170 lbs. If Connor wants to weigh 190 lbs. by
the next basketball season, how many pounds per month does he need to
gain? The basketball season starts in 4 months.
7. What is the sum of these numbers: 123, 556, 2, and 2?
8. Find the product of these whole numbers: 23 x 54.
9. Round to the nearest whole number: 86.256
10.
Write a word name for the number in the sentence: In a recent year, the
average salary of a player in the NBA was $1,867,000.
11.
Kyle has to be at school by 8:00 a.m. He drives 30 mph and lives 5 miles from
school.
a. How long will it take him to get to school?
b. What time must Kyle leave for school to arrive five minutes
early?
12.
Dr. Schindler orders 20 mg. of Paxil in the morning and 20 mg. at night. He
wants his patient to be on this medication for 30 days. How many 20 mg. pills
will the patient receive from the pharmacist?
13.
Amie needs to buy a graphing calculator for college. The one she wants
costs $110. Amie only has $65. If she budgets $15 from her paycheck each
week, how long will Amie need to save before she can buy the calculator?
Revised 2016
Sharon Stiehm
Whole Number Problems - Answer Sheet
1. False. We use whole numbers to count objects. It is impossible to count
objects using negative numbers. Therefore, negative numbers are not
included and zero is the smallest whole number.
2.
True. Whole numbers increase to infinity.
3.
6 (2356)
4.
5 (2356)
5. Answers will vary; however, the number 250,000,000 is written as two-hundredfifty million.
6. Connor needs to gain 20 pounds and he has 4 months to do it. Divide the
number of pounds by the number of months to find how many pounds he
needs to gain each month. 20 ÷ 4 = 5. Answer: Connor will need to gain five
pounds per month.
7. 702
123
556
2
+ 21
702
8.
1,242
23
x 54
92
92
+ 1150
1242
9. 86 To round to the nearest tenth, find the tenths place (86.256). Look at the
number to the right. If the number is five or more, round up. If it is four or less,
round down by dropping the decimal numbers.
10.
One-million, eight-hundred sixty-seven thousand dollars.
11.
a. Ten minutes. Use the distance formula (D = r t) Distance is equal to rate
multiplied by the amount of time. If his distance is 5 miles and his rate is 30
mph, solve for “t” (time). (Express 30 mph as 30 ÷ 60 or 30/60)
30/60 t = 5 miles
1/2 t = 5 (Multiply both sides by 2 to eliminate the fraction)
t = 10 Answer: It takes Kyle 10 minutes to get to school.
b. 7:45 A.M. If it takes Kyle ten minutes to get to school by 8:00, then he must
leave by 7:45 to arrive five minutes early at 7:55.
Revised 2016
Sharon Stiehm
12.
60 20-mg pills. If the patient is taking two pills a day for 30 days, multiply the
number of pills per day by the number of days.
13.
Three weeks. Amie already has $65, subtract this amount from $110 and she
only needs $45. If Amie budgets $15 per week, divide the amount needed
by the amount budgeted each week, 45 ÷ 15 = 3. In three weeks, Amie will
have enough money to buy the graphing calculator.
Revised 2016
Sharon Stiehm
Reading Fractions
Fractions are a useful way to express remainders in math problems. The number .25
can also be written as 1/4. Five-tenths written in fraction form is 5/10 or when
reduced to lowest terms is 1/2.
Reducing Fractions
To reduce a fraction, follow these steps:
1. Find the “largest common factor” (LCF) for the numerator and denominator.
2. Then divide the numerator and denominator by this number. For example in
the fraction 21/49, the LCF is 7. 21 ÷ 7 = 3 and 49 ÷7 = 7. Therefore, 21/49
reduced to lowest terms is 3/7.
Mixed Numbers
In a mixed number, a whole number is written next to a proper fraction. Examples
are 1½, 3¾, and 1¼. To change an improper fraction into a mixed number, follow
these steps:
1. Divide the numerator by the denominator. The whole number in the quotient
is the whole number portion of the mixed number.
2. Any remainder in the division problem is placed over the divisor and
becomes the fraction portion of the mixed number.
Proper Fractions
In a proper fraction, the numerator is smaller than the denominator. Examples are
1/3, 2/5, and 7/19.
Improper Fractions
In an improper fraction, the numerator is greater than or equal to the denominator.
Examples of improper fractions are 9/4, 12/3, 4/4, and 23/7. To change a mixed
number into an improper fraction, follow these steps:
1. Multiply the whole number by the denominator.
2. Add the numerator to the result of step 1.
3. The answer from step 2 becomes the numerator.
4. The denominator remains the same.
Adding and Subtracting Fractions
Fractions with the same denominator are simple to add and subtract. Follow these
steps if the denominators are the same:
1. Add or subtract the numerators.
2. The denominator remains the same.
3. Reduce the final answer to lowest terms.
Revised 2016
Sharon Stiehm
Fractions that do not have the same denominator must be changed to the least
common denominator (LCD). To find the LCD of 2/3 + 7/24, follow these steps:
1. The LCD is the smallest number that is evenly divisible by both denominators.
(The LCD for 3 and 24 is 24.)
2. The number you used to multiply the denominator of a fraction is the same
number you used to multiply the numerator of that fraction. (Multiply the
denominator of 3 by 8 to equal 24 then multiply the numerator of 2 by 8. The
fraction 2/3 is changed to 16/24.)
3. Add or subtract the numerators. (16 + 7 = 23)
4. The denominator remains the same. (Answer: 23/24)
5. If necessary, reduce to lowest terms. (In this example 23/24 is in lowest terms.)
Multiplying Fractions
To multiply a fraction, follow these steps:
1. Check to see if it is possible to cross-cancel.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce to lowest terms.
Dividing Fractions
To divide fractions, follow these steps:
1. Use the reciprocal of the second fraction (interchange the placement of the
numerator and the denominator).
2. Cross-cancel if possible.
3. Multiply the numerators.
4. Multiply the denominators.
5. Reduce to lowest terms.
Revised 2016
Sharon Stiehm
Fraction Problems
1.
Change 21/9 into a mixed number.
2.
Reduce to lowest terms: 4/12.
3.
Change the fraction to a whole number or reduce: 49/7.
4.
Change the fraction to a whole number or reduce: 12/3.
5.
What does 4/4 equal?
6.
Change this mixed number into an improper fraction: 2¾.
7.
Change this improper fraction into a mixed number: 14/3.
8.
1/2 x 3/4 =
9.
1/2 ÷ 3/4 =
10.
1¾ x 2/3 =
11.
1¾÷ 2/3 =
12.
4 x 1/3 =
13.
2/3 – 4/5 =
14.
12/42 + 2/56 =
15.
4 ÷ 1/2 =
16.
(1/4 x 2/3) ÷ 1/2 =
17.
(1/2 + 2/5)(4/5 + 1 2/3) =
18.
(2/3 x 1/2) + 2/3 – 3/4 =
19.
1/2 – 2/3 + 3/2 =
20.
(1 – 2/3)(5 + 2 2/3) =
Revised 2016
Sharon Stiehm
Fractions – Answers
1. Divide 21 by 9. The remainder is the fraction. 2 3/9 or 2 1/3
2. 1/3
4. 4
3. 7
5. 1
6. Multiply 2 by the denominator of 4. Then add the numerator of 3 to get 11. This is
numerator. The denominator remains 4. The
answer is 11/4.
7. Divide 14 by 3. The remainder of 2 is placed over the divisor of 3 as
a fraction. Answer: 4 2/3
8. Multiply numerators, then multiply denominators. Answer: 3/8
9. 4/6 or 2/3
10.
First, change the mixed fraction to an improper fraction … 7/4 x 2/3.
Cross-cancel to get 7/2 x 1/3 = 7/6 or 1 1/6
11.
First, change the mixed fraction to an improper fraction … 7/4 ÷ 2/3.
Take the reciprocal of the second fraction and multiply. 7/4 x 3/2 =
21/8 or 2 5/8
12.
4/1 x 1/3 = 4/3 or 1 1/3
Revised 2016
Sharon Stiehm
13.
In adding or subtracting, fractions must have a common denominator. Multiply
the numerator and denominator of 2/3 by 5. Multiply the numerator and
denominator of 4/5 by 3. The equivalent fractions of 2/3 and 4/5, are now 10/15
and 12/15.
10/15 – 12/15 = - 2/15 (negative two-fifteenths).
14.
12/42 + 2/56 = 48/168 + 6/168 = 54/168 or 9/28
15.
4/1 ÷ ½ = 4/1 x 2/1 = 8
16.
Reduce the fractions within the parenthesis; the problem now becomes (1/2 x
1/3) ÷ ½. Next, evaluate the fractions within the parenthesis to get (1/6) ÷ ½.
Take the reciprocal of the second fraction, and problem becomes. 1/6 x 2/1.
Reduce by crosscanceling to get
17.
1/3 x 1/1 = 1/3
(1/2 + 2/5) (4/5 + 1 2/3) = (5/10 + 4/10) (4/5 + 5/3) = (9/10) (12/15 +
25/15) = 9/10 x 37/15 = 3/10 x 37/5 = 111/50
18.
or
2 11/50
(2/3 x ½) + 2/3 – ¾ = (1/3 x 1/1) + 2/3 – ¾ = 1/3 + 2/3 – ¾ = 3/3 – 9/12 = 12/12 –
9/12 = 3/12 = 1/4
19.
½ - 2/3 + 3/2 = 3/6 – 4/6 + 9/6 = 8/6 =
20.
(1 – 2/3) (5 + 2 2/3) = (3/3 – 2/3) (15/3 + 8/3) = 1/3 x 23/3 = 23/9 or 2 5/9
Revised 2016
4/3 or
1 1/3
Sharon Stiehm
More Fraction Problems
1. Multiply: 2/3 and 5/6
2. Divide: 13/5 by 4/5
3. Add: 1/2, 3/4, and 2/5
4. Subtract: 1/2 from 7/8
5. Write .5 as a fraction in lowest terms.
6. Write .75 as a fraction and reduce to lowest terms.
7. Evaluate: w/g if, w = 36 and g = 4.
8. Evaluate: a/b if a = 25 and b = 5.
9. Evaluate: 10 x (p/s) if p = 40 and s = 25.
10.
Simplify: – 24/8
11.
Add: - 3/4 and – 1/3
12.
Evaluate: 5r + 6t – 4g – k if, r = 2; t = 1/2; g = 1/4; and k = 18.
13.
Alex scored 1/2 of what Adam scored. If Adam received a 90%, what did Alex
receive?
14.
If Ranita weighs 3/4 of what Megan weighs, and Megan weighs 144
lbs., how much does Ranita weigh?
15.
Find the fractional equivalent of .625 reduced to lowest terms.
16.
Solve for x.
17.
Chris makes $1044 per month. If he wants to save 1/3 of his monthly earnings,
how much will Chris have in eight months?
18.
Find the average of these numbers: 2, 1, and 1/2.
19.
Find the average of these numbers: 11/24, 1⅞, and 2/3.
Revised 2016
x/6 = 5
Sharon Stiehm
More Fractions - Answer Sheet
1. Multiply the numerators then multiply the denominators. Then check to see if your final
answer is reduced to lowest terms. 10/18 = 5/9
2. To divide fractions, use the reciprocal of the 2nd term then multiply. (First, check to see if
the fractions can be reduced by cross-canceling.) 13/5 ÷ 4/5 = 13/5 x 5/4, Cross-cancel
the denominator of five in the first fraction and the numerator of five in the second
fraction. This leaves 13/1 times 1/4. Multiply the numerators then multiply the
denominators. 13/1 x 1/4 = 13/4
3. Find the least common denominator (LCD). In this problem 1/2, 3/4, 2/5 the LCD is 20.
Using the LCD 1/2 + 3/4 + 2/5 = 10/20 + 15/20 +8/20 = 33/20
4. The LCD is 8.
Change 7/8 – 1/2 = 7/8 – 4/8 = 3/8
5. 5/10 = 1/2
7. 36/4 = 9
6. 75/100 = 3/4
8. 25/5 = 5
9. 10 x 40/25 = 10/1 x 8/5 = 16
10.
– 24/8 = – 3
11.
Find the LCD. In this problem the LCD is 12. – 9/12 – 4/12 = - 13/12
12.
5(2) + 6(1/2) – 4(1/4) – 18 = 10 + 3 – 1 – 18 = - 6
13.
1/2 x 90/100 (Cross cancel the denominator of 2 in the first fraction and the numerator
of 90 in the second fraction to get 1/1 x 45/100). 1/1 x 45/100 = 45/100 = 45%
14.
3/4 x 144 = 3/4 x 144/1 After cross-canceling the problem is 3/1 x 36/1 = 108/1 = 108
Answer: Ranita weighs 108 lbs.
15.
0.625 is read as six-hundred twenty-five thousandths, which is 625/1000 in fraction
form. 625/1000 is reduced to 5/8
16.
Multiplying both sides by six (or for the left-side in fraction form, six over one) and crosscancel. 6(x/6) = 6 (5); X = 30
17.
1/3 x $1044 = 348 per month. $348 x 8 = $2784
18.
First change 2 and 1 into fraction form (2/1 and 1/1). Then find the LCD and add. In this
problem the LCD is 2, 2/1 + 1/1 + 1/2 becomes 4/2 + 2/2 + 1/2. After adding the
numerators, we have 7/2. To find the average of these numbers, divide 7/2 by 3 (the
number of fractions in this problem).
7/2 ÷ 3 or 7/2 ÷ 3/1 = 7/2 x 1/3 = 7/6. The answer is 7/6
19.
First change the mixed number of 1 7/8 to the improper fraction of 15/8. Then follow the
same procedure as in number 18 by finding the LCD. In this problem the LCD is 24.
11/24 + 45/24 + 16/24 = 72/24 = 3/1 = 3
Revised 2016
Sharon Stiehm
Decimal – Word Problems
Examples of using decimals in everyday life include… This Saturday everything in Kohl’s
Department store is on sale for 20% (or 0.20) off the regular price. You can figure how
much money you will save on an item that originally costs $25.00 by formulating a
question. What is 20% of $25.00?
In a mathematical word problem, the word “is” means equals. To rewrite the example
above as an equation, use a letter such as “X” to represent the unknown amount (this
letter is called a variable) followed by an equal sign X =
Convert 20% to the decimal 0.20 X = 0.2…
The word “of” means multiply. Where you see the word “of” in the sentence is where
you place a multiplication sign in the equation. (Multiplication signs include any of the
following symbols x, ·, (amount to be multiplied). It is normal practice to use the dot or
parenthesis when the equation has a variable X = 0.2 x 25; or X = 0.2 · 25; or X = 0.2 (25).
The word “and” is used for addition; however, the word “and” is also used in reading a
decimal number (the decimal point is read as “and”). For example, 1.02 would be
written as one and two-hundredths.
Decimal Name
# of Places after the decimal
Tenths
Hundredths
Thousandths
Ten-thousandths
Hundred-thousandths
Millionths
One Place
Two Places
Three Places
Four Places
Five Places
Six Places
Examples
.3
.19
.007
.0067
.00183
.000023
1. What is one-tenth of 100?
2. Write the following number in word form: .0051
3. Write the following number in word form: 1.002
4. Of the following number, what digit is in the hundredth’s place? 135.2435
5. Of the following number, what digit is in the tenth’s place? 106.90?
6. Of the following number, what digit is in the thousandth’s place? 12. 245
7. What is one-hundredth of 2400?
8. Write the following number in word form: 10.2
9. Write two-thousand and four tenths in numerical form.
10.
Write one-hundred and thirty-four hundredths in numerical form.
Answers: 1) 100 x .1 = 10; 2) Fifty-one, ten-thousandths; 3) One and two-thousandths;
4) 4; 5) 9; 6) 5; 7) .01 x 2400 = 24; 8) Ten and two-tenths; 9) 2,000.4; 10) 100.34
Revised - 2016
Sharon Stiehm
Decimal Operations
1. In the number 34.683, which digit is in the tenths place?
2. Using the number above, which digit is in the tens place?
3. Add: 2.5 + 3.746 + .004 + 12.4 =
4. Subtract: 1277 – 82.78.
5. Write out the word name for 5.462
6. Divide: 54.7 by 2.5
7. Multiply: 4.00 x 68.125
8. Write three-fourths in decimal form.
9. What is 5699 divided by 10.25?
10.
Perform the following operations: 3.75 – 2.4 - .001 – 23.6 =
11.
Find the product of .001 and .35
12.
Write the decimal notation for 2/5.
13.
Normal body temperature is 98.6°. If Roberto’s temperature is 101.4°, how much
is his temperature above normal?
14.
A lab technician draws 9.85 mL of blood and uses 4.68 mL for lab testing. How
much blood was discarded?
15.
On a three-day trip, Jessica drove these distances: 110.35 miles the first day,
90.02 miles the second day, and 84.63 miles the third day. What was the
average distance traveled per day?
16.
If Sean fills his car with gas that is 105 cents a gallon, how many gallons will he put
in his car if he only has $15.75? (Hint: use decimal form of 105 cents.)
17.
A group of four students went out for lunch. They decided to split the bill equally
four ways. The total cost for the meal was $48.00. If the students left a 15% tip,
what did each student pay for lunch?
Revised - 2016
Sharon Stiehm
Decimal Operations - Answer Sheet
1. 6
2. 3
3. Line up the decimals before adding.
2.500
3.746
.004
+12.400
18.650 or 18.65
4. 1194.22
5. Five and four-hundred sixty-two thousandths
6. 21.88
7. 272.5
8. Multiply the denominator by a number to equal a multiple of ten (10, 100, etc.).
In this case, we multiply the denominator of 4 by 25 to equal 100. Then multiply
the numerator by 25. (3/4 x 25/25 = 75/100 = .75)
9. 556
10.
Line up the decimals before adding or subtracting.
3.75
- 2.40
1.35
1.350
- .001
1.349
11.
0.00035
12.
0.4
13.
2.8º higher
14.
5.17mL of blood was discarded
16.
15 gallons
Revised - 2016
1.349
-23.600
- 22.251
15. 95 miles per day
17. $13.80
Sharon Stiehm
Decimal Problems
Numbers that are written as decimals such as 5.75 actually mean five and seventy-five
one-hundredths. When division problems do not come out evenly, you can easily write
the answer in a decimal from.
Example: 15 ÷ 7 = 2.14286
1. What is 5.67 + 23.78?
2. Multiply: 45.7 by .005
3. Divide: 45.7 by .005
4. What is 34.6 – 23.76?
5. If Joe weighs 167.94 pounds, how many pounds does he need to gain before he
weighs 170?
6. What is 24 divided by 16?
7. Francis wants to pay $50.00 on her phone bill for right now. If the total cost is
$126.73. What is the remaining balance on her phone bill?
8. What is 23.5 + 23.5 – 23.5 + (– 23.5)?
9. John needs twenty-three units of UltraLente insulin before he goes to bed. If
there is a total of 100 units in the bottle, how many units will be left?
10.
Kwik Trip charges $.75 for a money order. If Jose buys three money orders. The
amount of each money order is as follows: $12.37, $78.86, $153.74. How much
will the money orders cost?
11.
[4(7.5 – 4.9)] + 23.89 – 49 = ? (Remember when working with ( ), [ ], and { } begin
with the innermost expression and work from the inside out.
12.
Rachel goes to Wal-Mart to buy shampoo at $2.65 per bottle, toothpaste at
$1.69 per tube, and a pair of sunglasses at $9.99 a pair. If she pays with a twentydollar bill, and there is no tax on these items, how much money will she receive
back?
13.
In the question 12, how much will Rachel receive if there is a 6 percent (.06) sales
tax on all items purchased?
Revised - 2016
Sharon Stiehm
14.
Sarah wants a Grilled Chicken Salad, fries, a large Coke at McDonald’s for lunch.
The Grilled Chicken Salad Meal Deal costs $6.79. However, today there is a 15
percent discount on all individual menu items.
The individual prices for the items Sarah is ordering.
Grilled Chicken Salad
$4.69
Fries
$1.49
Large
$1.59
Would it be less expensive for Sarah to purchase the Meal Deal or each item
separately?
Revised - 2016
Sharon Stiehm
Decimal - Answer Sheet
1.
5.67
+ 23.78
29.45
(When adding or subtracting decimal numbers, always line up the decimal
points vertically)
2.
45.7
x .005
.2285
(Multiply 457 by 5. From the right, count the number of decimal places
in the first and second lines. This is the number of decimal places
used in the product)
3.
45.7 ÷ .005 = 9140
(45.7 is the dividend and .005 is the divisor. The divisor must be a whole
number. Move the decimal point of the divisor three places to the right.
Then move the decimal point of the dividend three places to the right,
adding two zeros after seven to complete the move. Complete the
problem by dividing 45700 by 5 to obtain the quotient of 9140.)
4.
34.60
- 23.76
10.84
5.
170.00
- 167.94
2.06
6.
24 ÷ 16 = 1.5
7.
$126.73
- 50.00
$ 76.73
8.
23.5
+ 23.5
- 23.5
- 23.5
0
9.
10.
100
23
77
$12.37
78.86
+153.74
$244.97
Revised - 2016
$.75
x 3
$2.25
$244.97
+ 2.25
$247.22
Sharon Stiehm
11.
[4(7.5 – 4.9)] + 23.89 – 49 =
[4(2.6)] + 23.89 – 49 =
(10.4) + 23.89 – 49 =
10.4 + 23.89 – 49 =
34.29 – 49 = – 14.71
12.
2.65
1.69
+ 9.99
14.33
13.
$14.33 x .06 = .8598 (round to the nearest cent, $0.86)
$14.33
$20.00
+ .86
- 15.19
$15.19
$ 4.81
14.
$4.69
1.49
1.59
$7.77
Revised - 2016
20.00
- 14.33
5.67
$7.77
x .15
$1.1655
(round to the nearest cent)
$7.77
- 1.17
$6.60
Sharon Stiehm
Percentage Problems
1. Twelve is what percent of 30?
2. Astronauts lose 1% of their bone mass for each month of weightlessness. If Matt is
weightless in space for 5 months, how much bone mass did he lose?
3. What is 15% of 50?
4. Six is what percent of 20?
5. Change 0.45 into a percentage.
6. Change 2/3 into a percentage.
7. Change 5.1% into decimal form.
8. Change 5.1% into fractional form.
9. Change 1/8 into a percentage form.
10.
20% of what is 45?
11.
If 30% of the students failed the exam and there are 180 students in the course,
how many students passed the exam?
12.
X = 85% (200-180)
13.
If Katie weighs 125 lbs. and Marie weighs 10% more than Katie, how much does
Marie weigh?
14.
The skirt Mattie wants to buy is 25% off this week. If the original price was $49.99,
what is the sale price?
15.
Tony’s Bakery usually sells 250 desserts a day and typically 40 of these desserts
are pies. What percent of the desserts sold will be pies?
16.
Kurt buys 5 boxes of CDs in New Jersey where the sales tax rate is 7%. If each box
of CD costs $14.95, how much tax will be charged? How much money will Kurt
spend?
Revised - 2016
What does “x” equal?
Sharon Stiehm
Percentage Problems - Answers
1. 12 = 30x,
12 ÷ 30 = x,
x = .4 or 40%
2. 5%
3. 7.5
4. 30%
5. 45%
6. 66.7%
7. 0.051
8. 51/1000
9. 12.5%
10.
225
11.
0.3 x 180 = 54, 180 – 54 = 126
12.
x = 0.85 x 20,
13.
137.5 lbs. or rounded to 138 lbs.
14.
$49.99 x .25 = $12.50,
15.
40 = 250x,
16.
14.95 x 5 = $74.75,
Revised - 2016
x = 17
$49.99 - 12.50 = $37.49
40 ÷ 250 = x, x = .16 or 16%
$74.75 x .07 = 5.23 (tax),
$74.75 + 5.23 = $79.98
Sharon Stiehm
Arithmetic Problems
1.
Is negative five (–5) a whole number?
2.
Using whole numbers, complete the following problem:
Kari weighs 120 lbs. and Rachel weighs 150 lbs. How many more pounds does
Rachel weigh than Kari?
3.
Simplify the following: 15/3 =
4.
Multiply: 65 x 27 =
5.
12 + 235 + 4567 + 23,784 =
6.
A bag of oranges weighs 27 lbs. A bag of apples weighs 32 lbs. Find the total
weight of 16 bags of oranges and 5 bags of apples.
7.
A rectangular lot measures 200 ft. x 600 ft. What is the area of the lot? What is
the perimeter of the lot?
8.
482 + 1232 ÷ (50-42) = ____
9.
Simplify the following: 5.9 + 10.5 = ___; 12.9 – 8.6= ___; 3.8 x 2.9 = ___
10.
What is 5% of 20?
11.
Jenny weighs 10% less than Josh, who weighs 165 pounds. How much does
Jenny weigh?
12.
A box contains 5,000 staples. How many staplers can you fill from the box if each
stapler holds 250 staples?
13.
James Dean was only 24 years old when he died. He was born in 1931. In what
year did he die?
14.
Two with an exponent of 5 is equal to what?
15.
On Bailey’s first three math tests, she earned the following scores: 60%, 93%, and
86%. What is Bailey’s average score in math?
16.
True or False, 154 is evenly divisible by (6) six.
Revised - 2016
Sharon Stiehm
Arithmetic Problems - Answer Sheet
1.
No, the smallest whole number is (0) zero.
2.
Answer: 30
3.
Answer: 15 ÷ 3 = 5
4.
Answer: 1755
5.
Answer: 28,598
Subtract Kari’s weight from Rachel’s weight.
65
x 27
455
130
1755
12
235
4,567
+ 23,784
28,598
6. Answer: 592
First, multiply the number of bags by the number of pounds in
each bag. Then, add the two numbers together.
7. Area is 120,000 square feet. (The formula for the area of a rectangle is length
times width or A = wl).
The perimeter is 1600 feet. (The formula for the perimeter of a rectangle is two
times the length plus two times the width or 2L + 2w).
8. Answer: 636 First, do the subtraction within the parenthesis. Next, divide 1232
by the difference (the answer to the subtraction problem). Finally, add 482 to
the quotient (the answer to the division problem).
9.
10.
5.9
+10.9
Answers: 16.4
12.9
- 8.6
4.3
3.8
x 2.9
11.02
(Notice: the decimal points line up for
additional and subtraction problems)
In word problems, “of” means “to MULTIPLY” and “is” means “it EQUALS”.
Change 5% to the decimal form of .05 and the equation becomes:
X = .05 (20) or x = 1
(Note: Parentheses between numbers in the absence of an addition or
subtraction symbol, means “to multiply”).
Revised - 2016
Sharon Stiehm
11. Answer: 148.5 lbs Ten percent of 165 pounds is 16.5 pounds. Subtract 16.5 from
Josh’s weight to get Jenny’s weight.
Divide 5,000 by 250. 5,000 ÷ 250 = 20
12.
Answer: Twenty staplers
13.
Answer: 1955 Add the year James was born to the age at which he died.
14.
Answer: 32
15.
79.67%
(25 = 2 x 2 x 2 x 2 x 2 = 32)
60
93
+ 86
239 ÷ 3 = 79.67%
16. False, if you divide 154 by 6, you get a number containing a decimal (154 ÷ 6 =
25.67). Therefore, one-hundred fifty-four (154) is not evenly divisible by six (6).
Revised - 2016
Sharon Stiehm