HESI A-2 MATH
When working with fractions, which operations require a common denominator/
Addition and Subtraction
What are the metric units for volume of liquids from least to greatest?
A) Millimeter (ml) B) Centiliter (cl) C) Deciliter D) Liter E) Kiloliter (kl)
What are the US customary system units for weight from least to greatest?
A) Ounce B) Pound (lb) C) Ton
What are the US customary units for length from least to greatest?
A) Inch (in) B) Foot (ft) C) Yard (yd) D) Mile (mi)
When working with fractions, which operations require a common denominator?
Addition & Subtraction
What is a fraction?
It is an equation that represents a part of a whole, but can also be used to present ratios or division problems. An example of a fraction is x/y. in this ex, x is called the numerator, while y is the denominator
What are percentages?
They can be thought of as fractions with a denominator of 100
How many centiliters are in 4.7 kiloliters?
To convert a number with a unit prefixed as kilo into a unit prefixed centi, move across five columns to the right, meaning move the decimal place five places to the right. 4.7kl = 470,000 cl
Explain decimal addition, subtraction, multiplication, and division
* Addition & Subtraction; It is done the same way as regular addition and subtraction. Line up numbers at the decimal place and add or subtract. * Multiplication; Multiply as if the decimals are not there, then count the decimal places there are in the original problem. Use the total to place the decimal the same number of places over, counting from right to left. * Division; Remove the decimals from the denominator and mirror that movement in the numerator. The numerator does not need to be decimal free.
Explain decimal addition, subtraction, multiplication, and division
* Addition & Subtraction; It is done the same way as regular addition and subtraction. Line up the numbers at the decimal place and add or subtract. * Multiplication; Multiply as if the decimals are not there, then count the decimal places there are in the original problem. Use that total to place the decimal the same number of places over, counting from right to left. * Division; Remove the decimals from the denominator and mirror that movement in the numerator. The numerator does not need to be decimal free.
How are decimals converted to percentages and vice versa?
* Decimals and percentages can be converted by multiplying or dividing by 100 * To convert a percentage to a decimal, move the decimal point two places to the left and remove the % sign; 65% = 0.65 * To convert a decimal to a percentage, move the decimal point two places to the right and add a % sign; 0.33 = 33%
How do you change a fraction into a decimal and vice versa?
* Fraction to decimal; divide the denominator into the numerator until there are no remainders. There may be repeating decimals, so rounding is often acceptable. * Decimal to fraction; Place the decimal portion of the number over the respective place value, then reduce if possible. example; Express 0.25 as a fraction. This is read as twenty-five hundredths, so put 25 over 100. Then reduce to find the solution.
What are the metric system units for mass from least to greatest?
A) Milligram (mg) B) Centigram (cg) C) Gram (g) D) Kilogram (kg) E) Metric ton (MT)
Change 3 3/5 to a decimal. A) 3.6 B) 3.67 C) 3.3 D) 3.28
A) Divide 3 by 5 to get 0.6 and add that to the whole number 3, to get 3.6. An alternative is to incorporate the whole number 3 earlier on by creating an improper fraction: 18/5. Then dividing 18 by 5 to 3.6
How is a percentage converted into a fraction?
A percentage is a number per one hundred. So, a percentage can be converted toa fraction by making the number in the percentage the numerator and putting 100 as the denominator; 43% = 43/100
A bucket can hold 11.4 liters of water. A kiddie pool needs 35 gallons of water to be full. How many times will the bucket need to be filled to fill the kiddie pool? A) 12 B) 35 C) 11 D) 45
A) 12 Calculate how many gallons the bucket holds: 11.4 x 1gal/3.8l = 3gal. Now how many buckets to fill the pool which needs 35 gallons: 35/3 = 11.67. Since the amount is more is more than 11 but less than 12, we must fill the bucket 12 times.
The hospital has a nurse to patient ratio of 1:25. If there are 325 patients admitted, how many nurses are there. A) 13 nurses B) 25 nurses C) 325 nurses D) 12 nurses
A) 13 nurses. Using the given information of 1 nurse to 25 patients and 325 patients, set up an equation to solve for number of nurses. (N) : N/325 = 1/25.Multiply both sides by 325/25 = 13 nurses
Convert 2/9 to a percentage. A) 22% B) 4.5% C) 450% D) 0.22%
A) 22% - Converting from a fraction to a percentage generally involves two steps. First, the fraction needs to be converted to a decimal. Divide 2 by 9 which results in 0.22/ The top line indicates that the decimal actually goes on forever with an endless amount of 2's.Second, the decimal needs to be moved two places to the right: 22%
Convert 2/9 to a percentage A) 22% B) 4.5% C) 450% D) 0.22%
A) 22% Converting from a fraction to a percentage generally involves two steps. First, the fraction needs to be converted to a decimal. Divide 2 by 9 which results in 0.22 (repeating) The top lAine indicates that the decimal actually goes on forever with an endless amount of 2's. Second, the decimal needs to be moved two places to the right: 22%
Divide and reduce; 4/13 divided by 27/169 A) 52/169 B) 51/27 C) 52/29 D) 51/29
A) 52/27. Set up the division problem. 4/13 divided by 27/169. Flip the second fraction and multiply 4/13 x 169/27. Simplify and reduce with cross multiplication. 4/1 x 13/27. Multiply across the top and across the bottom to solve. 4x13 / 1x27 = 52/27
Multiply and reduce: 15/23 x 54/127 A) 810/2921 B) 81/292 C) 69/150 D) 810/2929
A) 810/2921 Line up the fractions 15/18 x 54/127. Multiply across the top and across the bottom. 15x54/23x127 = 810/2921
What time is 5:00 p.m. in military (24-hr clock) time? A) 1500 hours B) 1700 hours C) 0500 hours D) 0700 hours
B) 1700 hrs. To convert 5:00 P.m. into 24-hr time, add 12 to 5
A National Hockey League store in the state of Michigan advertises 50% off all items. Sales tax in Michigan is 6%. How much would a hat originally priced at $32.99 and a jersey originally priced at $64.99 cost during this sale? Round to the nearest penny. A) $97.98 B) $103.86 C) $51.93 D) $48.99
C) $51.93 calculate the sales prices; Hat Sale = 0.5 (32.99) = 16.495; Jersey Sale = 0.5 (64.99) = 32.495. Total the sales prices; Hat sale + jersey sale = 16.495 + 32.495= 48.99. Calculate the tax and add it to the total sale prices. Total after tax = 48.99 + (48.99 x 0.06) = $51.93
subtract and express in reduced form: 23/24 - 1/6 A) 22/18 B) 11/9 C) 19/24 D) 4/5
C) 19/24 Set up the problem and find a common denominator for both fractions. 23/24 - 1/6 multiply each fraction across by 1 to convert to a common denominator. 23/24 x 1/1 - 1/6 x 4/4 Once over the same denominator, subtract across the top. 23-4/24 = 19/24
Add and express in reduced form; 14/33 + 10/11 A) 2/11 B) 6/11 C) 4/3 D) 44/33
C) 4/3 set up the problem and find a common denominator for both fractions. 14/33 + 10/11 Multiply each fraction across by 1 to convert to a common denominator. 14/33 x 1/1 + 10/11 x 3/3 Once over the same denominator, add across the top .The total is over the common denominator. 14 = 30/33 = 44/33 Reduce by dividing both numerator and denominator by 11. 44 divided by 11 / 33 divided by11 = 4/3
What are mixed numbers?
Combine a whole number with a proper fraction, such as 3 1/2 . Any mixed number can be written as an improper fraction by multiplying the integer by the denominator, adding the product to the value of the numerator, and dividing the sum by the original denominator. ex; 3 1/2 = 3x2+1/2 = 7/2
What are mixed numbers?
Combine a whole number with a proper fraction, such as 3 1/2. Any mixed number can be written as an improper fraction by multiplying the interger by the denominator, adding the product to the value of the numerator, and dividing the sum by the original denominator. ex; 3 1/2 = 3x2+1/2 =7/2
8.4 is 20% of what number?
Convert the percent into a useable number 20% = 0.20 the given number is a percent of the answer needed, so divide the given number by this decimal rather than multiplying it. 8.4/0.20 = 42
What is 30% of 760?
Convert the percent into a useable number 30% = 0.30 "of" means to multiply. Set up the problem based on the givens, and solve 0.30 x 760 = 228
Multiply; 578 x 15= A) 8770 B) 8760 C) 8660 D) 8670
D) 8670 Begin with the left column on top and left column on the bottom (8x5). Move one column left on top and multiply by the far right column on the bottom. Starting on the far right column, on top, repeat this pattern for the next number left on the bottom. Continue the pattern. Add the answer rows together.
What number is MCDXXXII A) 1422 B) 1642 C) 1632 D) 1432
D) Break down the roman numerals into parts. M is equal to 1000. C is before D and is smaller than D, so it means D - C. CD = 500 - 100 = 400. Add the following; XXX = 10 + 10 + 10 = 30; II = 1 + 1 = 2. Add all parts, 1000 + 400 + 30 + 2 = 1432
How do you simplify the fraction 6/8?
Divide the numerator and denominator by 2 results in3/4, which is a simple fraction.
How do you simplify the fraction 6/8?
Divide the numerator and the denominator by 2 results in 3/4 which is a simple fraction.
How do you simplify the fraction 18/54 y dividing y the greatest common factor
First, determine the factors for the numerator and denominator. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54. Thus, the greatest common factor is 18. Dividing 18/54 by 18 leaves 1/3, which is the simplest fraction.
How do you simplify the fraction 18/54 by dividing the greatest common factor?
First, determine the factors for the numerator and denominator. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. Thus, the greatest common factor is 18. Dividing 18/54 by 18 leaves 1/3, which is the simplest fraction.
How do you convert military to regular time?
If the time is twelve hundred hours or less, it is equivalent to the am version in regular time. If the time is thirteen hundred hours or more, subtract twelve and add pm to convert it to regular time.
What is a proper fraction?
It has a numerator that is less than the denominator, such as 3/8
What is the order of operations?
It is a set of special rules to follow when solving equations with multiple operations. The order is as follows. * Parentheses * Exponents * Multiplication & Division from left to right * Addition & Subtraction from left to right A popular mnemonic device to help remember the order is; Please Excuse My Dear Aunt Sally (PEMDAS)
What is a fraction?
It is an equation that represents a part of a whole, but can also be used to present ratios or division problems. An example of a fraction is x/y. In this ex; x is called the numerator, while y is the denominator.
What is a ratio?
It shows the relationship between two quantities. If the ratio of boys to girls is given as 2 to 5, that means there are 2 boys to every 5 girls in the class. Ratios can also be compared if the units in each ratio are the same. The ratio of boys to girls in the math class can be compared to the ratio of boys to girls in a science class by stating which ratio is higher and which is lower.
What is military time?
It uses a 24 hour clock. What regular time considers 1 am is called 0100 (pronounced zero one hundred hours) in military time. This continues until you reach 12pm or 1200, pronounced "twelve hundred hours" and then continues the count to 1300, 1400, 1500, and so on. Midnight is the 24th hour in the count.
What is the guaranteed way to find a common denominator?
Multiply the two denominators together
How are fractions added and subtracted?
Once equivalent fractions have been found with common denominators, simply add or subtract the numerators to arrive at the answer ex; 1/2 + 3/4 = 2/4 + 3/4 = 5/4 ex; 7/9 - 4/15 = 35/45 - 12/25 = 23/45
How are whole numbers converted to fractions?
Place the whole number as the numerator and make the denominator 1 Ex; 3 = 3/1
How are whole numbers converted to fractions?
Place the whole number as the numerator and make the denominator 1 ex; 3 = 3/1
What are rates and unit rates?
Rates - compare two qualities with different units Unit rates - the denominator in the comparison of two units is 1 EXAMPLE: If you can type at a rate of 1000 words in 5 min, then your unit rate is 1000/5=200 wpm. Any rate can be converted into a unit rate by dividing to make the denominator 1
How do you multiply two fractions?
Simply multiply the numerators, multiply the denominators, and place the products as a fraction. ex; 2/5 x 3/4 = 6/20 = 3/10
If 20% of the class is girls and 30 students are in the class, how many girls are in the class?
Start with the common proportion %/100 = is/of. Within the proportion, % is the % of girls, 100 is the total % of the class. "is" is the number of girls, and "of" is the total number of students in the class. Placing the known values in appropriate spots gives you 20/100 = x/30. Solve for x. Cross-multiplying results in the equation; 20 x 30 = 100x; x=6
How many liters are there in 30 microliters?
Start with the unit marked micro and count the columns moving to the left until you reach the base unit for liters. Be sure to count the blank columns, as they important placeholders. There are six columns from micro to the base unit moving to the left, so move the decimal place six places to the left. 30ml = 0.000030 L
XXIX is what number?
There are two identical numbers next to each other (XX) so add them; 10+10 = 20 Next there is a smaller number (I) in front of a larger number (X) so subtract those 10-1=9 Finally combine all portions to get the total 20 + 9 =29
What are equivalent fractions?
They are fractions of the same value. For ex; 2/4, 4/8, 50/100, and 75/150 are equivalent, as they all equal 1/2
What are equivalent fractions?
They are fractions of the same value. ex; 2/4, 4/8, and 75/150 are equivalent as they all equal 1/2
What are variables?
They represent the unknown quantities or values. Variables are usually represented by a letter, such as X or Y. These are helpful when attempting to solve story problems. In algebra, letters are sometimes used to symbolize fixed values. In this case, the letters are called constants.
Express 0.455 as a fraction
This is read as four hundred fifty - five thousandths, so put 455 over 1000. Then reduce to find the solution 445/1000 = 91/200
What do the roman numerals below stand for? V X L C D M
V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000