NH Test 4 math

How many grams are in a kilogram? 1,000 1/100 1/1,000 100

1,000 There are 1,000 grams in a kilogram. Here are some other metric length conversions to remember: kilometer = 1,000 meters meter = 100 centimeters 1 centimeter = 10 millimeters 2.54 centimeters = 1 inch

A pharmacist divided 8/9 of a kilogram of medication into 8 equal packages to be distributed to local hospitals. What was the weight of each package in kilograms? 1/4 1/9 2/9 3/8

1/9 We can solve this problem by dividing the total weight of the medication (8/9) by 8 packages. Step 1: Use this rule to divide fractions: a ÷ b/c = a × c/b All the rule above states is: to divide fractions, flip the second fraction and multiply. Note that any whole number written as a fraction is that number over 1, so we can express 8 as a fraction as 8/1. Of course, when we flip the second fraction in division, 8/1 becomes 1/8. Step 2: Simplify. 8 x 1 = 8 and 9 x 8 = 72. Step 3: Reduce the fraction to its simplest form. The numerator (8) and denominator (72) are both divisible by 8. Answer: 1/9

Solve for g: (3g − 10)/4 = 5 -8 -10 10 8

10 (3g − 10)/4 = 5 Step 1: Multiply both sides of the equation by 4. (3g − 10)/4 × 4 = 5 × 4 3g − 10 = 20 Step 2: Add 10 to both sides. 3g − 10 + 10 = 20 + 10 3g = 30 Step 3: Divide both sides by 3. 3g ÷ 3 = 30 ÷ 3 g = 10 Answer: 10

What number in Arabic numerals is Roman numeral MCLVI? (Enter numeric value only.)

1156 The Arabic numeral conversion for the number MCLVI: M = 1000 C = 100 L = 50 VI = 6 1000 + 100 + 50 + 6 = 1156 Answer: 1156 NurseHub Hint: Here are a couple of quick rules to help you when it comes to Roman numerals: You cannot have more than three of the same symbols in a row. (You will never see XXXX or DDDD.) Add smaller symbol values that are placed after large symbol values. (XI = 10 + 1 = 11.) Subtract smaller symbol values that are placed before large symbols values. (IX = 10 - 1 = 9.) And here are some symbols you should memorize: I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1,000

For every 20 patients that spend the night, Stoney Brook Hospital must have 5 nurses working the night shift. How many nurses must Stoney Brook Hospital have working the night shift if 48 patients are spending the night? 10 20 12 15

12 This is a ratio/proportion problem. We have 20 patients require 5 nurses. So, how many nurses will 48 patients require? We can write that as a proportion: 20: 5 :: 48: x Step 1: Rewrite the proportion as a fraction. Step 2: Cross multiply. Step 3: Simplify the right side of the equation. 48 x 5 = 240 Step 4: Simplify by dividing both sides of the equation by 20.

Convert to military time: 4:25:20 P.M. 2025:20 hours 1325:20 hours 1604:20 hours 1625:20 hours

1625:20 hours Step 1: Since the time is P.M., we need to add 12 to obtain the hours. 4 + 12 = 16 Step 2: Write as military time. Note that military time has a colon (:) separating minutes and seconds only. 1625:20 hours.

2⁄3 × 3⁄4 × 5 = 3 1⁄2 1 1⁄2 4 1⁄2 2 1⁄2

2 1⁄2 Step 1: Use this rule: a/b × c/d × e/f= ace/bdf to multiply fractions. Note that a whole number as a fraction is that number over 1. Step 2: Simplify. 2 x 3 x 5 = 30 and 3 x 4 x 1 = 12. Step 3: Both the numerator (30) and the denominator (12) is divisible by 6, so we can reduce the fraction. Step 4: Convert to a mixed fraction. To convert to a mixed fraction, we divide the numerator by the denominator. The quotient is the whole number. Any remainder stays in the numerator. Answer: 2 1⁄2

Subtract: 11/15 - 3/5 = 2/15 2/11 1/15 4/15

2/15 Step 1: Find the Least Common Denominator (LCD). There are two ways we can do this: Method 1: Find the first common multiple. List out all multiples of each denominator and find the first common one. Multiples of 15: 15, 30, 45... Multiples of 5: 5, 10, 15... Therefore, LCD is 15. Method 2: Prime Factors. The LCD will be the product of the largest multiple of each prime that appears on at least one list. Prime factors of 15: 3, 5 Prime factors of 5: 5 So, the LCD is 3 x 5 = 15 Step 2: Make the denominators the same as the LCD. Step 3: Simplify. The denominators are now the same. Step 4: Join the denominators. Step 5: Simplify. Answer: 2/15

A cafe offers two kinds of espresso: single-shot and double-shot. Yesterday, the cafe sold 120 espressos in all, 75% of which were single-shot. How many double-shot espressos did the cafe sell?

20 50 30 60 Incorrect Answer: 30 Since the cafe only sold two types of espresso and 75% of the total sold espressos (120) are single-shot, the number of double-shot espressos should be 100% - 75% = 25% of the total espressos. Step 1: Use the percent formula to calculate the number of double-shot espressos. The percent formula is below: We know that the "whole" is 120, and 25% of the whole is the number of double-shot espressos. So, we are looking for the "part", and that is where we will put our x. Step 2: Cross multiply. Step 3: Simplify the right side of the equation. 25 x 120 = 3000. Step 4: Simplify by dividing both sides of the equation by 100. Answer: 30

A patient complaining of restlessness drinks 5 12-oz cups of coffee each day. If the doctor recommends cutting the coffee intake back by 60%, how many ounces of coffee can the patient have each day? 24 32 42 36

24 We can solve this problem by calculating how many ounces of coffee the patient drinks each day, and then calculating how many ounces they are allowed to drink. Since we are told they need to cut back 60%, this means they are allowed to drink 100% - 60% = 40% of their current daily intake. Step 1: Calculate the total number of ounces of coffee the patient currently drinks. 5 cups × 12 ounces = 60 ounces Step 2: Use the percent formula to calculate how much of the current 60 ounces the patient is allowed to drink. The percent formula is below: We know that the current "whole" is 60 oz. We also know that, since they need to cut back by 60%, they are only permitted to drink 100% - 60% = 40% of the current whole value. We are searching for "part", so that is where we will place our x. Step 3: Cross multiply. Step 4: Simplify the right side of the equation. 60 × 40 = 2,400. Step 5: Simplify by dividing both sides of the equation by 100. NurseHub Hint: Read the problem carefully. Many people fall into the trap of solving for 60%. However, this is how much the patient needs to cut back, not how much they are allowed to drink, which is what the problem asks.

A hospital staff member is filling IV bags with saline. They have 6 1/4 liters of saline. Each IV bag requires 1 2/3 liters of saline. How many IV bags can the staff member fill with saline? 3 3/4 10 5/12 6 3/8 13/15

3 3/4 We can solve this problem by dividing the amount of saline the staff member has (6 1/4 ) by the amount each IV bag requires (1 2/3). Step 1: Convert 6 1/4 and 1 2/3 into improper fractions. Use the rule a b/c = (ac + b)/c to convert a mixed number to an improper fraction. In words, you multiply the denominator (bottom number) by the whole number and then add the numerator. Put that number over the denominator to create the improper fraction. Step 2: Simplify. 6 × 4 + 1 = 25 and 1 × 3 + 2 = 5 Step 3: Use this rule to divide fractions: a ÷ b/c = a × c/b All the rule above states is: to divide fractions, flip the second fraction and multiply. Step 4: Simplify. 25 × 3 = 75 and 4 × 5 = 20 Step 5: Reduce the fraction to its simplest form. We can divide both the numerator (75) and denominator (20) by 5. Step 6: Convert to a mixed fraction. To convert to a mixed fraction, we divide the numerator by the denominator. The quotient is the whole number. Any remainder stays in the numerator. Answer: 3 3/4

Change 0.006 into a fraction and reduce to the lowest term. (Use a backslash "/" when entering your answer. e.g. 1/2)

3/500 Step 1: Figure out which place the last digit is in. The last digit of 0.006 is in the thousandths place, so our denominator will be 1,000. The numerator is 6. Step 2: Simplify by reducing the fraction to its lowest term. Answer:3/500

Convert 108°Fahrenheit to Celsius. (Enter numerical values only. If rounding is necessary round to the nearest whole number.)

42 Step 1: Use the following formula to convert temperature from °F to °C: Step 2: Substitute °F with the value we are converting from. Step 3: Simplify inside the parentheses. 54 - 32 = 22. Step 4: Simplify. 76 × 5/9 = 42.22 Step 5: Round to the nearest whole number. 42.22 → 42 Answer: 42

Evaluate the expression (m − n)(3m + n²) + 5mn if m = 10 and n = 3. 270 273 423 8,673

423 Step 1: Substitute the numbers into the given expression. m = 10 and n = 3 (m − n)(3m + n²) + 5mn (10 − 3)(3 • 10 + 3²) + 5(10)(3) Step 2: Simplify following the order of operations (PEMDAS): Parentheses and Exponents (10 − 3)(3 • 10 + 3²) + 5(10)(3) (10 − 3)(3 • 10 + 9) + 5(10)(3) (10 − 3)(30 + 9) + 5(10)(3) (7)(39) + 5(10)(3) Multiplication and Division (7)(39) + 5(10)(3) 273 + 150 Addition and Subtraction 273 + 150 = 423 Answer: 423

Solve the proportion: x: 9 :: 140: 28 5 45 15.6 120

45 Step 1: Rewrite the proportion as a fraction. Step 2: Cross multiply. Step 3: Simplify the right side of the equation. 9 × 140 = 1,260. Step 4: Simplify by dividing both sides of the equation by 28. Answer: 45

How many milliliters are in 15 ounces? 450 150 30 300

450 There are 30 milliliters in 1 ounce. To get how many milliliters are in 15 ounces, we multiply 30 milliliters by 15 ounces. 15 ounces × 30 ml /1 ounce = 450 ml NurseHub Hint: In dimensional analysis, the unit that you want to convert to goes on the top of the fraction. The unit you want to convert from goes on the bottom.

Change 47.365 into a fraction and reduce to the lowest term. (Use a backslash "/" when entering your answer. e.g. 1/2)

47 73/200 Step 1: Split the number into its whole number and decimal components. Step 2: Convert the decimal to a fraction. In order to do so, we first need to figure out which place the last digit is in. The last digit (5) is in the thousandths place, so our denominator will be 1000. The numerator is 365. Step 3: Simplify by reducing the fraction to its lowest term. We simplify by dividing the numerator and denominator by their greatest common factor. The greatest common factor of our numerators (365) and (1000) is 5. 365 ÷ 5 = 73 1000 ÷ 5 = 200 so we have: Answer: 47 73/200

How many feet are in 60 inches? 5 600 720 6

5 1 foot is made up of 12 inches. To get how many feet are in 60 inches, we divide 60 inches by 1 foot (12 inches). 60 in * 1 ft/12in = 5 ft NurseHub Hint: In dimensional analysis, the unit that you want to convert to goes on the top of the fraction. The unit you want to convert from goes on the bottom.

Solve for f: f − 10 + 3f = (f + 9)/2 + 3 -5 5 3 -3

5 f − 10 + 3f = (f + 9)/2 + 3 Step 1: Simplify 4f − 10 = (f + 9)/2 + 3 Step 2: Multiply both sides by 2. (4f − 10) × 2 = ( (f + 9)/2 + 3) × 2 8f − 20 = f + 9 + 6 Step 3: Simplify 8f − 20 = f + 15 Step 4: Add 20 to both sides. 8f − 20 + 20 = f + 15 + 20 8f = f + 35 Step 5: Subtract f from both sides. 8f − f = f − f + 35 7f = 35 Step 6: Divide both sides by 7. 7f ÷ 7 = 35 f = 5 Answer: 5

Evaluate the expression (a² + b² + c²) − 2(ab + bc) if a= −1, b= −2, and c= −5 2 4 6 7

6 Step 1: Substitute the numbers into the given expression. a= −1, b= −2, and c= −5 (a² + b² + c²) − 2(ab + bc) (−1² + −2² + −5²) − 2(−1 • −2 + −2 • −5) Step 2: Simplify following the order of operations (PEMDAS): Parentheses and Exponents (−1² + −2² + −5²) − 2(−1 • −2 + −2 • −5) (1 + 4 + 25) − 2(−1 • −2 + −2 • −5) (30) − 2(2 + 10) (30) − 2(12) Multiplication and Division (30) − 2(12) 30 − 24 Addition and Subtraction 30 − 24 = 6 Answer: 6

Add: 14/3 + 12/15 + 9/5 = 7 2/15 7 7/15 7 4/15 7 1/15

7 4/15 Step 1: Find the Least Common Denominator (LCD). There are two ways we can do this: Method 1: Find the first common multiple. List out all multiples of each denominator and find the first common one. Multiples of 3: 3, 6, 9, 12, 15... Multiples of 15: 15, 30... Multiples of 5: 5, 10, 15... Therefore, the LCD is 15. Method 2: Prime Factors. The LCD will be the product of the largest multiple of each prime that appears on at least one list. Prime factors of 3: 3 Prime factors of 15: 3, 5 Prime factors of 5: 5 Therefore, the LCD is 3 x 5 = 15. Step 2: Make the denominators the same as the LCD. Step 3: Simplify. The denominators are now the same. Step 4: Join the denominators. Step 5: Simplify. Step 6: Convert to a mixed number. Answer: 7 4/15

A vehicle requires 10 gallons of fuel to reach a certain destination, how many pints of fuel is required for that trip? (Enter numerical values only)

80 We can solve this problem using dimensional analysis. Here are the measurement conversions we will need to know: 1 gallon = 4 quarts 1 quart = 2 pints Step 1: 1 gallon equals 4 quarts. So, 10 gallons equal 40 quarts. Step 2: 1 quart equals 2 pints. So, 40 quarts equal 80 pints. Answer: 80 NurseHub Hint: In dimensional analysis, the unit that you want to convert to goes on the top of the fraction. The unit you want to convert from goes on the bottom.

On Saturday the farmers at Pacific Farm picked 3/4 of a barrel of tomatoes. Sunday, the farmers picked 6/7 as many tomatoes as on Saturday. How many barrels of tomatoes did the farmers pick on Sunday? 11/14 9/14 9/11 13/14

9/14 The number of barrels of tomatoes can be found by multiplying 3/4 and 6/7. The phrase "as many" usually means you need to multiply. Step 1: Use this rule: a/b × c/d = ac/bd to multiply fractions. Step 2: Simplify. 3 x 6 = 18 and 4 x 7 = 28. Step 3: Reduce the fraction to its simplest form. We can divide both the numerator (18) and the denominator (28) by 2. Answer: 9/14

Lisa has prepared 2 gallons of a chemical solution for a science project. How much solution did she prepare in quarts? (Enter numerical values only)

We can solve this problem using dimensional analysis. Here are the measurement conversions we will need to know: 1 gallon = 4 quarts Step 1: 1 gallon equals 4 quarts. So, 2 gallons equal 8 quarts. NurseHub Hint: In dimensional analysis, the unit that you want to convert to goes on the top of the fraction. The unit you want to convert from goes on the bottom.