Perform Arithmetic Operations - TEAS Mathematics

1. Subtract: $\dfrac{9}{10}-\dfrac{1}{3}$.
   Answer: $\dfrac{17}{30}$ When subtracting fractions with different denominators, you must first find a common denominator before performing the operation. This ensures you're subtracting like quantities. To subtract $\frac{9}{10}-\frac{1}{3}$, find the least common denominator (LCD) of 10 and 3. Since these numbers share no common factors other than 1, multiply them: 10 × 3 = 30. Convert each fraction to an equivalent fraction with denominator 30: - $\frac{9}{10} = \frac{9 \times 3}{10 \times 3} = \frac{27}{30}$ - $\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}$ Now subtract: $\frac{27}{30} - \frac{10}{30} = \frac{27-10}{30} = \frac{17}{30}$ Looking at the wrong answers: Choice B ($\frac{7}{30}$) results from incorrectly subtracting 9 - 1 = 8 and 10 - 3 = 7, then writing $\frac{7}{30}$—this shows a fundamental misunderstanding of fraction subtraction. Choice C ($\frac{8}{30}$) likely comes from subtracting numerators without proper conversion: 9 - 1 = 8. Choice D ($\frac{19}{30}$) might result from adding instead of subtracting: $\frac{27}{30} + \frac{10}{30} = \frac{37}{30}$, then somehow getting confused about the calculation. The correct answer is A: $\frac{17}{30}$. Study tip: Always convert to a common denominator first, then perform operations only on the numerators. Double-check that you're performing the correct operation (addition vs. subtraction) and that your equivalent fractions are accurate.
2. Simplify $\dfrac{3}{4}+\dfrac{5}{6}$ and express the answer as a mixed number.
   Answer: $1\dfrac{7}{12}$ When adding fractions, you need a common denominator before you can combine the numerators. Here, you're working with $\frac{3}{4}$ and $\frac{5}{6}$, which have different denominators. To find the least common denominator (LCD), look for the smallest number that both 4 and 6 divide into evenly. The multiples of 4 are 4, 8, 12, 16... and the multiples of 6 are 6, 12, 18... So the LCD is 12. Convert each fraction: $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$ and $\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$ Now add: $\frac{9}{12} + \frac{10}{12} = \frac{19}{12}$ Since 19 > 12, this improper fraction converts to a mixed number. Divide 19 by 12: $19 ÷ 12 = 1$ remainder $7$, so $\frac{19}{12} = 1\frac{7}{12}$. This confirms answer B. Choice A ($1\frac{1}{6}$) likely comes from incorrectly using 6 as the common denominator or making an arithmetic error. Choice C ($1\frac{5}{12}$) suggests adding the numerators incorrectly, perhaps getting 14 instead of 19. Choice D ($1\frac{3}{8}$) might result from using 8 as the common denominator or other conversion mistakes. Remember: always find the LCD first, convert both fractions, then add the numerators. When your result is an improper fraction, divide the numerator by the denominator to create the mixed number.
3. Evaluate $15.3-(2.75+4.605)$.
   Answer: $7.945$ This problem tests your ability to correctly apply the order of operations with decimal numbers. When you see parentheses in an expression, you must evaluate what's inside them first before performing any other operations. Start by calculating what's inside the parentheses: $2.75 + 4.605$. Line up the decimal points carefully: 2.750 + 4.605 = 7.355. Now substitute this back into the original expression: $15.3 - 7.355$. Again, align the decimal points: 15.300 - 7.355 = 7.945. Looking at the wrong answers: Choice B ($8.055$) likely results from a decimal alignment error when subtracting, possibly miscalculating $15.3 - 7.355$ as $15.3 - 7.245$. Choice C ($12.555$) represents the common mistake of adding instead of subtracting: $15.3 + 2.75 - 4.605$ or ignoring the parentheses entirely and calculating left to right incorrectly. Choice D ($7.655$) probably comes from an error in the initial addition within parentheses, perhaps calculating $2.75 + 4.605$ as $7.645$ instead of $7.355$. The correct answer is A: $7.945$. For TEAS math success, always follow order of operations religiously: parentheses first, then work outward. When working with decimals, write out extra zeros as placeholders (like 15.300) to help with alignment. Double-check your decimal addition and subtraction by verifying that your decimal points stay aligned throughout your calculations.
4. Evaluate $(6-2.4)\div0.3$.
   Answer: $12$ This problem tests your ability to follow the order of operations (PEMDAS) when working with decimal arithmetic. When you encounter expressions with parentheses and division, always work from left to right, handling parentheses first. Start by evaluating the expression inside the parentheses: $6 - 2.4 = 3.6$. Now you have $3.6 \div 0.3$. To divide by a decimal, you can think of this as asking "how many groups of 0.3 fit into 3.6?" You can solve this by converting to a fraction: $\frac{3.6}{0.3} = \frac{36}{3} = 12$. Alternatively, multiply both numbers by 10 to eliminate the decimal: $36 \div 3 = 12$. Looking at the wrong answers: Choice A (10) likely comes from incorrectly calculating $6 - 2.4$ as 4.0, then dividing by 0.3, or making an arithmetic error in the division step. Choice C (8) might result from mishandling the decimal placement or confusing the order of operations. Choice D (14) could come from adding instead of subtracting in the first step ($6 + 2.4 = 8.4$), then making an error in division. The correct answer is B (12). When working with decimal operations on the TEAS, always double-check your arithmetic by estimating first. Here, $3.6 \div 0.3$ should give you a number larger than 3.6 since you're dividing by something less than 1. This estimation helps you catch calculation errors quickly.
5. A cleaner is mixing a solution. They are supposed to mix $\frac{1}{8}$ cup of concentrate for every $1\frac{1}{2}$ cups of water. The cleaner needs to make a large batch and uses a full 6-cup bottle of concentrate. However, they mistakenly use $0.25$ cups less water for every $\frac{1}{8}$ cup of concentrate used. How many cups of water did the cleaner actually use?
   Answer: 60 cups This problem requires determining the number of units, calculating the correct amount of water, and then calculating the error. Step 1: Determine how many units of the recipe ratio the cleaner is making. The base unit of concentrate is $\frac{1}{8}$ cup. The cleaner uses 6 cups. $$\text{Number of units} = 6 \div \frac{1}{8} = 6 \times 8 = 48 \text{ units}$$ Step 2: Calculate the correct amount of water that should have been used. Each unit requires $1\frac{1}{2}$ or 1.5 cups of water. $$\text{Correct water} = 48 \times 1.5 = 72 \text{ cups}$$ This is a distractor. Step 3: Calculate the amount of water the cleaner actually used per unit. They used 0.25 cups less than the required 1.5 cups. $$\text{Actual water per unit} = 1.5 - 0.25 = 1.25 \text{ cups}$$ Step 4: Calculate the total amount of water actually used for all 48 units. $$\text{Total actual water} = 48 \times 1.25 = 60 \text{ cups}$$
6. A nurse shares $0.75\text{ L}$ of solution equally among 4 patients. How many liters does each patient receive?
   Answer: $0.1875\text{ L}$ When you encounter a problem asking you to divide a quantity equally among a certain number of people or groups, you're dealing with a straightforward division problem. Here, you need to find how much solution each patient receives when $0.75\text{ L}$ is shared equally among 4 patients. To solve this, divide the total amount by the number of patients: $0.75 ÷ 4 = 0.1875\text{ L}$. You can think of this as $\frac{0.75}{4}$ or convert to fractions: $\frac{3}{4} ÷ 4 = \frac{3}{4} × \frac{1}{4} = \frac{3}{16} = 0.1875$. Answer A ($0.1875\text{ L}$) is correct because it represents the exact result of dividing $0.75$ by $4$. Answer B ($0.1750\text{ L}$) likely results from a calculation error, perhaps incorrectly computing the division or rounding prematurely during the process. Answer C ($0.2000\text{ L}$) suggests the error of dividing by 3 instead of 4, or possibly estimating $0.75 ÷ 4$ as approximately $0.8 ÷ 4 = 0.2$. Answer D ($0.0250\text{ L}$) appears to result from a major computational error, possibly dividing by a much larger number or misplacing decimal points. For division problems involving decimals on the TEAS, always double-check your work by multiplying your answer by the divisor to see if you get back to the original number. Here: $0.1875 × 4 = 0.75$ ✓.
7. A complex chemical process involves three stages. In Stage 1, the temperature of a substance is increased from an initial -18.5°C by 42.8°C. In Stage 2, the new temperature is reduced by exactly $\frac{2}{5}$ of its current value. In Stage 3, the temperature is then divided by -0.3. What is the final temperature in degrees Celsius?
   Answer: -48.6°C This is a multi-step problem involving operations with decimals and fractions. Step 1: Calculate the temperature after Stage 1. $$-18.5°C + 42.8°C = 24.3°C$$ Step 2: Calculate the temperature reduction in Stage 2. The reduction is $\frac{2}{5}$ of the current temperature (24.3°C). $\frac{2}{5} \times 24.3 = 0.4 \times 24.3 = 9.72°C$. The new temperature is $24.3°C - 9.72°C = 14.58°C$. Step 3: Calculate the final temperature after Stage 3. Divide the result from Stage 2 by -0.3. $$14.58°C \div (-0.3) = -48.6°C$$ The final temperature is -48.6°C.
8. Simplify $12\dfrac{5}{8}-4\dfrac{3}{4}$.
   Answer: $7\dfrac{7}{8}$ When subtracting mixed numbers, you need to handle the whole numbers and fractions separately, but first ensure the fractions have a common denominator. Start by converting both fractions to the same denominator. Since $\frac{3}{4} = \frac{6}{8}$, you can rewrite the problem as: $12\frac{5}{8} - 4\frac{6}{8}$. Now you face a key challenge: you can't subtract $\frac{6}{8}$ from $\frac{5}{8}$ directly since $\frac{5}{8} < \frac{6}{8}$. You need to borrow 1 from the whole number part. Convert $12\frac{5}{8}$ to $11\frac{13}{8}$ (since $1 = \frac{8}{8}$, and $\frac{5}{8} + \frac{8}{8} = \frac{13}{8}$). Now subtract: $11\frac{13}{8} - 4\frac{6}{8} = (11-4) + (\frac{13}{8} - \frac{6}{8}) = 7\frac{7}{8}$. Choice A ($7\frac{7}{8}$) is correct. Choice B ($8\frac{1}{8}$) results from forgetting to borrow and somehow getting $8 - 4 = 4$ plus an incorrect fraction calculation. Choice C ($7\frac{3}{4}$) comes from incorrectly subtracting $\frac{3}{4} - \frac{5}{8}$ without proper borrowing. Choice D ($8$) suggests subtracting just the whole numbers ($12 - 4 = 8$) while ignoring the fractional parts entirely. Remember: when the fraction you're subtracting is larger than the fraction you're subtracting from, always borrow 1 from the whole number and add it to your fraction as an improper fraction before proceeding.
9. Calculate $\dfrac{5}{8}\times\dfrac{4}{15}$.
   Answer: $\dfrac{1}{6}$ When you see fraction multiplication problems, remember that you multiply straight across: numerator times numerator, denominator times denominator. However, the key to efficiency is simplifying before you multiply to avoid working with large numbers. Let's calculate $\dfrac{5}{8}\times\dfrac{4}{15}$. Before multiplying, look for common factors you can cancel. Notice that 5 (from the first numerator) and 15 (from the second denominator) share a common factor of 5. Also, 4 (from the second numerator) and 8 (from the first denominator) share a common factor of 4. Simplifying first: $\dfrac{5}{8}\times\dfrac{4}{15} = \dfrac{5÷5}{8}\times\dfrac{4}{15÷5} = \dfrac{1}{8}\times\dfrac{4}{3}$ Now simplify 4 and 8: $\dfrac{1}{8÷4}\times\dfrac{4÷4}{3} = \dfrac{1}{2}\times\dfrac{1}{3} = \dfrac{1}{6}$ This confirms answer A is correct. Looking at the wrong answers: B ($\dfrac{1}{12}$) likely comes from incorrectly canceling factors or making arithmetic errors during simplification. C ($\dfrac{2}{15}$) might result from only partially simplifying or mixing up which numbers to cancel. D ($\dfrac{3}{10}$) could come from adding instead of multiplying the fractions or making calculation mistakes. For TEAS success with fraction multiplication: always look for opportunities to simplify before multiplying. Cross-canceling common factors between any numerator and any denominator saves time and reduces errors. Practice identifying these patterns quickly.
10. A pharmacist is preparing a diluted medication. She starts with $12.5$ milliliters (mL) of a concentrated drug, which she mixes into $237.5$ mL of a saline solution. The total mixture is then divided into 5 equal doses. Over the course of a day, a patient receives 3 of these doses. What is the total volume of the concentrated drug the patient has received?
    Answer: 7.5 mL This problem includes extra information to distract from the core question. The key is to track only the volume of the concentrated drug. Step 1: Identify the starting amount of the concentrated drug. This is given as 12.5 mL. The amount of saline (237.5 mL) and the total initial mixture volume (12.5 + 237.5 = 250 mL) are relevant for context but not for the final calculation about the drug itself. Step 2: The total amount of concentrated drug (12.5 mL) is distributed equally among 5 doses. Find the amount of drug per dose. $$\frac{12.5 \text{ mL of drug}}{5 \text{ doses}} = 2.5 \text{ mL of drug per dose}$$ Step 3: The patient receives 3 doses. Calculate the total amount of concentrated drug in those 3 doses. $$2.5 \text{ mL/dose} \times 3 \text{ doses} = 7.5 \text{ mL}$$ The total volume of concentrated drug received by the patient is 7.5 mL.
11. A water tank is filled to $\frac{7}{8}$ of its capacity. A pump removes water at a rate of 3.5 gallons per minute. After 15 minutes, the tank is exactly $\frac{1}{4}$ full. What is the total capacity of the tank in gallons?
    Answer: 84.0 gallons This problem requires finding a whole from a part. Step 1: Calculate the total volume of water removed from the tank. $$3.5 \text{ gallons/minute} \times 15 \text{ minutes} = 52.5 \text{ gallons}$$ Step 2: Calculate the fraction of the tank's capacity that this removed water represents. The level dropped from $\frac{7}{8}$ to $\frac{1}{4}$. Find the difference. $\frac{7}{8} - \frac{1}{4} = \frac{7}{8} - \frac{2}{8} = \frac{5}{8}$. So, 52.5 gallons is equal to $\frac{5}{8}$ of the tank's total capacity. Step 3: Let 'C' be the total capacity. Set up an equation: $\frac{5}{8} \times C = 52.5$. Step 4: Solve for C. $$C = 52.5 \div \frac{5}{8} = 52.5 \times \frac{8}{5} = \frac{420}{5} = 84$$ The total capacity of the tank is 84.0 gallons.
12. Find $2\dfrac{3}{4}\times\dfrac{8}{11}$.
    Answer: $2$ When multiplying a mixed number by a fraction, you have two main approaches: convert the mixed number to an improper fraction, or use the distributive property. Let's use the first method since it's typically more straightforward. First, convert $2\frac{3}{4}$ to an improper fraction: $2\frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{11}{4}$ Now multiply: $\frac{11}{4} \times \frac{8}{11} = \frac{11 \times 8}{4 \times 11} = \frac{88}{44}$ Notice that both the numerator and denominator contain the factor 11, so they cancel: $\frac{88}{44} = \frac{8}{4} = 2$ The answer is B) $2$. Let's examine why the other choices are incorrect. Choice A) $1\frac{8}{11}$ would result from incorrectly multiplying just the whole number part (2) by the fraction, ignoring the fractional part $\frac{3}{4}$. Choice C) $2\frac{2}{11}$ likely comes from calculation errors when converting between mixed numbers and improper fractions. Choice D) $1\frac{9}{11}$ might result from adding the fractions instead of multiplying, or from other computational mistakes during the conversion process. Study tip: When multiplying mixed numbers and fractions, always convert mixed numbers to improper fractions first. Look for opportunities to cancel common factors before multiplying—this prevents working with unnecessarily large numbers and reduces calculation errors. In this problem, recognizing that 11 appears in both fractions saves significant computation time.
13. Find the value of $\frac{2}{5}+\frac{1}{4}+\frac{3}{10}$.
    Answer: $\dfrac{19}{20}$ When adding fractions with different denominators, you need to find a common denominator before combining the numerators. This question tests your ability to work with multiple fractions simultaneously. To solve $\frac{2}{5}+\frac{1}{4}+\frac{3}{10}$, first identify the least common denominator (LCD) of 5, 4, and 10. The LCD is 20 because it's the smallest number that all three denominators divide into evenly. Convert each fraction to have denominator 20: - $\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}$ - $\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$ - $\frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}$ Now add the numerators: $\frac{8}{20} + \frac{5}{20} + \frac{6}{20} = \frac{19}{20}$ Choice A ($\frac{19}{20}$) is correct. Choice B ($\frac{21}{20}$) results from incorrectly adding 8 + 5 + 8 instead of 8 + 5 + 6, likely from miscalculating $\frac{3}{10}$ as $\frac{8}{20}$. Choice C ($\frac{17}{20}$) comes from adding 8 + 3 + 6, which happens when you forget to convert $\frac{1}{4}$ and mistakenly use 3 instead of 5. Choice D ($\frac{23}{20}$) results from adding 8 + 9 + 6, probably from converting $\frac{1}{4}$ incorrectly. Always double-check your fraction conversions by ensuring each numerator times the original denominator equals the original numerator times the new denominator. This prevents the calculation errors that create these common wrong answers.
14. Compute $3\dfrac{2}{5}\div1\dfrac{1}{2}$.
    Answer: $2\dfrac{4}{15}$ When you encounter division with mixed numbers, you need to convert them to improper fractions first, then multiply by the reciprocal of the divisor. Start by converting both mixed numbers to improper fractions. For $3\frac{2}{5}$: multiply the whole number by the denominator and add the numerator: $(3 \times 5) + 2 = 17$, so $3\frac{2}{5} = \frac{17}{5}$. For $1\frac{1}{2}$: $(1 \times 2) + 1 = 3$, so $1\frac{1}{2} = \frac{3}{2}$. Now you have $\frac{17}{5} \div \frac{3}{2}$. To divide fractions, multiply by the reciprocal: $\frac{17}{5} \times \frac{2}{3} = \frac{17 \times 2}{5 \times 3} = \frac{34}{15}$. Convert back to a mixed number: $34 \div 15 = 2$ remainder $4$, so $\frac{34}{15} = 2\frac{4}{15}$. This matches choice A. Choice B ($2\frac{2}{5}$) likely comes from incorrectly multiplying the mixed numbers instead of dividing. Choice C ($2\frac{1}{5}$) might result from calculation errors when converting or simplifying fractions. Choice D ($1\frac{4}{15}$) suggests an error in the division step when converting the improper fraction back to a mixed number. Remember: division problems with fractions always require you to "keep, change, flip" - keep the first fraction, change division to multiplication, and flip the second fraction to its reciprocal. Always convert mixed numbers to improper fractions before performing operations.
15. What is the product of $0.36\times0.25\,?$
    Answer: $0.090$ When multiplying decimals, you need to carefully track decimal placement to avoid common calculation errors. To find $0.36 \times 0.25$, multiply the numbers as if they were whole numbers: $36 \times 25 = 900$. Now count the total decimal places in both original numbers: $0.36$ has 2 decimal places, and $0.25$ has 2 decimal places, giving you 4 total decimal places. Place the decimal point 4 positions from the right in your answer: $0.0900$, which equals $0.090$. You can verify this using fractions: $0.36 = \frac{36}{100}$ and $0.25 = \frac{25}{100}$, so $\frac{36}{100} \times \frac{25}{100} = \frac{900}{10000} = 0.090$. Answer choice A ($0.090$) is correct. Answer choice B ($0.009$) represents placing the decimal one position too far left—this happens when students miscount decimal places. Answer choice C ($0.900$) occurs when you forget that both numbers have decimal places and only account for decimals in one factor. Answer choice D ($0.625$) suggests adding the decimals ($0.36 + 0.25 = 0.61$, rounded) instead of multiplying them. Remember the decimal multiplication rule: multiply the numbers as whole numbers first, then count the total decimal places in both factors to determine where to place the decimal point in your final answer. This systematic approach prevents the decimal placement errors that commonly appear as wrong answers on the TEAS.
16. A land surveyor is measuring a rectangular plot of land. The length is measured as 150 feet. The width is exactly $\frac{2}{3}$ of the length. A new regulation requires a setback, reducing the effective length by $7\frac{1}{2}$ feet and the effective width by $0.1$ of its original value. What is the area, in square feet, of the effective plot of land?
    Answer: 12,825 sq ft This multi-step problem requires calculating dimensions and then an area. Step 1: Calculate the original width of the plot. $$\text{Original width} = \frac{2}{3} \times 150 \text{ feet} = 100 \text{ feet}$$ Step 2: Calculate the effective length after the setback. $7\frac{1}{2} = 7.5$ feet. $$\text{Effective length} = 150 \text{ feet} - 7.5 \text{ feet} = 142.5 \text{ feet}$$ Step 3: Calculate the effective width. It is reduced by 0.1 of its original value. The reduction is $0.1 \times 100 \text{ feet} = 10 \text{ feet}$. $$\text{Effective width} = 100 \text{ feet} - 10 \text{ feet} = 90 \text{ feet}$$ Step 4: Calculate the area of the effective plot using the new dimensions. $$\text{Area} = \text{Effective length} \times \text{Effective width} = 142.5 \text{ ft} \times 90 \text{ ft} = 12,825 \text{ sq ft}$$
17. A ball is dropped from a height of 48 feet. On each bounce, it returns to a height that is exactly $\frac{3}{4}$ of its previous height. What is the total vertical distance the ball has traveled at the exact moment it hits the ground for the third time?
    Answer: 174 feet This problem requires careful tracking of the ball's movement, both down and up. Path 1 (Initial Drop): The ball falls 48 feet. It hits the ground for the first time. Total distance so far: 48 feet. Path 2 (First Bounce): The ball bounces up $\frac{3}{4}$ of 48 feet, which is $48 \times \frac{3}{4} = 36$ feet. It then falls 36 feet back down. It hits the ground for the second time. Distance traveled in this bounce: $36 + 36 = 72$ feet. Path 3 (Second Bounce): The ball bounces up $\frac{3}{4}$ of the previous height (36 feet), which is $36 \times \frac{3}{4} = 27$ feet. It then falls 27 feet back down. It hits the ground for the third time. Distance traveled in this bounce: $27 + 27 = 54$ feet. Total Distance: Add the distances from all paths. $$48 \text{ (drop)} + 72 \text{ (1st bounce)} + 54 \text{ (2nd bounce)} = 174 \text{ feet}$$
18. Compute $\dfrac{2}{3}\div\dfrac{5}{8}$.
    Answer: $\dfrac{16}{15}$ When you encounter division of fractions, remember the fundamental rule: dividing by a fraction is the same as multiplying by its reciprocal. This transforms what might seem like a complex operation into straightforward multiplication. To solve $\frac{2}{3}\div\frac{5}{8}$, you first flip the second fraction to get its reciprocal, changing $\frac{5}{8}$ to $\frac{8}{5}$. Now multiply: $\frac{2}{3} \times \frac{8}{5}$. Multiply the numerators together (2 × 8 = 16) and the denominators together (3 × 5 = 15), giving you $\frac{16}{15}$. Looking at the wrong answers reveals common mistakes: Answer B ($\frac{15}{16}$) results from incorrectly flipping the final answer instead of the divisor. Answer C ($\frac{10}{24}$) comes from mistakenly adding numerators and denominators (2 + 8 = 10, 3 + 8 = 11... wait, that doesn't even work), or possibly from some confused cross-multiplication. Answer D ($\frac{8}{15}$) happens when you flip the wrong fraction—taking the reciprocal of $\frac{2}{3}$ instead of $\frac{5}{8}$. The correct answer is A: $\frac{16}{15}$. Remember this simple phrase: "Keep, Change, Flip." Keep the first fraction unchanged, change division to multiplication, and flip the second fraction. This systematic approach prevents the confusion that leads to most fraction division errors on the TEAS.
19. Find $5\dfrac{1}{4}\times3$.
    Answer: $15\dfrac{3}{4}$ When you encounter multiplication involving mixed numbers, you have two main approaches: convert to improper fractions or use the distributive property. Both methods work, but converting to improper fractions is often more straightforward. To convert $5\frac{1}{4}$ to an improper fraction, multiply the whole number by the denominator and add the numerator: $5 \times 4 + 1 = 21$, so $5\frac{1}{4} = \frac{21}{4}$. Now you can multiply: $\frac{21}{4} \times 3 = \frac{21 \times 3}{4} = \frac{63}{4}$. Converting back to a mixed number: $63 \div 4 = 15$ remainder $3$, so $\frac{63}{4} = 15\frac{3}{4}$. This confirms answer A is correct. Looking at the wrong answers: Answer B ($14\frac{3}{4}$) results from incorrectly calculating $4 \times 3 + 1 = 13$ instead of $5 \times 4 + 1 = 21$ when converting to an improper fraction. Answer C ($16\frac{1}{4}$) comes from mistakenly multiplying $5 \times 3 = 15$ and $\frac{1}{4} \times 3 = \frac{3}{4}$, then adding incorrectly to get $16\frac{1}{4}$. Answer D ($15\frac{1}{2}$) occurs when you forget to multiply the fractional part by 3, keeping it as $\frac{1}{4}$, then somehow arriving at $\frac{1}{2}$. Remember this key strategy: when multiplying mixed numbers, always convert to improper fractions first. This eliminates the chance of forgetting to multiply both the whole and fractional parts correctly, which is the most common error on these types of TEAS problems.
20. Evaluate: $18-5.724$
    Answer: $12.276$ This question tests your ability to subtract decimals, a fundamental skill that appears frequently on the TEAS mathematics section. When subtracting decimals, proper alignment and careful borrowing are crucial for accuracy. To solve $18 - 5.724$, first rewrite 18 as 18.000 to align the decimal places properly: 18.000 - 5.724 ________ Starting from the rightmost column, you need to borrow since you can't subtract 4 from 0. After borrowing through the columns, you get: - Thousandths: 10 - 4 = 6 - Hundredths: 9 - 2 = 7 - Tenths: 9 - 7 = 2 - Ones: 17 - 5 = 12 This gives you $12.276$. Looking at the wrong answers: Choice A ($12.176$) results from an error in the hundredths place, likely from incorrect borrowing or misaligning the decimal places. Choice B ($12.286$) shows an error in the thousandths place, possibly from subtracting 4 from 10 incorrectly. Choice D ($13.724$) appears to come from adding instead of subtracting, or from a major computational error in the ones place. When working with decimal subtraction on the TEAS, always write out extra zeros to align decimal places clearly, work systematically from right to left, and double-check your borrowing. These problems often include answer choices that reflect common computational mistakes, so careful step-by-step work will help you avoid these traps.

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