TEAS 7 Math flashcards
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How to convert between fractions, decimals and percents
- How do you turn 3/5 into a decimal?
- Divide top by bottom: 3 ÷ 5 = 0.6. The digits of a fraction are not the digits of its decimal.
- Convert 0.375 to a percent.
- 37.5%. Move the decimal point two places right and add the % sign.
- Convert 12.5% to a decimal.
- 0.125. Drop the % and move the point two places left. A percent under 100% is a decimal under 1.
- Write 35% as a fraction in simplest form.
- 7/20. Put 35 over 100, then divide top and bottom by 5.
- Write 0.65 as a fraction in simplest form.
- 13/20. 0.65 is 65 hundredths, so 65/100. Divide top and bottom by 5.
- Convert 0.6% to a decimal.
- 0.006. Move the point two places left. A tiny percent becomes a tiny decimal, not 0.6 or 0.06.
How to add, subtract, multiply and divide fractions, decimals and negatives
- What is 1/2 + 1/3?
- 5/6. Use the common denominator 6: 3/6 + 2/6. Adding tops and bottoms to get 2/5 is wrong.
- How do you divide fractions? Try 2/5 ÷ 1/10.
- Keep the first, change ÷ to ×, flip the second: 2/5 × 10/1 = 20/5 = 4.
- How do you change 2 1/3 into an improper fraction?
- 7/3. Multiply the whole number by the denominator and add the numerator: 2 × 3 + 1 = 7.
- What is 10 − (−6)?
- 16. Subtracting a number is the same as adding its opposite: 10 + 6 = 16.
- What is 12 ÷ 3 × 2?
- 8. Multiplication and division share a step and go left to right: 12 ÷ 3 = 4, then 4 × 2 = 8.
- What is the difference between −4² and (−4)²?
- −4² is −16, because only the 4 is squared. (−4)² is 16, because the parentheses square the negative too.
How to compare and order fractions, decimals, percents and negatives
- Which is greater, 0.6 or 0.58?
- 0.6. Pad it to 0.60, then compare 60 with 58. More digits does not mean a bigger number.
- Which is smaller, −0.9 or −0.2?
- −0.9 is smaller. Among negatives, the number farther from zero is smaller, because it sits farther left on the number line.
- How do you compare a mix of fractions, decimals and percents?
- Turn all of them into decimals, pad to the same number of places, then compare. Example: 40% = 0.4, which is less than 0.45.
- Which is greater, 5/8 or 3/5?
- 5/8. As decimals, 5 ÷ 8 = 0.625 and 3 ÷ 5 = 0.6. With a common denominator of 40, it is 25/40 versus 24/40.
- Why is 1/8 less than 1/5?
- A bigger denominator means the whole is cut into more, smaller pieces. Eighths are smaller than fifths.
How to solve a one-variable equation
- What is the one rule for solving any equation?
- Do the same thing to both sides. Use the inverse operation to peel away whatever is attached to the variable.
- Solve 4x − 9 = 27.
- x = 9. Add 9 to both sides to get 4x = 36, then divide by 4. Check: 4(9) − 9 = 27.
- In 5x + 6 = 41, do you undo + 6 or × 5 first?
- The + 6. Undo adding or subtracting before multiplying or dividing. Subtract 6 to get 5x = 35, so x = 7.
- Expand 3(x + 4).
- 3x + 12. The number outside the parentheses multiplies every term inside.
- Solve (2/3)x + 5 = 17.
- x = 18. Subtract 5 to get (2/3)x = 12, then multiply by the reciprocal 3/2: 12 × 3/2 = 18.
- How do you check the solution to an equation?
- Put the answer into the original equation. Both sides must come out equal. Do not check in a line you already rewrote.
How to solve multi-step word problems
- What are the three moves for any multi-step word problem?
- Plan, solve, check. Read twice and mark what is asked. Work one labeled step at a time. Then check the answer is reasonable.
- A rental costs $40 plus $15 per day. The bill is $145. How many days?
- 7 days. Subtract the fee first: 145 − 40 = 105. Then divide by the rate: 105 ÷ 15 = 7.
- 45 tablets, 2 tablets three times daily. How many full days?
- 7 full days. 2 × 3 = 6 tablets a day, and 45 ÷ 6 = 7.5. 'Full days' means round down.
- You spent $135.50 of a $150 gift card. How much money is left?
- $14.50. Subtract: 150 − 135.50. The question asks for money left, not money spent.
- With $162 and items at $14.50 each, how many can you afford?
- 11. 162 ÷ 14.50 is about 11.2. Let the story decide the rounding: you can afford 11 whole items, not 12.
How to solve percent problems
- What equation sits behind every percent problem?
- Part = percent × whole. Change the percent to a decimal first. 'Of' means multiply and 'is' means equals.
- What is 7.5% of $64?
- $4.80. Write 7.5% as 0.075, then 0.075 × 64 = 4.80. The total with tax is $68.80.
- 360 mL is 30% of a daily goal. What is the goal?
- 1,200 mL. Divide the part by the percent: 360 ÷ 0.30 = 1,200. The whole must be bigger than the part.
- A dose drops from 40 mg to 30 mg. What is the percent decrease?
- 25%. The change is 10, and 10 ÷ 40 = 0.25. Always divide by the original amount.
- A price is $48 after 20% off. What was the original price?
- $60. You paid 80%, so divide: 48 ÷ 0.80 = 60. Multiplying 48 by 1.20 is wrong.
- What single discount equals 25% off, then 10% off the sale price?
- 32.5% off. Multiply what is left: 0.75 × 0.90 = 0.675. Back-to-back percents do not add to 35%.
How to round and estimate without going blank
- What is the rule for rounding to a chosen place?
- Look only at the digit just right of that place. If it is 5 or more, round up. If it is 4 or less, leave the digit alone.
- Round 2.449 to the nearest tenth.
- 2.4. Check only the hundredths digit, which is 4, so the 4 stays. Do not let the 9 push it up.
- Round 68.47 to the nearest whole number.
- 68. The digit right of the ones place is 4, so leave it. Never round in a chain (68.5, then 69).
- What is front-end rounding?
- Round each number to its first place, then do easy math. 47.85 becomes 50 and 312 becomes 300. The result is a ballpark.
- A calculator answer is about 10 times your estimate. What do you check?
- Look for a misplaced decimal point. Example: 48 × $11.75 is about $500, so $5,640 is wrong. The true answer is $564.
- When should you round if the problem multiplies numbers?
- Round only the final answer. Rounding $3.45 down to $3 before multiplying by 40 gives $120 instead of the true $138.
How to set up and solve a proportion
- How do you solve a proportion a/b = c/d?
- Cross-multiply: a × d = b × c. Then divide to get the unknown alone. Keep matching units in matching spots.
- 3 cups of broth serve 4 people. How much broth serves 10?
- 7.5 cups. Set 3/4 = x/10, so 4x = 30 and x = 7.5. Scaling multiplies; it does not add.
- On a map, 2 cm stands for 15 km. How far is 7 cm?
- 52.5 km. Set 2/15 = 7/x, so 2x = 105 and x = 52.5. Map length goes on top on both sides.
- An order is 3 mg per kg. The patient weighs 154 lb. How many mg?
- 210 mg. First 154 ÷ 2.2 = 70 kg, then 3 × 70 = 210. Using 154 as kilograms gives a dose far too big.
- Is g/mL = mL/g a valid proportion setup?
- No. One side is upside down. Units must line up across the equals sign, like g/mL = g/mL.
How to work with ratios, unit rates and rate of change
- Write the ratio of 12 blue tubes to 28 red tubes in simplest form.
- 3:7. Blue goes first, and both parts divide by 4. Part to part is not part to whole (12:40).
- What is a unit rate?
- A rate with 1 in the denominator, such as 125 mL per hour. Divide the first amount by the second.
- 1,000 mL of fluid runs over 8 hours. What is the flow rate?
- 125 mL per hour. Divide 1,000 ÷ 8. The word after 'per' goes on the bottom.
- Convert 45 minutes to hours.
- 0.75 hour. Divide minutes by 60. It is not 0.45 hour, because an hour has 60 minutes, not 100.
- A runner covers 6 miles in 48 minutes. Find miles per hour.
- 7.5 miles per hour. Convert the time first: 48 ÷ 60 = 0.8 hour. Then 6 ÷ 0.8 = 7.5.
- How do you find a rate of change?
- Change in output ÷ change in input, subtracted in the same order. A negative rate means the quantity is falling. On a graph, it is the slope.
How to turn words into expressions, equations and inequalities
- Write '5 less than x' as an expression.
- x − 5. 'Less than' flips the order, so start with x and take away 5.
- Translate 'the sum of 3 times x and 4' into symbols.
- 3x + 4. Compare '3 times the sum of x and 4', which is 3(x + 4). Parentheses follow the words.
- A courier charges $30 plus $12 per sample. Write the cost for s samples.
- 12s + 30. The variable goes with the per-item rate, never with the one-time fee.
- What symbols mean 'at least' and 'at most'?
- At least means ≥. At most means ≤. Both include the boundary number, so both get a closed circle on a number line.
- For x < 6, which circle goes at 6, and which way do you shade?
- An open circle at 6, shaded to the left. The circle is open because 6 is not part of the answer.
- Solve −3x > 12.
- x < −4. Dividing both sides by a negative number flips the inequality sign.
How to read tables, bar graphs, line graphs and pie charts
- What should you read before any number on a chart?
- The title, labels or headings, units, scale and key. Most chart mistakes happen before any math starts.
- What does 'how many more' mean in a table question?
- Subtract the two values. Adding them is a common wrong turn. Find the right row and column first.
- On a line graph, how do you find the biggest change?
- Find the steepest segment between neighboring points. It is not the highest or the lowest point.
- A pie slice is 15% of a $2,400 budget. How many dollars is that?
- $360. Amount = percent as a decimal × whole: 0.15 × 2,400. All pie slices add to 100%.
- What if a bar graph's vertical axis does not start at 0?
- A bar that looks twice as tall may not be twice as large. Read the numbers, not the picture.
- What do dots rising from left to right on a scatter plot show?
- High values on one axis go with high values on the other. Each dot is one item with two measurements.
How to find the mean, median, mode and range
- Find the mean of 12, 8, 15, 10 and 20.
- 13. The sum is 65, and 65 ÷ 5 values = 13. The mean always lands between the smallest and largest value.
- How do you find the median of 5, 6, 6, 7, 8, 9?
- Order the list, then average the two middle values because the count is even: (6 + 7) ÷ 2 = 6.5.
- What is the mode of 5, 6, 6, 7, 8, 9?
- 6, because it appears most often. A set can have no mode, or more than one mode.
- What is the range of 5, 6, 6, 7, 8, 9?
- 4. Range is the largest value minus the smallest: 9 − 5. It measures spread, not the center.
- Three quiz scores have a mean of 80. What is their total?
- 240. Total = mean × number of values: 80 × 3. This helps you find a missing value.
- Which is pulled more by an outlier, the mean or the median?
- The mean. Adding $70 to wages of $18, $19, $20, $21 and $22 lifts the mean from $20 to about $28.33. The median moves to $20.50.
How two variables are related: correlation, direct and inverse variation
- Which is the independent variable in 'pay depends on hours worked'?
- Hours worked. The input (x, horizontal axis) is independent. The result that depends on it (y) is dependent.
- What do dots falling from left to right on a scatter plot show?
- Negative correlation: as x increases, y tends to decrease. Dots with no pattern show no correlation.
- How can you test for direct variation, y = kx?
- Check that y ÷ x is the same for every pair. Doubling x doubles y. A line like y = 35x + 150 fails the test.
- A pump gives 150 mL in 2 hours. How much in 5 hours?
- 375 mL. The constant is 150 ÷ 2 = 75 mL per hour, so 75 × 5 = 375.
- Two technicians restock a room in 6 hours. How long would 3 take?
- 4 hours. In inverse variation, x × y stays constant: 2 × 6 = 12, and 12 ÷ 3 = 4.
- Does a strong correlation prove that one variable causes the other?
- No. Correlation does not imply causation. Two variables can move together without one causing the other.
How to find perimeter, area and volume, even for odd shapes
- What are the rectangle perimeter and area formulas?
- Perimeter P = 2L + 2W. Area A = L × W. Perimeter is in linear units; area is in square units.
- What is the formula for the area of a triangle?
- A = 1/2 × b × h. The height meets the base at a right angle. A slanted side is not the height.
- What are the circumference and area formulas for a circle?
- C = π × d (or 2 × π × r) and A = π × r². Use 3.14 for π unless told otherwise.
- A circle has a diameter of 8 in. What is its area?
- 50.24 in². The radius is 4, so 3.14 × 4 × 4 = 50.24. Using 8 as the radius makes the area four times too big.
- What are the volume formulas for a box and a cylinder?
- Box: V = L × W × H. Cylinder: V = π × r² × h. Volume is in cubic units.
- A right triangle has legs 6 and 8. Find the hypotenuse.
- 10. Square and add: 36 + 64 = 100. The square root of 100 is 10. The hypotenuse is not 6 + 8.
How to convert units without guessing: metric, US and health-care units
- Convert 0.4 g to milligrams.
- 400 mg. Moving to a smaller unit gives a bigger number. Multiply by 1,000, which moves the decimal 3 places right.
- How many micrograms are in 1 milligram?
- 1,000 µg. Below milli, the next metric prefix is three decimal places away.
- Convert 2,750 mL to liters.
- 2.75 L. Since 1,000 mL = 1 L, move the decimal 3 places left. A bigger unit gives a smaller number.
- How many cubic centimeters equal 1 mL?
- 1 cm³. So a box with a volume of 200 cm³ holds 200 mL.
- How do you change pounds to kilograms? Try 44 lb.
- Divide by 2.2: 44 ÷ 2.2 = 20 kg. The kilogram number is always the smaller one.
- How many ounces are in 1 pound?
- 16 oz. That is weight. A cup is 8 fluid ounces, so do not use 16 for a cup.
- How many centimeters are in 1 inch?
- 2.54 cm, an exact value. So 10 in × 2.54 = 25.4 cm.
- How many inches is 5 ft 7 in?
- 67 inches. 1 ft = 12 in, so 5 × 12 + 7 = 67. It is not 5.7 feet.
- How many kilometers are in 1 mile?
- About 1.61 km. So 10 miles is about 16.1 km.
- How many mL are in 1 teaspoon?
- About 5 mL. This is the rounded value used in health-care math.
- How many mL and teaspoons are in 1 tablespoon?
- About 15 mL, and 1 tbsp = 3 tsp.
- How many mL and tablespoons are in 1 fluid ounce?
- About 30 mL, and 1 fl oz = 2 tbsp.
- How many fluid ounces and mL are in 1 cup?
- 8 fl oz, which is about 240 mL. So 3/4 cup is 6 fl oz, or about 180 mL.
- Convert 38 °C to Fahrenheit.
- 100.4 °F. Multiply by 9/5 first: 38 × 1.8 = 68.4. Then add 32.
- What is the formula for °F to °C? Try 50 °F.
- °C = (°F − 32) × 5/9. Subtract 32 first: 18 × 5/9 = 10 °C.
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