ATI TEAS Numbers and Algebra Summary

To change a fraction to a percent, divide and then multiply by 100.

1. 3 ÷ 4 = 0.75
2. 0.75 × 100 = 75%

Check: 75% of 4 is 3, so 3/4 = 75%.

Wrong choices

• 34%: This just puts the 3 and 4 side by side; it is not a conversion.
• 7.5%: The decimal point is in the wrong place; 0.75 × 100 = 75, not 7.5.
• 43%: This reverses the digits and does not convert the fraction.

0.6 means six tenths.

1. 0.6 = 6/10
2. Divide top and bottom by 2: 6/10 = 3/5

Check: 3 ÷ 5 = 0.6.

Wrong choices

• 6/100: 0.6 is six tenths, not six hundredths (0.06).
• 1/6: 1/6 is about 0.17, not 0.6.
• 3/50: 3/50 equals 0.06, not 0.6.

Change every number to a decimal, then compare.

1. 0.45 = 0.45
2. 1/2 = 0.50
3. 3/8 = 0.375
4. 40% = 0.40

Least to greatest: 0.375, 0.40, 0.45, 0.50 → 3/8, 40%, 0.45, 1/2.

Wrong choices

• 40%, 3/8, 0.45, 1/2: 3/8 is 0.375, which is less than 40% (0.40).
• 1/2, 0.45, 40%, 3/8: This is greatest to least, the reverse order.
• 3/8, 0.45, 40%, 1/2: 0.45 is greater than 40% (0.40), so they are out of order.

"Percent of" means multiply by the percent as a decimal.

1. 15% = 0.15
2. 0.15 × 80 = 12

Check: 10% of 80 is 8 and 5% is 4, so 15% is 8 + 4 = 12.

Wrong choices

• 1.2: The decimal point is off; 0.15 × 80 = 12, not 1.2.
• 120: This multiplies 15 × 80 and divides by 10 instead of 100.
• 65: This subtracts 15 from 80 instead of finding a percent.

Undo the operations in reverse order.

1. Subtract 7 from both sides: 3x = 15
2. Divide both sides by 3: x = 5

Check: 3(5) + 7 = 15 + 7 = 22.

Wrong choices

• x = 15: This subtracts 7 but forgets to divide by 3.
• x = 29/3: This adds 7 to 22 instead of subtracting it.
• x = 3: Check it: 3(3) + 7 = 16, not 22.

Set up a proportion: 1 nurse / 4 patients = x nurses / 32 patients.

1. 32 ÷ 4 = 8
2. x = 8 nurses

Check: 8 nurses × 4 patients each = 32 patients.

Wrong choices

• 128: This multiplies 32 × 4 instead of dividing.
• 4: 4 is the number of patients per nurse, not the number of nurses.
• 36: This adds 4 to 32.

Find a common denominator before adding.

1. The least common denominator of 3 and 4 is 12.
2. 2/3 = 8/12 and 1/4 = 3/12
3. 8/12 + 3/12 = 11/12

Check: 2/3 ≈ 0.667 and 1/4 = 0.25; 0.667 + 0.25 ≈ 0.917, and 11/12 ≈ 0.917.

Wrong choices

• 3/7: This adds the tops and the bottoms; fractions need a common denominator first.
• 1/6: This multiplies the fractions instead of adding them.
• 9/12: 8/12 + 3/12 is 11/12, not 9/12.

Percent change = change ÷ original × 100.

1. Change = $50 − $40 = $10
2. $10 ÷ $40 = 0.25
3. 0.25 × 100 = 25%

Check: 25% of $40 is $10, and $40 + $10 = $50.

Wrong choices

• 20%: This divides the change by the new price ($50) instead of the original price ($40).
• 10%: $10 is the amount of change in dollars, not the percent.
• 80%: This is 40 ÷ 50 as a percent, which is not the change.

Set up a proportion: 125 mg / 5 mL = 300 mg / x mL.

1. Cross-multiply: 125x = 300 × 5 = 1,500
2. x = 1,500 ÷ 125 = 12 mL

Check: 12 mL holds 12 × 25 mg = 300 mg (since 1 mL holds 25 mg).

Wrong choices

• 2.4 mL: 300 ÷ 125 = 2.4 is the number of 5-mL portions, not the number of mL.
• 60 mL: This divides 300 by 5 and ignores the 125 mg.
• 25 mL: This is 125 ÷ 5 (mg in 1 mL), not the dose volume.

The fee is paid once, and $30 is paid each month.

1. One-time fee: 25
2. Monthly cost for m months: 30m
3. Total: 25 + 30m

Check with m = 2: 25 + 60 = $85, which is $25 + $30 + $30.

Wrong choices

• 30 + 25m: This switches the one-time fee and the monthly charge.
• 55m: This charges the sign-up fee every month.
• 30(m + 25): This multiplies the fee by $30, which does not match the problem.