Reversed difference sprint

Compute a - b when b - a is required (or subtract in the wrong order).

An error-pattern drill: practice spotting and avoiding this specific SHSAT trap.

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How to avoid subtracting in the wrong order

Brand A costs 4.25 dollars per pound and Brand B costs 2.90 dollars per pound. How much more does Brand A cost? The answer is \(4.25 - 2.90 = 1.35\) dollars. If you subtract the other way, you get \(-1.35\), and that trap is often in the choices.

Order matters in subtraction but not in addition, so it is easy to forget. Word problems make it harder: "5 less than \(x\)" means \(x - 5\), not \(5 - x\). "Sam is 6 years older than Jo" means \(S - J = 6\).

Check habits:

Worked examples

Example 1.
Brand A's cheddar cheese costs \(\$18.50\) for 5 pounds. Brand B's cheddar cheese costs \(\$16.00\) for 8 pounds. How much more per pound, in dollars, does Brand A cost than Brand B?
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Answer:
C

Unit prices: A \(= \$18.50 \div 5 = \$3.70\), B \(= \$16.00 \div 8 = \$2.00\). Difference \(= \$3.70 - \$2.00 = \$1.70\). (Subtracting in the reversed order gives -$1.70. Subtracting the total prices instead of the prices per pound gives $2.50. Stopping at Brand A's price per pound gives $3.70.)

Example 2.
Find the slope of the line through \((-4, 5)\) and \((-6, 9)\).
Show answer and explanation
Answer:
B

Slope \(= \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{9 - 5}{-6 - (-4)} = \dfrac{4}{-2} = -2\). (Dividing the change in \(x\) by the change in \(y\) gives \(-1/2\). Subtracting the \(y\)-values and the \(x\)-values in opposite orders gives \(2\). Adding the coordinates, \(\dfrac{5 + 9}{-4 + (-6)}\), gives \(-7/5\).)

Example 3.
Write an algebraic expression for: "20 less than a number".
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Answer:
D

"20 less than a number" means start with the number and take 20 away: \(x - 20\). (Writing the parts in the order you read them gives \(20 - x\), which subtracts in the wrong order. \(x + 20\) adds instead of subtracting. \(20 < x\) is an inequality, not an expression: "less than" here means subtract.)