AR · 8 cards

Ratios and Proportions flashcards

8 cards with the formulas, rules and traps from this lesson. Answer in your head, then flip to check.

Term · 1/8
What is the difference between part-to-part and part-to-whole ratios?
Part-to-part compares one group with another (8 sedans to 12 trucks is 2:3). Part-to-whole compares a group with the total, which is the sum of the parts (8 to 20 is 2:5).
Rule · 2/8
How do you simplify the ratio of 2 feet to 8 inches?
Convert to the same unit first, then divide by the greatest common factor: 24 inches to 8 inches is 24:8, which is 3:1.
Formula · 3/8
In a proportion $\frac{a}{b} = \frac{c}{d}$ , what must be true?
The cross products are equal: $a \times d = b \times c$ . For $\frac{5}{12} = \frac{x}{36}$ , $12 x = 180$ , so $x = 15$ . Multiply diagonally, never straight across.
Strategy · 4/8
How do you split 84 tools between two shops in the ratio 2:5?
Add the terms to get 7 parts, find one part ( $84 \div 7 = 12$ ), then multiply: $2 \times 12 = 24$ and $5 \times 12 = 60$ tools.
Strategy · 5/8
Rifles to pistols is 7:3, with 28 more rifles than pistols. Total?
The difference is $7 - 3 = 4$ parts, so one part is $28 \div 4 = 7$ . Rifles: 49, pistols: 21, total: 70. Ratio terms are not counts until you find one part.
Formula · 6/8
What is a scale factor, and how does it change area?
$k = \frac{new length}{original length}$ ; $k > 1$ enlarges and $0 < k < 1$ shrinks. Areas change by $k^{2}$ : with $k = 2.5$ , the area becomes 6.25 times as large.
Common trap · 7/8
When does a simple direct proportion NOT apply?
When the quantities do not rise together at a constant ratio, such as workers and time to finish a job: more workers means less time. Cost and quantity at a fixed price are direct.
Strategy · 8/8
Solve $\frac{7}{12} = \frac{x}{60}$ without cross-multiplying.
60 is 5 times 12, so scale the numerator by 5 as well: $x = 7 \times 5 = 35$ . Look for a whole-number scale factor before cross-multiplying.

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