Solving Proportions

Learn solving proportions, scale drawings.

Lesson 3 of 32 parts Practice Flashcards

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Solving Proportions

Objective: Explain solving proportions, apply the stated method, and check its conditions.

A proportion asserts equality of two ratios. With nonzero denominators, cross multiplication produces an equivalent equation ad=bc for a/b=c/d. Solve the unknown and check both the algebra and the order of corresponding quantities. Keep corresponding quantities in the same order.

Formulas

$a/b=c/d ⇒ ad=bc$

Worked examples

Try itSolve x/7=7/6.Show answer

Step 1: Multiply both sides by the nonzero denominator. Step 2: x=7·(7/6). Step 3: x=49/6.

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Solving Proportions

Objective: Explain solving proportions, apply the stated method, and check its conditions.

Formulas

$a/b=c/d ⇒ ad=bc$

Worked examples

Try itSolve x/7=7/6.Show answer

Step 1: Multiply both sides by the nonzero denominator. Step 2: x=7·(7/6). Step 3: x=49/6.

Scale Drawings

Objective: Explain scale drawings, apply the stated method, and check its conditions.

A scale maps drawing lengths to actual lengths by a constant factor. Multiply a drawing distance by its stated length-per-drawing-unit scale. Linear scaling is distinct from area or volume scaling, whose factors are squared or cubed. A length scale factor is not an area scale factor.

Formulas

Actual length = drawing length × scale factor

Worked examples

Try itA map uses 1 cm for 6 km. A route is 7 cm on the map. Find actual distance in km.Show answer

Step 1: Use actual distance = map distance times scale. Step 2: Multiply 7 cm by 6 km/cm. Step 3: The distance is 42 km.

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