Equivalent Ratios

Learn equivalent ratios, simplifying ratios.

Lesson 1 of 32 parts Practice Flashcards

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Equivalent Ratios

Objective: Explain equivalent ratios, apply the stated method, and check its conditions.

A ratio compares quantities in a specified order. Multiplying both ratio terms by the same positive factor preserves the relationship. Changing only one term generally changes the ratio. Context determines whether units match or a rate must be retained. The order of ratio terms matters.

Formulas

a:b = ka:kb for k>0

Worked examples

Try itFor ratio 6:7, what first number matches second number 49?Show answer

Step 1: The second number was multiplied by 7. Step 2: Multiply the first number by the same factor. Step 3: The first number is 42.

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Equivalent Ratios

Objective: Explain equivalent ratios, apply the stated method, and check its conditions.

Formulas

a:b = ka:kb for k>0

Worked examples

Try itFor ratio 6:7, what first number matches second number 49?Show answer

Step 1: The second number was multiplied by 7. Step 2: Multiply the first number by the same factor. Step 3: The first number is 42.

Simplifying Ratios

Objective: Explain simplifying ratios, apply the stated method, and check its conditions.

For positive integer quantities, divide both ratio terms by their greatest common factor to obtain lowest integer terms. The simplified ratio preserves the comparison, not the original counts. Ratios with mixed units require unit conversion before simplification. A simplified ratio does not state the original total count.

Formulas

a:b → (a/g):(b/g), g=GCF(a,b)

Worked examples

Try itSimplify the ratio 42:49. Give the first term in lowest integer terms.Show answer

Step 1: Divide both terms by GCF=7. Step 2: The ratio becomes 6:7. Step 3: The requested first term is 6.

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