Reduce a ratio while preserving the comparison

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Reduce a ratio while preserving the comparison

A ratio compares corresponding quantities by their multiplicative relationship. Dividing every entry by the same nonzero factor preserves that relationship. The ratio 12: 8 becomes 3: 2 after dividing both entries by 4.

Ratios can begin with decimals or fractions. Multiply all entries by a common factor to obtain convenient whole numbers, then simplify. A common factor must act on every entry; changing just one changes the comparison.

When entries describe the same type of quantity, convert units before simplifying. For 1.5 m: 50 cm, write 150 cm: 50 cm, giving 3: 1. State the order of the quantities so a reversed ratio is not mistaken for the same relationship.

Worked example: Simplify 0.6: 0.4.

Multiply both entries by 10 to get 6: 4.

Divide both by 2.

Answer: 3: 2.

Check your understanding: Simplify 2 hours: 30 minutes.

Answer: 4: 1.

Why: Use 120 minutes: 30 minutes before dividing.