How to Find Equivalent Ratios to Fractions

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A ratio expresses the relation between an independent and dependent variable or the relation of different parts of a whole to each other. Rewriting a fraction as a ratio provides the additional information of units, making it easier to interpret the information. You must first convert fractions to simplest form or find the common denominator of multiple fractions before finding the equivalent ratio.

Rewriting a Single Fraction as a Ratio

• Write the fraction in simplest form by identifying the greatest common factor between the numerator and denominator and dividing it into both numbers. For example, the fraction 15/25 is 3/5 in simplest form because the greatest common factor of 15 and 25 is 5, and dividing the top and the bottom of the fraction by 5 results in 3/5.

• Identify the units of the numerator and denominator in the fraction. The numerator is usually the independent variable of a story problem, and the denominator is usually the dependent variable. For example, if the fraction of a pie eaten in an hour is 3/5, the numerator is in units of pies and the denominator is in units of hours.

• Rewrite the fraction as a ratio by writing the units after their corresponding number and connecting them with the word "to." For example, the fraction 3/5 would be written as a ratio of 3 pies to 5 hours.

Rewriting a Set of Fractions as a Ratio

• Find the least common multiple of all the denominators of the fractions.

• Rewrite all fractions by determining the number you have to multiply each denominator by to make it equal the least common multiplier, and then multiplying the numerator and denominator by that number. This will make it so that all the fractions have a common denominator.

• Rewrite the fractions as a ratio by taking the numerators of all the fractions and separating them with colons or the word "to." For example, if the a pie was 2/5 blueberry, 1/5 rhubarb and 2/5 apple, the ratio of ingredients would be "2 : 1 : 2" or "2 to 1 to 2." Include the units if desired: "2 blueberry to 1 rhubarb to 2 apple."

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