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Solving problems with rational numbers in fraction form

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Rational Numbers in Fraction Form

A rational number written in fraction form is a ratio of two integers. Learn to add and subtract fractions using a common denominator, multiply fractions directly, divide by multiplying by the reciprocal, and solve word problems involving recipes, ratios, and measurements.

Rational numbers written as fractions

A rational number written in fraction form looks like a/b, where a and b are integers and b is not zero. Fractions are the natural way to express parts of a whole — a quantity like "three quarters of a cup" — and many real-world problems involving ratios, recipes, and measurements are easiest to solve by staying in fraction form throughout, though the same value could also be written as a decimal and compared to other rational numbers.

Solving a word problem with fractions Word problem: a recipe needs 3/4 cup of flour for one batch. For 1 and 1/2 batches, multiply 3/4 by 3/2 (the fraction form of 1.5) to get 9/8, or 1 and 1/8 cups. A recipe needs 3/4 cup flour per batch. How much flour for 1½ batches? 3 4 × 3 2 = 9 8 = 1ῗ cups
Multiplying fractions: ¾ × ¾₁₂ =  /₁₀ = 1ῗ cups.

Adding and subtracting fractions

To add or subtract fractions, they need a common denominator. Once the denominators match, add or subtract the numerators and keep the denominator the same. If the denominators are already equal, this is a single step.

Multiplying and dividing fractions

To multiply fractions, multiply the numerators together and the denominators together — no common denominator needed. To divide by a fraction, multiply by its reciprocal instead (flip the second fraction and multiply).

Solving word problems

Fraction word problems often involve scaling a recipe, splitting a quantity, or combining parts. Convert any mixed numbers (like 1½) to improper fractions first, then apply the right operation: multiplying scales a quantity up or down, while dividing splits a quantity into equal parts.

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