Add, subtract, multiply, or divide two fractions: word problems

Learning Objectives Identify the correct operation (addition, subtraction, multiplication, or division) needed to solve a fraction word problem. Translate real-world scenarios into mathematical expressions involving two fractions. Accurately add and subtract two fractions, including those with unlike denominators, within a word problem context. Accurately multiply and divide two fractions, including mixed numbers, to solve word problems. Simplify fraction answers to their lowest terms and interpret them within the context of the original word problem. Convert between mixed numbers and improper fractions as needed to solve word problems. Apply problem-solving strategies to multi-step fraction word problems. Ever wondered how much of a recipe you need to adjust if you only h...

TermDefinitionExample FractionA number representing a part of a whole, expressed as a numerator over a denominator.In the fraction $\frac{3}{4}$, 3 is the numerator (parts we have) and 4 is the denominator (total parts in the whole). NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.If you eat $\frac{1}{2}$ of a pizza, 1 is the numerator, meaning you ate 1 out of 2 equal slices. DenominatorThe bottom number in a fraction, indicating the total number of equal parts that make up the whole.In $\frac{5}{8}$ of a pie, 8 is the denominator, meaning the pie was cut into 8 equal pieces. Mixed NumberA number consisting of a whole number and a proper fraction.$\text{2}\frac{1}{2}$ represents two whole units and an additional half unit. Improper Fract...

Adding or Subtracting Fractions $\frac{a}{b} \pm \frac{c}{d} = \frac{a \cdot (LCD/b) \pm c \cdot (LCD/d)}{LCD}$ To add or subtract fractions, first find the Least Common Denominator (LCD) of the fractions. Convert each fraction to an equivalent fraction with the LCD. Then, add or subtract the numerators and keep the common denominator. Simplify the result if possible. Multiplying Fractions $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ To multiply fractions, multiply the numerators together and multiply the denominators together. Simplify the resulting fraction. If mixed numbers are involved, convert them to improper fractions first. Dividing Fractions $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$ To...