Multiplying Fractions
Multiplying fractions in Grade 8 Saxon Math Course 3 involves multiplying numerators together and denominators together, then simplifying the result to lowest terms. Students learn to simplify by cross-canceling common factors before multiplying to keep numbers smaller. Fraction multiplication is applied in area calculations, scaling, and proportional reasoning.
Key Concepts
Property To multiply fractions, multiply the numerators to find the numerator of the product, and multiply the denominators to find the denominator of the product.
Examples To solve $\frac{1}{4} \cdot \frac{3}{5}$, we multiply the numerators and denominators: $\frac{1 \cdot 3}{4 \cdot 5} = \frac{3}{20}$. What is $\frac{2}{5}$ of $\frac{5}{8}$? We can cancel before multiplying: $\frac{\stackrel{1}{\cancel{2}}}{\underset{1}{\cancel{5}}} \cdot \frac{\stackrel{1}{\cancel{5}}}{\underset{4}{\cancel{8}}} = \frac{1}{4}$. Simplify $\frac{2}{3} \cdot \frac{4}{5}$: $\frac{2 \cdot 4}{3 \cdot 5} = \frac{8}{15}$.
Explanation Ever wondered what a 'half of a quarter' really is? Multiplying fractions lets you find a part of a part! Just as a pint is half of a quart (which is a quarter of a gallon), you multiply the top numbers and the bottom numbers together to find the final, smaller fraction. It’s a simple way to combine parts.
Common Questions
How do you multiply two fractions?
Multiply the numerators together and the denominators together. Then simplify the resulting fraction if possible. For example, 2/3 x 3/4 = 6/12 = 1/2.
What is cross-canceling in fraction multiplication?
Cross-canceling means simplifying before multiplying by dividing a numerator and a diagonal denominator by their common factor. For example, in 2/3 x 3/4, cancel the 3s to get 2/1 x 1/4 = 2/4 = 1/2.
How do you multiply a fraction by a whole number?
Write the whole number as a fraction with denominator 1, then multiply. For example, 5 x 2/3 = 5/1 x 2/3 = 10/3 = 3 1/3.
Why is the product of two proper fractions smaller than either fraction?
Multiplying two fractions between 0 and 1 gives a value smaller than both, because you are taking a fraction of a fraction, which is less than either original fraction.
How does Saxon Math Course 3 teach fraction multiplication?
Saxon Math Course 3 teaches the multiply-then-simplify method and also the simplify-first (cross-cancel) method, applying both to word problems involving area and proportional reasoning.