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How to Fully Simplify the Algebraic Fraction Product $\\frac{16q}{r} \\times \\frac{r}{2}$
Mathematics
Grade 8 (Junior High School)
Question Content
Fully simplify $\\frac{16q}{r} \\times \\frac{r}{2}$
Correct Answer
$8q$
Detailed Solution Steps
1
Step 1: Recall the rule for multiplying fractions: multiply the numerators together and the denominators together, so $\\frac{16q}{r} \\times \\frac{r}{2} = \\frac{16q \\times r}{r \\times 2}$
2
Step 2: Cancel out the common factor $r$ in the numerator and denominator (since $r \\neq 0$), leaving $\\frac{16q}{2}$
3
Step 3: Simplify the numerical fraction $\\frac{16}{2} = 8$, resulting in the final simplified form $8q$
Knowledge Points Involved
1
Fraction Multiplication Rule
When multiplying two fractions $\\frac{a}{b}$ and $\\frac{c}{d}$, the product is $\\frac{a \\times c}{b \\times d}$, where $b \\neq 0$ and $d \\neq 0$. This rule applies to algebraic fractions with variables as well, as long as the denominator terms are not zero.
2
Canceling Common Factors
When a non-zero term appears in both the numerator and denominator of a fraction, it can be canceled out (divided out) to simplify the expression. This is based on the property that $\\frac{x \\times k}{y \\times k} = \\frac{x}{y}$ for $k \\neq 0$.
3
Simplifying Numerical Coefficients
After canceling variable factors, numerical coefficients in the numerator and denominator should be simplified by dividing them by their greatest common divisor. For example, 16 and 2 have a greatest common divisor of 2, so $\\frac{16}{2} = 8$.
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