Simplify [tex]\frac{1}{5} \times \frac{5}{6} \times \frac{3}{7} \times \frac{21}{26}[/tex]
Answer (1)
Multiply the fractions: 5 1 × 6 5 × 7 3 × 26 21 = 5 × 6 × 7 × 26 1 × 5 × 3 × 21 .
Factor the numbers: 5 × 2 × 3 × 7 × 26 1 × 5 × 3 × 3 × 7 .
Cancel common factors: 5 × 2 × 3 × 7 × 26 5 × 3 × 7 × 3 = 2 × 26 3 .
Simplify the expression: 52 3 .
Explanation
Understanding the Problem We are given the expression 5 1 × 6 5 × 7 3 × 26 21 . Our goal is to simplify this expression by multiplying the fractions and canceling common factors.
Multiplying the Fractions First, let's multiply the numerators and the denominators: 5 × 6 × 7 × 26 1 × 5 × 3 × 21
Rewriting with Factors Now, we can simplify by canceling common factors. Notice that 21 = 3 × 7 and 6 = 2 × 3 . So we can rewrite the expression as: 5 × 2 × 3 × 7 × 26 1 × 5 × 3 × 3 × 7
Canceling Common Factors We can cancel the common factors 5, 3, and 7 from the numerator and the denominator: 5 × 2 × 3 × 7 × 26 1 × 5 × 3 × 3 × 7 = 2 × 26 1 × 3
Simplifying Now, we simplify further: 2 × 26 3 = 52 3
Final Answer Therefore, the simplified expression is 52 3 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 4 1 cup of sugar and you want to double the recipe, you need to multiply 4 1 by 2, which gives you 2 1 cup of sugar. Simplifying fractions helps us understand proportions and ratios, which are essential in various fields like finance, engineering, and science.
