Multiply. Express your answer in simplest form. 7/10 × 2/5
The Correct Answer and Explanation is:
To multiply the fractions: 710×25\frac{7}{10} \times \frac{2}{5}107×52
Step 1: Multiply the numerators (top numbers)
7×2=147 \times 2 = 147×2=14
Step 2: Multiply the denominators (bottom numbers)
10×5=5010 \times 5 = 5010×5=50
Now you have: 1450\frac{14}{50}5014
Step 3: Simplify the fraction
To simplify, find the greatest common divisor (GCD) of 14 and 50.
The factors of 14 are: 1, 2, 7, 14
The factors of 50 are: 1, 2, 5, 10, 25, 50
The greatest common factor is 2.
Now divide both numerator and denominator by 2: 14÷250÷2=725\frac{14 \div 2}{50 \div 2} = \frac{7}{25}50÷214÷2=257
✅ Final Answer:
725\boxed{\frac{7}{25}}257
Explanation:
Multiplying fractions is a fundamental skill in math that builds on understanding parts of a whole. In this case, we are multiplying 7/10 by 2/5. The process for multiplying fractions is straightforward: multiply the numerators together, then multiply the denominators.
When we multiply the numerators, 7 and 2, we get 14. This tells us how many parts we have. When we multiply the denominators, 10 and 5, we get 50, which tells us how many equal parts make up the whole. So, the product of 7/10 × 2/5 is 14/50.
However, this fraction is not yet in its simplest form. Simplifying fractions is the process of reducing them to the smallest possible numerator and denominator while keeping the value the same. To simplify 14/50, we find the greatest common factor (GCF) of 14 and 50, which is 2. Dividing both the numerator and denominator by 2 gives us 7/25.
So, the simplest form of 14/50 is 7/25.
Understanding how to multiply and simplify fractions helps in solving real-world problems involving portions, ratios, and rates. It also lays a foundation for more complex math, such as algebra and equations. Always remember: after multiplying, check if the result can be simplified for a cleaner, more understandable answer.
