Select The Best Answer For The Question.9. Multiply 3 4 × 16 9 \frac{3}{4} \times \frac{16}{9} 4 3 ​ × 9 16 ​ .A. 64 27 \frac{64}{27} 27 64 ​ B. 3 4 \frac{3}{4} 4 3 ​ C. 4 3 \frac{4}{3} 3 4 ​ D. 27 64 \frac{27}{64} 64 27 ​

by ADMIN 223 views

Understanding the Basics of Multiplying Fractions

Multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together. In this article, we will focus on multiplying two fractions, specifically 34×169\frac{3}{4} \times \frac{16}{9}, and provide a step-by-step guide on how to solve it.

Why is Multiplying Fractions Important?

Multiplying fractions is an essential skill in mathematics that has numerous applications in real-life situations. For instance, in cooking, you may need to multiply a recipe by a certain fraction to serve a larger group of people. In science, you may need to multiply measurements by a fraction to calculate the volume of a substance. In finance, you may need to multiply interest rates by a fraction to calculate the total interest earned.

The Basics of Multiplying Fractions

To multiply fractions, you need to follow a simple rule: multiply the numerators (the numbers on top) together and multiply the denominators (the numbers on the bottom) together. The resulting fraction is then simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Step-by-Step Guide to Multiplying Fractions

Now that we have covered the basics, let's move on to the step-by-step guide to multiplying fractions.

Step 1: Multiply the Numerators

To multiply the numerators, we simply multiply the two numbers together.

34×169=3×164×9\frac{3}{4} \times \frac{16}{9} = \frac{3 \times 16}{4 \times 9}

Step 2: Multiply the Denominators

To multiply the denominators, we simply multiply the two numbers together.

3×164×9=4836\frac{3 \times 16}{4 \times 9} = \frac{48}{36}

Step 3: Simplify the Fraction

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 48 and 36 is 12.

4836=48÷1236÷12=43\frac{48}{36} = \frac{48 \div 12}{36 \div 12} = \frac{4}{3}

Answer Options

Now that we have simplified the fraction, let's take a look at the answer options.

A. 6427\frac{64}{27} B. 34\frac{3}{4} C. 43\frac{4}{3} D. 2764\frac{27}{64}

Which Answer is Correct?

Based on our step-by-step guide, we can see that the correct answer is:

C. 43\frac{4}{3}

Conclusion

Q: What is the rule for multiplying fractions?

A: The rule for multiplying fractions is to multiply the numerators (the numbers on top) together and multiply the denominators (the numbers on the bottom) together. The resulting fraction is then simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Q: How do I multiply fractions with different denominators?

A: To multiply fractions with different denominators, you need to follow the same rule as multiplying fractions with the same denominator. For example, to multiply 12\frac{1}{2} and 34\frac{3}{4}, you would multiply the numerators together and the denominators together: 1×32×4=38\frac{1 \times 3}{2 \times 4} = \frac{3}{8}.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder. For example, the GCD of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 without leaving a remainder.

Q: How do I simplify a fraction after multiplying?

A: To simplify a fraction after multiplying, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD. For example, to simplify 1218\frac{12}{18}, you would find the GCD of 12 and 18, which is 6, and then divide both numbers by 6: 12÷618÷6=23\frac{12 \div 6}{18 \div 6} = \frac{2}{3}.

Q: Can I multiply a fraction by a whole number?

A: Yes, you can multiply a fraction by a whole number. To do this, you simply multiply the numerator of the fraction by the whole number. For example, to multiply 12\frac{1}{2} by 3, you would multiply the numerator by 3: 1×32=32\frac{1 \times 3}{2} = \frac{3}{2}.

Q: Can I multiply a fraction by a decimal?

A: Yes, you can multiply a fraction by a decimal. To do this, you simply multiply the numerator of the fraction by the decimal. For example, to multiply 12\frac{1}{2} by 0.5, you would multiply the numerator by 0.5: 1×0.52=0.52\frac{1 \times 0.5}{2} = \frac{0.5}{2}.

Q: What are some real-life applications of multiplying fractions?

A: Multiplying fractions has numerous real-life applications, including:

  • Cooking: When you need to multiply a recipe by a certain fraction to serve a larger group of people.
  • Science: When you need to multiply measurements by a fraction to calculate the volume of a substance.
  • Finance: When you need to multiply interest rates by a fraction to calculate the total interest earned.

Conclusion

Multiplying fractions is a fundamental concept in mathematics that has numerous applications in real-life situations. By following a simple rule and understanding the basics of multiplying fractions, you can multiply fractions with ease. In this article, we have covered some frequently asked questions about multiplying fractions and provided answers to help you better understand this concept.