Section 1.4 - Practice QuestionsMultiply The Following, Simplify Before You Multiply If Desired, And Leave The Answer In Simplified Form:1. \[$\frac{1}{3} \times \frac{12}{7}\$\]$\[ \begin{align*} \frac{1}{3} \times \frac{12}{7} &=

Section 1.4 - Practice Questions

Multiply the following, simplify before you multiply if desired, and leave the answer in simplified form:

1. $\frac{1}{3} \times \frac{12}{7}$

To multiply fractions, we need to multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). The result will be a fraction that we can simplify if necessary.

Step 1: Multiply the Numerators

The numerator of the first fraction is 1, and the numerator of the second fraction is 12. To multiply them, we simply multiply 1 and 12.

1 × 12 = 12

Step 2: Multiply the Denominators

The denominator of the first fraction is 3, and the denominator of the second fraction is 7. To multiply them, we simply multiply 3 and 7.

3 × 7 = 21

Step 3: Write the Result as a Fraction

Now that we have multiplied the numerators and the denominators, we can write the result as a fraction.

$\frac{12}{21}$

Step 4: Simplify the Fraction (if necessary)

To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. If the GCD is greater than 1, we can divide both the numerator and the denominator by the GCD to simplify the fraction.

In this case, the GCD of 12 and 21 is 3. We can divide both the numerator and the denominator by 3 to simplify the fraction.

$\frac{12}{21} = \frac{12 ÷ 3}{21 ÷ 3} = \frac{4}{7}$

Therefore, the simplified form of the product of $\frac{1}{3}$ and $\frac{12}{7}$ is $\frac{4}{7}$.

Practice Questions

Try multiplying the following fractions and simplifying the result:

• $\frac{2}{5} \times \frac{15}{8}$
• $\frac{3}{4} \times \frac{16}{9}$
• $\frac{1}{2} \times \frac{24}{11}$

Answer Key

• $\frac{2}{5} \times \frac{15}{8} = \frac{30}{40} = \frac{3}{4}$
• $\frac{3}{4} \times \frac{16}{9} = \frac{48}{36} = \frac{4}{3}$
• $\frac{1}{2} \times \frac{24}{11} = \frac{24}{22} = \frac{12}{11}$

Conclusion

Multiplying fractions is a straightforward process that involves multiplying the numerators and the denominators and simplifying the result if necessary. By following the steps outlined in this article, you can multiply fractions with confidence and accuracy.

Further Reading

If you want to learn more about multiplying fractions, you can try the following resources:

• Khan Academy: Multiplying Fractions
• Mathway: Multiplying Fractions
• IXL: Multiplying Fractions

Discussion Category

Section 1.4 - Practice Questions

Q&A: Multiplying Fractions

Q: What is the rule for multiplying fractions?

A: The rule for multiplying fractions is to multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). The result will be a fraction that we can simplify if necessary.

Q: How do I multiply fractions with different denominators?

A: To multiply fractions with different denominators, we need to find the least common multiple (LCM) of the denominators. Then, we can multiply the numerators and the denominators by the LCM to get a new fraction with the same denominator.

Q: Can I multiply fractions with negative numbers?

A: Yes, we can multiply fractions with negative numbers. When multiplying fractions with negative numbers, we need to remember that a negative times a negative is a positive, and a negative times a positive is a negative.

Q: How do I simplify a fraction after multiplying?

A: To simplify a fraction after multiplying, we need to find the greatest common divisor (GCD) of the numerator and the denominator. If the GCD is greater than 1, we can divide both the numerator and the denominator by the GCD to simplify the fraction.

Q: What is the difference between multiplying fractions and multiplying whole numbers?

A: The main difference between multiplying fractions and multiplying whole numbers is that when multiplying fractions, we need to multiply the numerators and the denominators, whereas when multiplying whole numbers, we only need to multiply the numbers.

Q: Can I multiply fractions with decimals?

A: Yes, we can multiply fractions with decimals. When multiplying fractions with decimals, we need to convert the decimals to fractions first, then multiply the fractions.

Q: How do I multiply fractions with variables?

A: To multiply fractions with variables, we need to multiply the numerators and the denominators, just like we do with regular fractions. However, we need to be careful when simplifying the result, as we may need to use algebraic properties to simplify the expression.

Practice Questions

Try answering the following questions:

• What is the product of $\frac{1}{2}$ and $\frac{3}{4}$?
• What is the product of $\frac{2}{3}$ and $\frac{5}{6}$?
• What is the product of $\frac{3}{4}$ and $\frac{2}{5}$?

Answer Key

• $\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$
• $\frac{2}{3} \times \frac{5}{6} = \frac{10}{18} = \frac{5}{9}$
• $\frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10}$

Conclusion

Multiplying fractions is a fundamental concept in mathematics that can be applied to a wide range of problems. By following the rules and examples outlined in this article, you can become more confident and proficient in multiplying fractions.

Further Reading

If you want to learn more about multiplying fractions, you can try the following resources:

• Khan Academy: Multiplying Fractions
• Mathway: Multiplying Fractions
• IXL: Multiplying Fractions

Discussion Category

This article is part of the mathematics discussion category. If you have any questions or comments about multiplying fractions, please feel free to ask.