Multiply. Write Your Answer As A Fraction In Simplest Form. 7 11 × 7 15 × 3 \frac{7}{11} \times \frac{7}{15} \times 3 11 7 ​ × 15 7 ​ × 3

Understanding the Problem

In this problem, we are required to multiply three numbers: two fractions and a whole number. The fractions are $\frac{7}{11}$ and $\frac{7}{15}$, and the whole number is $3$. Our goal is to find the product of these three numbers in simplest form.

Step 1: Multiply the Fractions

To multiply fractions, we simply multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). In this case, we have:

$\frac{7}{11} \times \frac{7}{15}$

Multiplying the numerators, we get:

$7 \times 7 = 49$

Multiplying the denominators, we get:

$11 \times 15 = 165$

So, the product of the two fractions is:

$\frac{49}{165}$

Step 2: Multiply the Result by the Whole Number

Now, we need to multiply the result from Step 1 by the whole number $3$. To do this, we can multiply the numerator (49) by $3$ and keep the denominator (165) the same:

$\frac{49}{165} \times 3 = \frac{49 \times 3}{165}$

Multiplying the numerator, we get:

$49 \times 3 = 147$

So, the final result is:

$\frac{147}{165}$

Simplifying the Result

To simplify the result, we need to find the greatest common divisor (GCD) of the numerator (147) and the denominator (165). The GCD is the largest number that divides both numbers without leaving a remainder.

Using a calculator or a GCD calculator, we find that the GCD of 147 and 165 is 3.

To simplify the fraction, we divide both the numerator and the denominator by the GCD:

$\frac{147 \div 3}{165 \div 3} = \frac{49}{55}$

Therefore, the final answer is:

$\frac{49}{55}$

Conclusion

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Frequently Asked Questions

In this article, we will answer some common questions related to the multiplication of fractions and whole numbers.

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). For example, to multiply $\frac{a}{b}$ and $\frac{c}{d}$, we get:

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

Q: How do I multiply a fraction by a whole number?

A: To multiply a fraction by a whole number, we can multiply the numerator (the number on top) by the whole number and keep the denominator (the number on the bottom) the same. For example, to multiply $\frac{a}{b}$ by $c$, we get:

$\frac{a}{b} \times c = \frac{a \times c}{b}$

Q: Can I multiply a fraction by a fraction with a different denominator?

A: Yes, you can multiply a fraction by a fraction with a different denominator. To do this, we need to find the least common multiple (LCM) of the two denominators. The LCM is the smallest number that both denominators can divide into evenly.

For example, to multiply $\frac{a}{b}$ by $\frac{c}{d}$, we need to find the LCM of $b$ and $d$. Once we have the LCM, we can rewrite the fractions with the LCM as the denominator and then multiply the numerators.

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. The GCD is the largest number that divides both numbers without leaving a remainder.

Once we have the GCD, 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 adding fractions?

A: Multiplying fractions involves multiplying the numerators and denominators separately, while adding fractions involves finding a common denominator and adding the numerators.

For example, to multiply $\frac{a}{b}$ and $\frac{c}{d}$, we get:

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

To add $\frac{a}{b}$ and $\frac{c}{d}$, we need to find a common denominator, which is the least common multiple (LCM) of $b$ and $d$. Once we have the LCM, we can rewrite the fractions with the LCM as the denominator and then add the numerators.

Q: Can I multiply a negative fraction by a positive fraction?

A: Yes, you can multiply a negative fraction by a positive fraction. When multiplying a negative fraction by a positive fraction, the result will be a negative fraction.

For example, to multiply $-\frac{a}{b}$ by $\frac{c}{d}$, we get:

$-\frac{a}{b} \times \frac{c}{d} = -\frac{a \times c}{b \times d}$

Conclusion

In this article, we have answered some common questions related to the multiplication of fractions and whole numbers. We have covered topics such as multiplying fractions, multiplying fractions by whole numbers, simplifying fractions, and more. We hope that this article has been helpful in clarifying any doubts you may have had about multiplying fractions and whole numbers.