Layla Has $\frac{3}{4}$ Of A Can Of Paint. She Uses $\frac{2}{3}$ Of The Paint For One Wall In Her Bedroom. How Much Of The Can Did She Use?A. $\frac{1}{12}$ Of The Can B. $\frac{5}{12}$ Of The Can C.

Feb 27, 2025 by ADMIN 203 views

Multiplying Fractions to Find the Amount of Paint Used

Understanding the Problem

Layla has a can of paint, and she wants to use it to paint one wall in her bedroom. To determine how much of the can she will use, we need to multiply the fraction of the can she has by the fraction of the paint she will use for the wall. This problem involves multiplying fractions, which is a fundamental concept in mathematics.

Multiplying Fractions

To multiply fractions, we multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). The result is a fraction that represents the product of the two fractions.

The Formula for Multiplying Fractions

The formula for multiplying fractions is:

(a/b) × (c/d) = (ac)/(bd)

Applying the Formula to the Problem

In this problem, Layla has $\frac{3}{4}$ of a can of paint, and she wants to use $\frac{2}{3}$ of the paint for one wall. To find the amount of paint she will use, we multiply the two fractions:

$\frac{3}{4}$ × $\frac{2}{3}$ = ?

Multiplying the Numerators and Denominators

To multiply the fractions, we multiply the numerators (3 and 2) and multiply the denominators (4 and 3):

(3 × 2) / (4 × 3) = 6/12

Simplifying the Fraction

The fraction 6/12 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 6. This gives us:

6 ÷ 6 / 12 ÷ 6 = 1/2

Conclusion

Therefore, Layla will use $\frac{1}{2}$ of the can of paint to paint one wall in her bedroom.

Answer

The correct answer is:

A. $\frac{1}{12}$ of the can

Explanation

The correct answer is not A. $\frac{1}{12}$ of the can. The correct answer is actually $\frac{1}{2}$ of the can, but this option is not available. The closest option is B. $\frac{5}{12}$ of the can, but this is not the correct answer.

Discussion

This problem involves multiplying fractions, which is a fundamental concept in mathematics. The formula for multiplying fractions is (a/b) × (c/d) = (ac)/(bd). In this problem, we applied the formula to find the amount of paint Layla will use to paint one wall in her bedroom. The correct answer is $\frac{1}{2}$ of the can, but this option is not available.

Real-World Applications

Multiplying fractions has many real-world applications, such as calculating the amount of materials needed for a project, determining the cost of a product, and finding the area of a shape. In this problem, we used multiplying fractions to find the amount of paint Layla will use to paint one wall in her bedroom.

Tips and Tricks

When multiplying fractions, make sure to multiply the numerators and denominators correctly. Also, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.

Conclusion

In conclusion, multiplying fractions is a fundamental concept in mathematics that has many real-world applications. In this problem, we used multiplying fractions to find the amount of paint Layla will use to paint one wall in her bedroom. The correct answer is $\frac{1}{2}$ of the can, but this option is not available.
Multiplying Fractions Q&A

Understanding Multiplying Fractions

Multiplying fractions is a fundamental concept in mathematics that has many real-world applications. In this article, we will answer some common questions about multiplying fractions.

Q: What is the formula for multiplying fractions?

A: The formula for multiplying fractions is (a/b) × (c/d) = (ac)/(bd).

Q: How do I multiply fractions?

A: To multiply fractions, you multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). The result is a fraction that represents the product of the two fractions.

Q: What if the fractions have different denominators?

A: If the fractions have different denominators, you need to find the least common multiple (LCM) of the denominators and then multiply the fractions. For example, if you have $\frac{1}{2}$ and $\frac{1}{3}$ , you need to find the LCM of 2 and 3, which is 6. Then, you multiply the fractions: $\frac{1}{2}$ × $\frac{1}{3}$ = $\frac{1}{6}$ .

Q: Can I simplify the fraction after multiplying?

A: Yes, you can simplify the fraction after multiplying. To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator and then divide both numbers by the GCD. For example, if you have $\frac{6}{12}$ , the GCD of 6 and 12 is 6. So, you divide both numbers by 6 to get $\frac{1}{2}$ .

Q: What if I have a fraction with a negative sign?

A: If you have a fraction with a negative sign, you need to multiply the numerator and the denominator by -1 to get a positive fraction. For example, if you have $-\frac{1}{2}$ , you multiply the numerator and the denominator by -1 to get $\frac{1}{2}$ .

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 multiply the numerator by the whole number and keep the denominator the same. For example, if you have $\frac{1}{2}$ and you multiply it by 3, you get $\frac{3}{2}$ .

Q: What if I have a mixed number?

A: If you have a mixed number, you need to convert it to an improper fraction before multiplying. A mixed number is a number that has a whole number part and a fractional part. For example, if you have 2 $\frac{1}{2}$ , you can convert it to an improper fraction by multiplying the whole number part by the denominator and then adding the numerator: 2 × 2 + 1 = 5. So, 2 $\frac{1}{2}$ is equal to $\frac{5}{2}$ .

Q: Can I multiply fractions with different units?

A: No, you cannot multiply fractions with different units. Fractions must have the same unit to be multiplied. For example, if you have $\frac{1}{2}$ of a pound and $\frac{1}{3}$ of a pound, you cannot multiply them because they have different units.

Conclusion

Multiplying fractions is a fundamental concept in mathematics that has many real-world applications. In this article, we answered some common questions about multiplying fractions, including how to multiply fractions, how to simplify fractions, and how to multiply fractions with different units. We hope this article has helped you understand multiplying fractions better.