Evaluate $1 \frac{5}{6} \cdot \frac{9}{4}$.$ \begin{array}{l} 1 \frac{5}{6} \cdot \frac{9}{4} = \frac{11}{6} \cdot \frac{9}{4} \\ \text{Enter Your Next Step Here} \end{array} $

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Introduction

In mathematics, mixed numbers are a combination of a whole number and a fraction. When we multiply mixed numbers, we need to follow a specific procedure to simplify the expression. In this article, we will evaluate the expression 156⋅941 \frac{5}{6} \cdot \frac{9}{4} using the correct steps.

Step 1: Convert the Mixed Number to an Improper Fraction

The first step is to convert the mixed number 1561 \frac{5}{6} to an improper fraction. To do this, we multiply the whole number by the denominator and add the numerator.

156=(1×6)+56=1161 \frac{5}{6} = \frac{(1 \times 6) + 5}{6} = \frac{11}{6}

Now, we can rewrite the original expression as:

116⋅94\frac{11}{6} \cdot \frac{9}{4}

Step 2: Multiply the Numerators and Denominators

Next, we multiply the numerators and denominators separately.

116⋅94=11×96×4\frac{11}{6} \cdot \frac{9}{4} = \frac{11 \times 9}{6 \times 4}

Step 3: Simplify the Expression

Now, we simplify the expression by multiplying the numbers in the numerator and denominator.

11×96×4=9924\frac{11 \times 9}{6 \times 4} = \frac{99}{24}

Step 4: Reduce the Fraction to its Lowest Terms

Finally, we reduce the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD).

The GCD of 99 and 24 is 3. Therefore, we can divide both numbers by 3 to get:

99÷324÷3=338\frac{99 \div 3}{24 \div 3} = \frac{33}{8}

Conclusion

In this article, we evaluated the expression 156⋅941 \frac{5}{6} \cdot \frac{9}{4} using the correct steps. We converted the mixed number to an improper fraction, multiplied the numerators and denominators, simplified the expression, and finally reduced the fraction to its lowest terms. The final answer is 338\boxed{\frac{33}{8}}.

Example Problems

Here are a few example problems to help you practice evaluating mixed numbers in multiplication.

Example 1

Evaluate the expression 234⋅562 \frac{3}{4} \cdot \frac{5}{6}.

Solution

234=(2×4)+34=1142 \frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{11}{4}

114⋅56=11×54×6=5524\frac{11}{4} \cdot \frac{5}{6} = \frac{11 \times 5}{4 \times 6} = \frac{55}{24}

5524=55÷124÷1=5524\frac{55}{24} = \frac{55 \div 1}{24 \div 1} = \frac{55}{24}

The final answer is 5524\boxed{\frac{55}{24}}.

Example 2

Evaluate the expression 323⋅783 \frac{2}{3} \cdot \frac{7}{8}.

Solution

323=(3×3)+23=1133 \frac{2}{3} = \frac{(3 \times 3) + 2}{3} = \frac{11}{3}

113⋅78=11×73×8=7724\frac{11}{3} \cdot \frac{7}{8} = \frac{11 \times 7}{3 \times 8} = \frac{77}{24}

7724=77÷124÷1=7724\frac{77}{24} = \frac{77 \div 1}{24 \div 1} = \frac{77}{24}

The final answer is 7724\boxed{\frac{77}{24}}.

Tips and Tricks

Here are a few tips and tricks to help you evaluate mixed numbers in multiplication:

  • Always convert the mixed number to an improper fraction before multiplying.
  • Multiply the numerators and denominators separately.
  • Simplify the expression by multiplying the numbers in the numerator and denominator.
  • Reduce the fraction to its lowest terms by dividing both the numerator and denominator by their GCD.

Introduction

In our previous article, we evaluated the expression 156⋅941 \frac{5}{6} \cdot \frac{9}{4} using the correct steps. We converted the mixed number to an improper fraction, multiplied the numerators and denominators, simplified the expression, and finally reduced the fraction to its lowest terms. In this article, we will answer some frequently asked questions about evaluating mixed numbers in multiplication.

Q: What is the first step in evaluating a mixed number in multiplication?

A: The first step is to convert the mixed number to an improper fraction. To do this, we multiply the whole number by the denominator and add the numerator.

Q: How do I multiply the numerators and denominators in a mixed number multiplication problem?

A: To multiply the numerators and denominators, we simply multiply the numbers in the numerator and denominator separately.

Q: What is the next step after multiplying the numerators and denominators?

A: After multiplying the numerators and denominators, we simplify the expression by multiplying the numbers in the numerator and denominator.

Q: How do I reduce a fraction to its lowest terms?

A: To reduce a fraction to its lowest terms, we divide both the numerator and denominator by their greatest common divisor (GCD).

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

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator of a fraction without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, we can use the Euclidean algorithm or simply list the factors of each number and find the largest common factor.

Q: What are some common mistakes to avoid when evaluating mixed numbers in multiplication?

A: Some common mistakes to avoid when evaluating mixed numbers in multiplication include:

  • Not converting the mixed number to an improper fraction before multiplying
  • Not multiplying the numerators and denominators separately
  • Not simplifying the expression after multiplying the numerators and denominators
  • Not reducing the fraction to its lowest terms

Q: How can I practice evaluating mixed numbers in multiplication?

A: You can practice evaluating mixed numbers in multiplication by working through example problems, such as the ones provided in our previous article. You can also try creating your own mixed number multiplication problems and solving them.

Q: What are some real-world applications of evaluating mixed numbers in multiplication?

A: Evaluating mixed numbers in multiplication has many real-world applications, including:

  • Calculating the cost of items on a shopping list
  • Determining the area of a room or a piece of land
  • Finding the volume of a container or a solid object
  • Calculating the interest on a loan or investment

By following these steps and tips, you can evaluate mixed numbers in multiplication with ease and apply your skills to real-world problems.

Example Problems

Here are a few example problems to help you practice evaluating mixed numbers in multiplication.

Example 1

Evaluate the expression 234⋅562 \frac{3}{4} \cdot \frac{5}{6}.

Solution

234=(2×4)+34=1142 \frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{11}{4}

114⋅56=11×54×6=5524\frac{11}{4} \cdot \frac{5}{6} = \frac{11 \times 5}{4 \times 6} = \frac{55}{24}

5524=55÷124÷1=5524\frac{55}{24} = \frac{55 \div 1}{24 \div 1} = \frac{55}{24}

The final answer is 5524\boxed{\frac{55}{24}}.

Example 2

Evaluate the expression 323⋅783 \frac{2}{3} \cdot \frac{7}{8}.

Solution

323=(3×3)+23=1133 \frac{2}{3} = \frac{(3 \times 3) + 2}{3} = \frac{11}{3}

113⋅78=11×73×8=7724\frac{11}{3} \cdot \frac{7}{8} = \frac{11 \times 7}{3 \times 8} = \frac{77}{24}

7724=77÷124÷1=7724\frac{77}{24} = \frac{77 \div 1}{24 \div 1} = \frac{77}{24}

The final answer is 7724\boxed{\frac{77}{24}}.

Tips and Tricks

Here are a few tips and tricks to help you evaluate mixed numbers in multiplication:

  • Always convert the mixed number to an improper fraction before multiplying.
  • Multiply the numerators and denominators separately.
  • Simplify the expression by multiplying the numbers in the numerator and denominator.
  • Reduce the fraction to its lowest terms by dividing both the numerator and denominator by their GCD.

By following these steps and tips, you can evaluate mixed numbers in multiplication with ease and apply your skills to real-world problems.