Calculate The Product Of The Following Expression:${ 1 \frac{5}{6} \times 7 }$

Introduction

In mathematics, mixed numbers and whole numbers are two types of numbers that can be used to represent quantities. A mixed number is a combination of a whole number and a fraction, while a whole number is a number without any fractional part. When we need to calculate the product of mixed numbers and whole numbers, we can use the concept of multiplication to find the result. In this article, we will discuss how to calculate the product of the expression $1 \frac{5}{6} \times 7$.

Understanding Mixed Numbers and Whole Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction. For example, $1 \frac{5}{6}$ is a mixed number where $1$ is the whole number part, $5$ is the numerator, and $6$ is the denominator.

A whole number is a number without any fractional part. It is a number that can be written without any decimal or fraction. For example, $7$ is a whole number.

Calculating the Product of Mixed Numbers and Whole Numbers

To calculate the product of mixed numbers and whole numbers, we can use the concept of multiplication. When we multiply a mixed number by a whole number, we can multiply the whole number part of the mixed number by the whole number, and then multiply the fraction part of the mixed number by the whole number.

Let's consider the expression $1 \frac{5}{6} \times 7$. To calculate the product, we can follow these steps:

1. Multiply the whole number part of the mixed number by the whole number: $1 \times 7 = 7$
2. Multiply the fraction part of the mixed number by the whole number: $\frac{5}{6} \times 7 = \frac{35}{6}$
3. Add the result of step 1 to the result of step 2: $7 + \frac{35}{6} = \frac{42}{6} + \frac{35}{6} = \frac{77}{6}$

Therefore, the product of the expression $1 \frac{5}{6} \times 7$ is $\frac{77}{6}$.

Simplifying the Result

To simplify the result, we can divide the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of $77$ and $6$ is $1$. Therefore, the simplified result is $\frac{77}{6}$.

Conclusion

In conclusion, calculating the product of mixed numbers and whole numbers involves multiplying the whole number part of the mixed number by the whole number, and then multiplying the fraction part of the mixed number by the whole number. The result can be simplified by dividing the numerator and denominator by their greatest common divisor. In this article, we discussed how to calculate the product of the expression $1 \frac{5}{6} \times 7$.

Example Problems

Here are some example problems that involve calculating the product of mixed numbers and whole numbers:

• $2 \frac{3}{4} \times 5$
• $3 \frac{1}{2} \times 4$
• $4 \frac{2}{3} \times 3$

Practice Problems

Here are some practice problems that involve calculating the product of mixed numbers and whole numbers:

• $1 \frac{1}{2} \times 6$
• $2 \frac{3}{4} \times 3$
• $3 \frac{1}{3} \times 2$

Answer Key

Here are the answers to the example problems and practice problems:

• $2 \frac{3}{4} \times 5 = \frac{15}{4} \times 5 = \frac{75}{4}$
• $3 \frac{1}{2} \times 4 = \frac{7}{2} \times 4 = \frac{28}{2} = 14$
• $4 \frac{2}{3} \times 3 = \frac{14}{3} \times 3 = \frac{42}{3} = 14$
• $1 \frac{1}{2} \times 6 = \frac{3}{2} \times 6 = \frac{18}{2} = 9$
• $2 \frac{3}{4} \times 3 = \frac{11}{4} \times 3 = \frac{33}{4}$
• $3 \frac{1}{3} \times 2 = \frac{10}{3} \times 2 = \frac{20}{3}$
  Frequently Asked Questions (FAQs) about Calculating the Product of Mixed Numbers and Whole Numbers =============================================================================================

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction.

Q: How do I calculate the product of a mixed number and a whole number?

A: To calculate the product of a mixed number and a whole number, you can multiply the whole number part of the mixed number by the whole number, and then multiply the fraction part of the mixed number by the whole number. The result can be simplified by dividing the numerator and denominator by their greatest common divisor (GCD).

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

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

Q: How do I simplify a fraction?

A: To simplify a fraction, you can divide the numerator and denominator by their greatest common divisor (GCD). For example, the fraction $\frac{12}{18}$ can be simplified by dividing both numbers by $6$, resulting in $\frac{2}{3}$.

Q: What is the product of $2 \frac{3}{4} \times 5$?

A: To calculate the product of $2 \frac{3}{4} \times 5$, you can multiply the whole number part of the mixed number by the whole number, and then multiply the fraction part of the mixed number by the whole number. The result is $\frac{15}{4} \times 5 = \frac{75}{4}$.

Q: What is the product of $3 \frac{1}{2} \times 4$?

A: To calculate the product of $3 \frac{1}{2} \times 4$, you can multiply the whole number part of the mixed number by the whole number, and then multiply the fraction part of the mixed number by the whole number. The result is $\frac{7}{2} \times 4 = \frac{28}{2} = 14$.

Q: What is the product of $4 \frac{2}{3} \times 3$?

A: To calculate the product of $4 \frac{2}{3} \times 3$, you can multiply the whole number part of the mixed number by the whole number, and then multiply the fraction part of the mixed number by the whole number. The result is $\frac{14}{3} \times 3 = \frac{42}{3} = 14$.

Q: How do I calculate the product of a mixed number and a fraction?

A: To calculate the product of a mixed number and a fraction, you can multiply the whole number part of the mixed number by the fraction, and then multiply the fraction part of the mixed number by the fraction. The result can be simplified by dividing the numerator and denominator by their greatest common divisor (GCD).

Q: What is the product of $1 \frac{1}{2} \times \frac{2}{3}$?

A: To calculate the product of $1 \frac{1}{2} \times \frac{2}{3}$, you can multiply the whole number part of the mixed number by the fraction, and then multiply the fraction part of the mixed number by the fraction. The result is $\frac{3}{2} \times \frac{2}{3} = \frac{6}{6} = 1$.

Q: What is the product of $2 \frac{3}{4} \times \frac{3}{5}$?

A: To calculate the product of $2 \frac{3}{4} \times \frac{3}{5}$, you can multiply the whole number part of the mixed number by the fraction, and then multiply the fraction part of the mixed number by the fraction. The result is $\frac{11}{4} \times \frac{3}{5} = \frac{33}{20}$.

Q: What is the product of $3 \frac{1}{3} \times \frac{2}{5}$?

A: To calculate the product of $3 \frac{1}{3} \times \frac{2}{5}$, you can multiply the whole number part of the mixed number by the fraction, and then multiply the fraction part of the mixed number by the fraction. The result is $\frac{10}{3} \times \frac{2}{5} = \frac{20}{15} = \frac{4}{3}$.

Conclusion

In conclusion, calculating the product of mixed numbers and whole numbers involves multiplying the whole number part of the mixed number by the whole number, and then multiplying the fraction part of the mixed number by the whole number. The result can be simplified by dividing the numerator and denominator by their greatest common divisor (GCD). We hope this article has provided you with a better understanding of how to calculate the product of mixed numbers and whole numbers.