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# How to Multiply a Whole Number by a Fraction

## Understanding the Basics of Multiplying Whole Numbers and Fractions

When multiplying a whole number by a fraction, it’s important to understand the basics of multiplying these two types of numbers. A whole number represents a complete unit, while a fraction represents a portion of a unit. To multiply a whole number by a fraction, you need to know how to multiply the numerator and denominator of the fraction by the whole number.

To begin, consider the following example: 2 x 1/3. Here, the whole number is 2, and the fraction is 1/3. To multiply these two numbers, you can follow these steps:

1. Multiply the whole number by the numerator of the fraction: 2 x 1 = 2.
2. Write the product above the denominator of the fraction: 2/3.
3. Simplify the resulting fraction if possible: 2/3 is already in its simplest form, so it cannot be simplified further.

Therefore, 2 x 1/3 = 2/3.

By understanding these basic principles of multiplying whole numbers and fractions, you can confidently solve more complex problems involving these types of numbers.

## Converting Mixed Numbers to Improper Fractions

When multiplying a whole number by a mixed number, it’s necessary to convert the mixed number into an improper fraction before proceeding with the multiplication. A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

To convert a mixed number to an improper fraction, you can follow these steps:

1. Multiply the whole number by the denominator of the fraction.
2. Add the resulting product to the numerator of the fraction.
3. Write the sum as the numerator of the new fraction, with the original denominator remaining the same.

For example, if you have the mixed number 2 1/3, you can convert it to an improper fraction as follows:

1. Multiply 2 by 3: 2 x 3 = 6.
2. Add the result to 1: 6 + 1 = 7.
3. Write 7 as the numerator of the new fraction, with the denominator remaining 3: 7/3.

Therefore, to multiply 2 1/3 by another fraction, you would first convert 2 1/3 to 7/3, and then proceed with the multiplication using the steps outlined in the previous section.

## Simplifying Fractions Before Multiplying

Before multiplying a whole number by a fraction, or a mixed number by a fraction, it’s often helpful to simplify the fraction as much as possible. Simplifying the fraction can make the multiplication easier and can also lead to a simpler answer.

To simplify a fraction, you can follow these steps:

1. Find the greatest common factor (GCF) of the numerator and denominator.
2. Divide both the numerator and denominator by the GCF.

For example, if you have the fraction 4/8, you can simplify it as follows:

1. The GCF of 4 and 8 is 4.
2. Divide both the numerator and denominator by 4: 4/8 = 1/2.

Now the fraction is simplified to its lowest terms, making multiplication easier.

By simplifying fractions before multiplying, you can reduce the number of steps required and decrease the likelihood of making errors.

## Multiplying the Numerators and Denominators

Once you have converted mixed numbers to improper fractions and simplified fractions, you can multiply the numerator of the fraction by the whole number, and then multiply the denominator of the fraction by the same whole number.

For example, if you want to multiply 3 by 2/5, you would follow these steps:

1. Multiply the numerator of the fraction by the whole number: 3 x 2 = 6.
2. Write the product above the denominator of the fraction: 6/5.

Therefore, 3 x 2/5 = 6/5.

If you are multiplying a mixed number by a fraction, you would first convert the mixed number to an improper fraction and then follow the same steps to multiply the numerator and denominator.

By multiplying the numerators and denominators separately, you can ensure that you are correctly calculating the value of the fraction and obtaining the correct product.

## Converting Improper Fractions to Mixed Numbers

After multiplying a whole number by a fraction or multiplying a mixed number by a fraction, you may end up with an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To simplify the answer, it’s often useful to convert the improper fraction back to a mixed number.

To convert an improper fraction to a mixed number, you can follow these steps:

1. Divide the numerator by the denominator.
2. Write down the whole number part of the answer.
3. Write down the remainder as the numerator of the new fraction.
4. The denominator of the new fraction is the same as the denominator of the original fraction.

For example, if you have the improper fraction 7/3, you can convert it to a mixed number as follows:

1. Divide 7 by 3: 7 Ã· 3 = 2 with a remainder of 1.
2. Write down the whole number part of the answer: 2.
3. Write down the remainder as the numerator of the new fraction: 1.
4. The denominator of the new fraction is the same as the denominator of the original fraction: 3.

Therefore, 7/3 can be converted to the mixed number 2 1/3.

By converting improper fractions to mixed numbers, you can obtain a simpler answer that is easier to understand and work with.