# How To Multiply A Whole Number By A Fraction

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This article was written by Mario Banuelos, PhD and staff writer, Jessica Gibson. Mario Banuelos is an Assistant Professor of Mathematics at California State University, Fresno. With more than eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at the high school and college level.

## How To Multiply A Whole Number By A Fraction

Multiply simple fractions by mixed fractions or whole numbers. Begin by converting your mixed fractions or whole numbers to improper fractions. Then multiply the numerators of both improper fractions. Multiply the denominator and simplify your result.

#### Multiplying Whole Numbers By Fractions

This article was written by Mario Banuelos, PhD and staff writer, Jessica Gibson. Mario Banuelos is an Assistant Professor of Mathematics at California State University, Fresno. With more than eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at the high school and college level. This article has been viewed 2,132,731 times.

To multiply a fraction by a whole number, first rewrite the whole number as a fraction by multiplying it by 1. For example, let’s say you’re trying to solve 5 x 8/10. You start by rewriting 5 as a fraction. Now the equation looks like 5/1 x 8/10. Then you have to multiply the numerator, or top number, of the fraction together. In our example, 5 and 8 are numerators, so you multiply 5 by 8 and get 40. Now do the same with the denominator, or bottom number, of the fraction. One and 10 are common denominators, so you multiply 1 by 10 and get 10. The new fraction is 40/10. If you can’t simplify the new fraction, you’re done and that’s your answer. If possible, simplify the fraction to the lowest term. In our example, we arrive at 40/10, which can be simplified by dividing the numerator and denominator by 10, which gives you 4/1. Therefore, 5 x 8/10 = 4/1, or 4. To learn how to multiply fractions by whole numbers, scroll down! Multiplying a fraction by a whole number is a simple operation. It is one of the basic concepts taught in the lower grades. It is taught to improve the arithmetical capacity of the students. Students often get confused while multiplying and dividing fractions. This article will review techniques for multiplying fractions by whole numbers with some examples.

Before learning how to multiply fractions with whole numbers, let’s look at some basic terminology used in multiplication. Do you know what a fraction is? A fraction, in general, is a number presented in the form of p/q. For example, 2/3, 9/2, etc.

You must understand that a fractional number has two parts. The part above the ‘dash’ is the numerator, and the amount below the ‘dash’ is called the denominator. All kinds of mathematical operations can be applied to fractions.

## Multiplying Fractions By A Whole Number Worksheet

When you divide the numerator and the denominator, you get a whole number or a decimal number. Not a fraction left. So the value of a can never be a fraction if the form is not p/q.

To begin learning how to multiply fractions with whole numbers, we need to learn how to multiply fractions with other fractions. Let us know about the same in the article.

Suppose we have two fractions, d/c and j/k. To multiply these fractions, you must write them exactly opposite each other. Then look at the numerator and the denominator of the fraction. Multiply the numerators together (d x j) = x. Write the result of multiplying the numerators in different fractions, say ‘x’.

Similarly, multiply the denominator of the fraction. Write the multiplicative result of the lowest denominator of the numerator, (c x k) = y. So the multiplication of two fractions can be described as:

### Math Clip Art Using Place Value To Multiply Decimals By Whole Numbers 15

The fraction after multiplying 4/5 and 3/7 is 12/35. If the number in the fraction is several smaller numbers, then you can easily reduce the fraction in simpler form. The only requirement is that if you divide the numerator by the number ‘a’, you must divide the denominator by the same number ‘a’.

Solution: We can see that the numerator = 12 and the denominator = 9 are multiples of 3. So we have to divide the numerator by 3 and the denominator by 3. This gives us

Now we have learned how to multiply two fractions. In this section you will learn how to multiply fractions with whole numbers. Note that we have the fraction d/c and the integer ‘k’. The first step to multiplying fractions and whole numbers is to start by writing them exactly opposite each other with the multiplication sign. We do not have the form ‘p/q’ in case of whole numbers. So we start changing the numbers into fractions. To do this, put a separator under all numbers with 1 as the denominator. Now we have the integer in the form ‘p/q’.

Now we follow the same steps mentioned in the multiplying fractions section. Now look at the numerator and denominator of the fraction and the whole number. Multiply the numerator by all the numbers ‘k’, so (d x k) = x. Now multiply the denominator of the fraction by 1 (because the denominator of the whole number is 1). This gives (c x 1 = c). So the multiplication of two fractions can be described as:

## Divide Whole Numbers By Fractions

In the case of multiplying fractions and whole numbers, the denominator of the fraction is retained. So when you encounter this type of multiplication, put the denominator as a fraction and multiply the numerator.

Step 2: Since we know that the denominator remains the same in such a case, we must multiply the numerator.

Hopefully now the question of how to multiply a fraction by a whole number is easy. Next, let’s look at a very interesting idea.

But we can see that if we eliminate 11 from the beginning, we still get the answer as 3.

## Worksheets For Fraction Multiplication

As mentioned in the example above. For example, a fraction multiplied by a whole number is either a multiple of the denominator or equal to the denominator. In that case, you can eliminate or reduce the numbers before the actual multiplication. Understand this with the example below:

We can see that all sums and denominators are the same. So we can eliminate them and get the digit of our fraction as the answer.

We observe that the denominator in all the numbers are multiples of 7. So we reduce them to their lowest form. 7 divided by itself and 1 and 21 divided by 7 and 3. Now we have 3 x 3 in the numerator. So the answer to this question is 9.

As we know, all numbers are the set of real numbers starting from zero and extending to positive infinity. We have all seen cases that occur when a fraction is multiplied by a whole number. When you multiply a fraction by 1, it produces its own number. But, what happens when you multiply a fraction by zero?

#### Ex 6.3, 5

We know that anything multiplied by zero is 0. So when a fraction is multiplied by zero, the resulting fraction is zero or 0/1.

The inverse of a number is when the numerator and denominator exchange their positions. Because 0 = 0/1 so the reciprocal is 1/0. Suppose we have a fraction ‘a / b’. Using the steps we have learned so far, a x 1 = a and b x 0 = 0. Therefore, the resulting fraction is a/0. In mathematics, 1/0 or everything divided by zero is undefined. So we cannot multiply the number back to zero.

Word problem: Jill makes homemade hot chocolate. She uses a quarter of a teaspoon of the hot chocolate mixture to make 1 cup of hot chocolate. Calculate the number of teaspoons needed to make 10 cups of hot chocolate.

Ans. You can multiply fractions by multiplying the numerator (top number) and then multiplying the denominator (bottom number).

## Inquiry Math Multiplying Fractions By Whole Numbers_0

Ans. There are many ways to multiply fractions. The easiest way is to find the least common multiple of the denominator and multiply it by the numerator of one fraction and then multiply by the numerator of the other fraction. If you have a calculator, this can be done very quickly.

Ans. The general rule for multiplying fractions is to multiply the numerator and multiply the denominator, then simplify.

Ans. To multiply fractions, you need to go into fraction mode on your calculator. Then you enter the first fraction (the one above) and press the multiplication button. The other one