**Multiplying Whole Numbers And Fractions** – Fifth grade may have been the last time you thought about multiplying fractions. But if you’re trying to cut a recipe in half using fractions or calculate the new price of a sweater on sale, you may need to dig to the bottom of your memory.

Each fraction has a top and bottom number separated by a short horizontal line. In good fractions, the smaller number (called the numerator) is always on top and the larger number (the denominator) is always on the bottom. The numerator indicates how many units there are in the whole, and the denominator indicates how many units make up the whole. So in the fraction 1/2, 1 is the numerator and 2 is the denominator. There are two units in total, but this fraction shows that there is only one of those units.

## Multiplying Whole Numbers And Fractions

Unlike adding or subtracting fractions, you can multiply fractions with different denominators. For example, multiplying by 3/4 x 2/5 is fine.

### Multiplying Fractions And Whole Numbers (video)

The third step is to simplify or reduce fractions. This is because there are better ways to read fractions.

To do this, divide both the numerator and denominator to find the largest number that can reduce the fraction. In this case, the largest number that is divisible by both is 2, so the simplified answer to this multiplication problem is 3/10.

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This article is co-authored by Dr. Mario Banuelos and his writer, Jessica Gibson. Mario Banuelos is an Assistant Professor of Mathematics at California State University, Fresno. With over 8 years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models of genome evolution, and data science. He earned a Bachelor’s degree in Mathematics from California State University, Fresno, and received his Ph.D. He holds a BA in Applied Mathematics from the University of California, Merced. He taught Mario in high school and college.

## Multiplying Whole Numbers By Fractions

Multiplying a fraction by a mixed number or an integer is easy. He begins by converting mixed numbers or integers to improper fractions. Then multiply the numerators of both improper fractions. Multiply by the denominator to simplify the result.

This article is co-authored by Dr. Mario Banuelos and his writer, Jessica Gibson. Mario Banuelos is an Assistant Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models of genome evolution, and data science. He earned a Bachelor’s degree in Mathematics from California State University, Fresno, and received his Ph.D. He holds a BA in Applied Mathematics from the University of California, Merced. Mario taught in high school and college. This article he has been viewed 2,132,295 times.

To multiply a fraction by an integer, first rewrite it as a fraction by placing the integer over 1. For example, say you are trying to solve 5 x 8/10. Start by rewriting 5 as a fraction. Now the equation looks like 5/1 x 8/10. Then you need to multiply by the numerator or maximum number of the fraction. In this example, 5 and 8 are numerators, so 5 multiplied by 8 equals 40. Do the same for the number in the base of the denominator or fraction. 1 multiplied by 10 equals 10 because 1 and 10 are denominators. The new fraction is 40/10. If the new fraction cannot be simplified, you are done and that is the answer. Simplify fractions to minterms if possible. In this example we got 40/10. This can be simplified by dividing the numerator and denominator by 10, resulting in 4/1. So 5 x 8/10 = 4/1 or 4. Scroll down for how to multiply regular fractions by integers. Multiplying fractions and integers is a simple operation. It is one of the basic terms learned in the lower grades. It is taught to improve students’ math skills. Students often get confused when multiplying and dividing fractions. This article uses some examples to demonstrate techniques for multiplying fractions by integers.

Before learning how to multiply fractions by whole numbers, let’s review some basic terms used in multiplication. Do you know minutes? Fractions are numbers usually expressed in the form p/q. For example, 2/3, 9/2, and so on.

#### Multiplying Mixed Numbers — Rules & Problems

It should be understood that fractions consist of two parts. The part above the hyphen is called the numerator, and the number below the hyphen is called the denominator. All kinds of mathematical operations can be applied to fractions.

Dividing the numerator by the denominator gives a whole number or a decimal number. Not even a fraction is left. Therefore, the values are never fractions unless the format is p/q.

First, to learn how to multiply a fraction by an integer, you need to learn how to multiply a fraction by another. Please tell me the same in the article.

Suppose we have two fractions d/c and j/k. To multiply these fractions, they must be written face-to-face. Now look at the numerator and denominator of the fraction. Multiply the numerator (d x j) = x. Write down the results of multiplying the numerator by various fractions. For example, “x”.

#### Multiply A Whole Number By A Fraction Using A Tape Diagram

Similarly, multiply the denominator of the fraction. Write the denominator multiplication result below the resulting numerator (c x k) = y. So the multiplication of two fractions can be expressed as

After multiplying 4/5 by 3/7, the fraction is 12/35. If the number of fractions is a multiple of a smaller number, we can easily reduce the fraction to a simple form. The only condition is that if the numerator is divided by any number ‘a’, the denominator must also be divided by the same number ‘a’.

Solution: We see that both numerator = 12 and denominator = 9 are multiples of 3. So divide the numerator by 3 and the denominator by 3.

You have now learned how to multiply two fractions. In this section, you will learn how to multiply fractions by integers. Suppose we have a fraction d/c and an integer ‘k’. The first step in multiplying fractions and integers always starts with writing one correctly opposite the other using the multiplication sign. For integers, there is no form “p/q”. So first change the number to fractional format. To do this, put a dash under the integer using 1 as the denominator. Now you have an integer of the form ‘p/q’.

## Multiplying Mixed Fractions

Then follow a similar procedure as described in the fraction multiplication section. Now look at the numerator and denominator of fractions and integers. Multiplying the numerator by the integer ‘k’ results in (d x k) = x. The denominator of the fraction is multiplied by 1 (because the denominator of the integer is 1). This gives (c x 1 = c). So the multiplication of two fractions can be expressed as

When multiplying a fraction by an integer, the fraction’s denominator is preserved. So when you find such a multiplication, take the denominator as a fraction and multiply the numerator.

Step 2: In such cases we need to multiply by the numerator since we know that the denominator remains.

I hope the problem of how to multiply a fraction by an integer is simple. Now let’s look at a very interesting idea.

#### Multiplication Of Fraction By Whole Number Worksheet

But even if you erase 11 from the beginning, you’ll find that the answer is 3.

As mentioned in the example above. Suppose fractions are multiplied by a multiple of the denominator or an integer equal to the denominator. In this case the numbers can be removed or reduced before the actual multiplication. Use the example below to understand this.

You can see that the integer and denominator are the same. So we can erase them and get the numerator of the fraction as the answer.

You can see that the denominator and integers are multiples of 7. So reduce them to a minimal form. 7 divided by 7 gives 1 and 21 divided by 7 gives 3. We are left with 3 x 3 in the numerator. So the answer for this question is 9.

#### Multiplying Fractions: The Complete Guide — Mashup Math

As you know, the integers are the set of real numbers starting at zero and extending to positive infinity. We’ve already seen all the cases of what happens when you multiply a fraction by an integer. Multiplying the fraction by 1 gives