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Children begin the study of fraction multiplication by learning how to multiply a fraction by a whole number (such as 5 × 2/3)—usually in fourth grade. Then, in fifth grade, they learn to multiply fractions by fractions and mixed numbers. In grades 6 and 7, students practice multiplying fractions with larger denominators and more complex problems.

## How To Multiply A Fraction By A Whole Number

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#### How To Teach Multiplying Fractions With Pattern Blocks — Mix And Math

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Grade 6 and Grade 7 students should use Grade 5 worksheets to review fraction multiplication. In addition, they can use the following worksheets that cover simple fraction-of-a-step equations. Multiplying fractions by whole numbers is a simple operation. This is one of the basic concepts taught in the early grades. It is taught to improve students’ math ability. Students often get confused when multiplying and dividing fractions. This article will review techniques for multiplying a fraction by a whole number with some examples.

Before learning how to multiply a fraction by a whole number, let’s look at some basic terms we use in multiplication. Do you know what fractions are? Fractions are, in general, numbers expressed in the p/q form. For example, 2/3, 9/2, etc.

#### Teaching Has Spilled Into My Everyday Life: Fraction February

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

If you divide the numerator by the denominator, you get either an integer or a decimal number. It no longer exists as a fraction. Therefore, a value of the form p/q or a value can never be a fraction.

To learn how to multiply fractions by a whole number, you need to learn how to multiply a fraction by another fraction. Let us know about it in the article.

Suppose we have two fractions d/c and j/k. To multiply these fractions, you need to write them correctly with each other. Then look at the numerators and denominators of the fractions. Multiply the numerators together (d x j) = x. Write the result of multiplying numbers into different fractions, say ‘x’.

## Multiplying Unit Fractions By Whole #

In the same way, multiply the denominators of fractions. Write the product of the denominator below the resulting numerator, (c x k) = y. Therefore, the product of two fractions can be represented as:

After multiplying 4/5 by 3/7, the fraction is 12/35. If the numbers in the fraction are multiples of some smaller number, you can reduce the fraction to a simpler form. The only condition is that if you divide the numerator by any number ‘a’ then you have to divide the denominator by the same number ‘a’.

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

Now we learn how to multiply two fractions. In this section, you’ll learn how to multiply fractions by whole numbers. Suppose we have the fraction d/c and the integer ‘k’. The first step in multiplying a fraction and a whole number always starts by writing each other correctly using the multiplication sign. In the case of integers we don’t have a ‘p/q’ form. Therefore, we will first convert the number to a fraction. To do this, place a dash below the integer with 1 as the denominator. Now we have the integer in the form ‘p/q’.

## Teaching Ideas For Virtual Math Manipulatives

Now we follow the same steps mentioned in multiplying fractions. Now look at the numerators and denominators of fractions and whole numbers. Multiply the numerators by the whole number ‘k’ so that (d x k) = x. Now multiply the denominator of the fraction by 1 (because the whole number has denominator 1). This gives (c x 1 = c). Therefore, the product of two fractions can be represented as:

When multiplying fractions by whole numbers, the denominator of the fraction is retained. So whenever you find such a multiplication, put the denominator as a fraction and multiply the numerator.

Step 2: Since we know that the denominator stays the same in these cases, we need to multiply the numerators.

Now, hopefully, the question of how to multiply fractions by a whole number is straightforward. Let’s look at a very interesting idea below.

#### Multiplying Fractions (w/ 15 Step By Step Examples!)

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

As mentioned in the example above. Consider multiplying a fraction by an integer that is a multiple of the denominator or equal to the denominator. In that case, you can eliminate or subtract the numbers before the actual multiplication. Understand this with the examples below:

We can see that the integer and the denominators are the same. So we can eliminate them and get the numerator of the fraction as an answer.

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

### Multiply Fractions With Visual Models

As we all know, integers are the set of real numbers starting from zero and extending to positive infinity. We’ve already seen all the cases of what happens when a fraction is multiplied by a whole number. If you multiply a fraction by 1, it gives the number itself. But what happens when you multiply a fraction by zero?

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

The reciprocal of a number is when the numerators and denominators swap places. 0 = 0/1 so its reciprocal is 1/0. Suppose we have a fraction ‘a/b’. Using the steps we’ve learned so far, a x 1 = a and b x 0 = 0. So the resulting fraction is a/0. In mathematics, 1/0 or division by zero is undefined. Therefore, we cannot multiply a number by the reciprocal of zero.

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

#### Th Grade Multiply Fractions By Whole Numbers Task Cards

The answer is You can multiply fractions by multiplying numerators (numbers above) and fractions (numbers below).

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

The answer is The general rule of thumb for multiplying fractions is to multiply the numerators, multiply the denominators, and then simplify.

The answer is To multiply fractions, you must enter fraction mode on your calculator. Then you type the first fraction (the one above) and press the multiplication key. The other fraction is automatically given and multiplied by the first. Then you can hit up to get your answer!

#### Fractions Xiii Multiplication Of Whole Numbers

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