Is [katex]1[/katex] always the denominator of the fraction of a whole number?

Yes, in order to make a whole number a fraction, place it over [katex] 1. [/katex] So the denominator of the fraction is always [katex] 1. [/katex]

Fractions of Numbers - Elementary Math - Steps, Examples & Questions

High Impact Tutoring Built By Math Experts

Personalized standards-aligned one-on-one math tutoring for schools and districts

Request a demo

In order to access this I need to be confident with:

Whole numbers Multiplying and dividing fractions Multiplying fractions

Math resources Number and quantity Fractions

Fractions of numbers

Here we will learn about fractions of numbers and how to solve problems involving fractions of numbers.

Students first learn about fractions of numbers in fourth grade in their work with number and operations – fractions. They will extend this understanding as they progress through 5th and 6th grade.

What are fractions of numbers?

Fractions of numbers are calculated when we multiply a fractional number by the whole number. The word “of” means to multiply.

For example, let’s look at how to use a visual model and the algorithm to calculate fractions of numbers.

What are fractions of numbers?

$What are fractions of numbers?$

Common Core State Standards

How does this relate to 4th grade math?

Grade 4 – Number and Operations – Fractions (4.NF.B.4.a)
Understand a fraction $katex is not defined$ as a multiple of $katex is not defined$ For example, use a visual fraction model to represent $katex is not defined$ as the product $katex is not defined$ recording the conclusion by the equation $katex is not defined$

Grade 4 – Number and Operations – Fractions (4.NF.B.4.b)
Understand a multiple of $katex is not defined$ as a multiple of $katex is not defined$ and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express $katex is not defined$ as $katex is not defined$ recognizing this product as $katex is not defined$ (In general, $katex is not defined$

How to calculate fractions of numbers

In order to find a fraction of a number using a model.

Draw one fraction horizontally and the other vertically.
Connect the fractions all the way across with $katex is not defined$ different colors.
Count up the shaded, overlapping parts.
If possible, simplify or convert to a mixed number.

In order to find a fraction of a number using the algorithm

Convert to a multiplication statement.
Convert the whole number to an improper fraction.
Multiply the numerators together and the denominators together.
If possible, simplify or convert to a whole number or mixed number.

[FREE] Fractions of Numbers Worksheet (Grade 4)

Use this worksheet to check your grade 4 students’ understanding of fractions of numbers. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE

[FREE] Fractions of Numbers Worksheet (Grade 4)

Use this worksheet to check your grade 4 students’ understanding of fractions of numbers. 15 questions with answers to identify areas of strength and support!

DOWNLOAD FREE

Fractions of numbers examples

Example 1: unit fraction of a number using a model

$katex is not defined$ of $katex is not defined$

Draw one fraction horizontally and the other vertically.

$katex is not defined$ or $katex is not defined$ is drawn vertically and $katex is not defined$ is drawn horizontally which is $katex is not defined$ wholes divided into $katex is not defined$ equal pieces.

2Connect the fractions all the way across with $katex is not defined$ different colors.

3Count up the shaded, overlapping parts.

$katex is not defined$ groups of $katex is not defined$ represents the overlap shaded pieces which is

katex is not defined

4If possible, simplify or convert to a mixed number.

There is no common factor between $katex is not defined$ and $katex is not defined$ which means $katex is not defined$ is in its simplest form.

$katex is not defined$ as a mixed number is $katex is not defined$

$katex is not defined$ of $katex is not defined$

Example 2: unit fraction of a number

$katex is not defined$ of $katex is not defined$

Convert to a multiplication statement.

$katex is not defined$

Convert the whole number to an improper fraction.

$katex is not defined$ as an improper fraction is $katex is not defined$ .

Multiply the numerators together and the denominators together.

$katex is not defined$

If possible, simplify or convert to a whole number or mixed number.

$katex is not defined$ has a common factor of $katex is not defined$ .

$katex is not defined$

Example 3: proper fraction of a number using a model

$katex is not defined$ of $katex is not defined$

Draw one fraction horizontally and the other vertically.

$katex is not defined$ or $katex is not defined$ drawn vertically and $katex is not defined$ drawn horizontally which is $katex is not defined$ wholes divided into $katex is not defined$ equal pieces.

Connect the fractions all the way across with $katex is not defined$ different colors.

Count up the shaded, overlapping parts.

$katex is not defined$ groups of $katex is not defined$ represent the overlap shaded pieces which is

$katex is not defined$

If possible, simplify or convert to a whole number or mixed number.

The common factor between $katex is not defined$ is $katex is not defined$

$katex is not defined$

Example 4: proper fractions of numbers

Find $katex is not defined$ of $katex is not defined$ .

Convert to a multiplication statement.

$katex is not defined$

Convert the whole number to an improper fraction.

$katex is not defined$

Multiply the numerators together and the denominators together.

$katex is not defined$

If possible, simplify or convert to a whole number or mixed number.

The common factor between $katex is not defined$ is $katex is not defined$

$katex is not defined$

$katex is not defined$ of $katex is not defined$ is $katex is not defined$ .

Example 5: proper fraction of a number

What is $katex is not defined$ of $katex is not defined$

Convert to a multiplication statement.

$katex is not defined$

Convert the whole number to an improper fraction.

$katex is not defined$

Multiply the numerators together and the denominators together.

$katex is not defined$

If possible, simplify or convert to a whole number or mixed number.

The common factor between $katex is not defined$ and $katex is not defined$ is $katex is not defined$

$katex is not defined$

$katex is not defined$ of $katex is not defined$ is $katex is not defined$ .

Example 6: word problem

Jenny went hiking and only walked two thirds of the $katex is not defined$ mile hiking trail. How many miles did she hike?

Convert to a multiplication statement.

$katex is not defined$ of $katex is not defined$ is $katex is not defined$

Convert the whole number to an improper fraction.

$katex is not defined$

Multiply the numerators together and the denominators together.

$katex is not defined$

If possible, simplify or convert to a whole number or mixed number.

The common factor between $katex is not defined$ and $katex is not defined$ is $katex is not defined$

$katex is not defined$

Two thirds of $katex is not defined$ is $katex is not defined$ so she hiked $katex is not defined$ miles.

Example 7: word problem

Dylan only filled $katex is not defined$ of his $katex is not defined$ -ounce water bottle. How much water is there in the bottle?

Convert to a multiplication statement.

$katex is not defined$

Convert the whole number to an improper fraction.

$katex is not defined$

Multiply the numerators together and the denominators together.

$katex is not defined$

If possible, simplify or convert to a whole number or mixed number.

The common factor between $katex is not defined$ and $katex is not defined$ is $katex is not defined$

$katex is not defined$

$katex is not defined$ of $katex is not defined$ is $katex is not defined$ so there are $katex is not defined$ ounces of water in the bottle.

Teaching tips for a fraction of a number

Use visual models so students can develop conceptual understanding.

Explore patterns so that students can make sense of the simple steps involved in multiplying a fraction by a whole number.

Use a number line to provide a visual representation of fractions of numbers and help students understand the concept as points on the number line.

Although practice worksheets have their place, reinforcing skills with visual models and hands-on activities is more effective for students to formulate deep understanding.

Easy mistakes to make

Confusing the meaning of the word “of”
Thinking “of” means division instead of multiplication.
For example, thinking $katex is not defined$ of $katex is not defined$ means $katex is not defined$

Cross multiplying
If students have been introduced to cross multiplying, they may get confused and use it when multiplying two fractions.
For example,

Confusing multiplying fractions and dividing fractions
For example,

Drawing a fraction model incorrectly
For example, when drawing a model to represent $katex is not defined$ of $katex is not defined$ not dividing the model into the correct number of equal parts.

Practice fractions of numbers questions

katex is not defined

katex is not defined

katex is not defined

katex is not defined

To use a model to find the answer:

Fractions of Numbers practice question 1

$katex is not defined$ or $katex is not defined$ is vertical and $katex is not defined$ is horizontal which is $katex is not defined$ divided into $katex is not defined$ equal pieces.

The overlap shaded region represents $katex is not defined$ groups of $katex is not defined$ or

katex is not defined

katex is not defined

$katex is not defined$ of $katex is not defined$ is $katex is not defined$

katex is not defined

katex is not defined

katex is not defined

katex is not defined

$katex is not defined$ of $katex is not defined$ is $katex is not defined$

$katex is not defined$ as an improper fraction is $katex is not defined$

So, $katex is not defined$

The common factor of $katex is not defined$ and $katex is not defined$ is $katex is not defined$

katex is not defined

$katex is not defined$ of $katex is not defined$ is $katex is not defined$

katex is not defined

katex is not defined

katex is not defined

katex is not defined

To use a model to find the answer:

Fractions of Numbers practice question 3

$katex is not defined$ is horizontal and $katex is not defined$ is vertical.

The overlap shaded region represents $katex is not defined$ groups of $katex is not defined$ or

katex is not defined

katex is not defined

katex is not defined

katex is not defined

katex is not defined

katex is not defined

$katex is not defined$ of $katex is not defined$ is $katex is not defined$

$katex is not defined$ as an improper fraction is $katex is not defined$

So, $katex is not defined$

The common factor of $katex is not defined$ and $katex is not defined$ is $katex is not defined$

katex is not defined

$katex is not defined$ of $katex is not defined$ is $katex is not defined$

$katex is not defined$ miles

$katex is not defined$ of $katex is not defined$ is $katex is not defined$

$katex is not defined$ as an improper fraction is $katex is not defined$

So, $katex is not defined$

The common factor between $katex is not defined$ and $katex is not defined$ is $katex is not defined$

katex is not defined

$katex is not defined$ of $katex is not defined$ is $katex is not defined$

$katex is not defined$ pages

$katex is not defined$ of $katex is not defined$ is $katex is not defined$

$katex is not defined$ as an improper fraction is $katex is not defined$

katex is not defined

The common factor between $katex is not defined$ and $katex is not defined$ is $katex is not defined$

katex is not defined

$katex is not defined$ of $katex is not defined$ is $katex is not defined$ pages

Fractions of numbers FAQs

Is finding a fraction of a number the same as when you multiply fractions?

Yes, the word “of” means to multiply. So finding the fraction of a number is the same as when you multiply fractions.

Is $katex is not defined$ always the denominator of the fraction of a whole number?

Yes, in order to make a whole number a fraction, place it over $katex is not defined$ So the denominator of the fraction is always $katex is not defined$

Is a mixed number the same as a mixed fraction?

Mixed fractions and mixed numbers mean the same thing.

Do you have to get a common denominator when multiplying fractions?

You can get a common denominator to multiply fractions, but it isn’t necessary for multiplication.

What are the different types of fractions?

There are proper fractions where the numerator (top number) is smaller than the denominator (bottom number). There are unit fractions where the numerator (top number) is $katex is not defined$ and the denominator (bottom number) is a whole number. There are improper fractions where the numerator (top number) is greater than the denominator (bottom number). There are mixed numbers or mixed fractions that are made up of a whole number and a proper fraction.

Are decimal numbers and fractional numbers the same?

They are similar because they can have a whole part and a fractional part.

The next lessons are

Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.