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?

Common Core Standards

How does this relate to 4th grade math?

• Grade 4 – Number and Operations – Fractions (4.NF.B.4.a)
  Understand a fraction \cfrac{a}{b} as a multiple of \cfrac{1}{b}. For example, use a visual fraction model to represent \cfrac{5}{4} as the product 5 \times (\cfrac{1}{4}), recording the conclusion by the equation \cfrac{5}{4} = 5 \times (\cfrac{1}{4}).

• Grade 4 – Number and Operations – Fractions (4.NF.B.4.b)
  Understand a multiple of \cfrac{a}{b} as a multiple of \cfrac{1}{b}, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 \times (\cfrac{2}{5}) as 6 \times (\cfrac{1}{5}), recognizing this product as \cfrac{6}{5}. (In general, n \times (\cfrac{a}{b}) = \cfrac{(n \, \times \, a)}{b}.)

How to calculate fractions of numbers

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

1. Draw one fraction horizontally and the other vertically.
2. Connect the fractions all the way across with 2 different colors.
3. Count up the shaded, overlapping parts.
4. If possible, simplify or convert to a mixed number.

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

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

Fractions of numbers examples

Example 1: unit fraction of a number using a model

\cfrac{1}{4} \, of 7

1. Draw one fraction horizontally and the other vertically.

7 or \, \cfrac{7}{1} \, is drawn vertically and \, \cfrac{1}{4} \, is drawn horizontally which is 7 wholes divided into 4 equal pieces.

2Connect the fractions all the way across with 2 different colors.

3Count up the shaded, overlapping parts.

7 groups of \, \cfrac{1}{4} \, represents the overlap shaded pieces which is

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

There is no common factor between 7 and 4 which means \, \cfrac{7}{4} \, is in its simplest form.

\cfrac{7}{4} \, as a mixed number is 1\cfrac{3}{4}

\cfrac{1}{4} \, of 7=1\cfrac{3}{4}

Example 2: unit fraction of a number

\cfrac{1}{2} \, of 16

Example 3: proper fraction of a number using a model

\cfrac{3}{10} \, of 5

Draw one fraction horizontally and the other vertically.

5 or \cfrac{5}{1} draw vertically and \cfrac{1}{10} drawn horizontally which is 5 wholes divided into 10 equal pieces

Connect the fractions all the way across with \bf{2} different colors.

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

The common factor between \cfrac{15}{10} \, is 5.

\cfrac{15 \, \div \, 5}{10 \, \div \, 5}=\cfrac{3}{2}=1\cfrac{1}{2}

Example 4: proper fractions of numbers

Find \, \cfrac{2}{7} \, of 28

Example 5: proper fraction of a number

What is \, \cfrac{3}{4} \, of 20?

Example 6: word problem

Jenny went hiking and only walked two thirds of the 24 mile hiking trail. How many miles did she hike?

Example 7: word problem

Dylan only filled \, \cfrac{2}{5} \, of his 20 -ounce water bottle. How much water is there 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 show student

• 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 \, \cfrac{1}{2} \, of 10 means \, \cfrac{1}{2} \div 10

• 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 \, \cfrac{1}{2} \, of 4, not dividing the model into the correct number of equal parts.

The next lessons are

• Decimals
• Place value
• Multipy
• Improper fractions and mixed numbers

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