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Operations with Fractions Facts & Worksheets

This lesson provides a step-by-step introduction to fractions through a visual and conceptual approach.

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This lesson provides a step-by-step introduction to fractions through a visual and conceptual approach. Basic terminology is covered, followed by procedures for decomposing, adding, subtracting, and multiplying fractions.

See the fact file below for more information on the operations with fractions or alternatively, you can download our 35-page Operations with Fractions worksheet pack to utilise within the classroom or home environment.

Key Facts & Information

INTRODUCING FRACTIONS

  • A circle is a geometric shape we have encountered in the previous lessons. The circle can be used to represent one whole. We can divide the circle into equal parts.
  • We can shade a portion of a circle to name a specific part of the whole as shown below.
  • The numbers ½, ⅔, and ¼ are all fractions.
  • Fraction
    • A fraction names part of a region or part of a group. We use them to write and work with amounts that are less than a whole number but more than zero. The form of a fraction is one number over another, separated by a fraction (divide) line.
  • Numerator
    • The top number of a fraction which shows the number of shaded parts.
  • Denominator
    • The bottom number of a fraction which shows the total number of equal parts.
  • Note that the fraction line means to divide the numerator by the denominator.
  • Why is the number ¾ written as “three-fourths”? We use a hyphen to distinguish a fraction from a ratio. A fraction names a number that represents the part of a whole. When writing a fraction, a hyphen is always used.
  • It is also important to take note that other shapes, aside from a circle, can be divided into equal parts. For example, we can let a rectangle represent one whole, and then divide it into equal parts.

UNIT FRACTIONS

  • A unit fraction is a fraction whose numerator is one. Each unit fraction is part of one whole (the number 1). The denominator names that part. Every fraction is a multiple of a unit fraction.

FRACTIONS OF A NUMBER

  • Rosie gave 1/2 of the apples to her brother. If there were 12 apples in the basket, how many apples did she give to her brother?
  • To solve this problem, we’ll have to find a fraction of a number. We need to figure out: What is 1/2 of 12?
  • Let’s try solving the problem using models or drawings. Let’s draw the apples in the basket.
  • Rosie gave 1/2 of the apples to her brother. The fraction 1/2 tells us that the whole is divided into 2 equal parts. We know this based on the denominator.
  • Drawing the model, we now have 12 apples that are divided into 2 groups. How many apples are there in each part?
  • There are 6 apples in each part. Therefore, 1/2 of 12 is 6.
  • Another way of solving the problem is by trying this easier and faster way – multiplication.
  • To find the fraction of a number, multiply the number by the numerator, then divide the answer you get by the denominator.
  • Using the same example, let’s try to write it this way:
    • 12 x 1/2 = ?
  • First, multiply 12 by the numerator.
    • 12 x 1 = 12
  • Then, divide the product you get by the denominator.
    • 12 ÷ 2 = 6
  • We arrived with the same answer. Think about fractions like a division problem where the numerator is divided by the denominator.
  • So, we can also think about 12 x 1/2 as:
    • 12 x (1 ÷ 2) which is the same as 12 x 1 ÷ 2
  • Here is another example:
    • What is 2/3 of 24?
  • We just have to solve it this way:
    • 24 x 2 ÷ 3
  • First, multiply 24 by the numerator.
    • 24 x 2 = 48
  • Then, divide the product you get by the denominator.
  • 48 ÷ 3 = 16
  • Therefore, 2/3 of 24 is 16.

DECOMPOSING FRACTIONS

  • To decompose a number, we break it into smaller parts. Fractions, like all numbers, can be decomposed in many ways.

ADDING OR SUBTRACTING FRACTIONS – SAME DENOMINATOR

  • Start adding and subtracting fractions with the same denominator before trying to work with fractions with different denominators.
  • Add or subtract the numerators, keeping the denominator the same.
  • It is also a good practice to finish by simplifying the answer to its lowest form.
  • Common fractions can be simplified to their lowest terms by applying the concept of equivalent fractions.
  • Let’s review. A mixed number is a whole number and a proper fraction combined.
  • When you combine the wholes and the fraction part, you get a mixed number.
  • To add mixed numbers with the same denominator:
    • Add the whole numbers together
    • Add the numerators
    • The denominator stays the same

Operations with Fractions Worksheets

This is a fantastic bundle which includes everything you need to know about the operations with fractions across 35 in-depth pages. These are ready-to-use Operations with Fractions worksheets that are perfect for teaching students about the fractions through a visual and conceptual approach. Basic terminology is covered, followed by procedures for decomposing, adding, subtracting, and multiplying fractions.

Complete List Of Included Worksheets

  • Lesson Plan
  • Operations with Fractions
  • Divide the Circle
  • Parts of a Whole
  • Unit Fraction Strips
  • You’re My Equal
  • Equivalent Fractions
  • Decomposing Fractions
  • Adding Mixed Fractions
  • Mixed Fraction Subtraction
  • Comparing Problem
  • Fraction Word Problems

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Link will appear as Operations with Fractions Facts & Worksheets: https://kidskonnect.com - KidsKonnect, June 1, 2020

Use With Any Curriculum

These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.

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