Need Help?

Get in touch with us

searchclose
bannerAd

Find Common Denominators

Grade 5
Feb 28, 2023
link

Key Concepts

  • Equivalent fractions and common denominators
  • Finding common denominators

Introduction

In this chapter, we will learn about common denominators, finding equivalent fractions and finding common denominators. 

Common denominator 

If two or more fractions have the same number as the denominator, then we can say that the fractions have a common denominator. 

Let us understand the common denominator in detail: 

1 pizza

Shape In this pizza, there are 4 slices. Thus, it is represented as 1, that is, a whole. 

ShapeIf we take away one slice, we have 3 out of 4 slices remaining. 

parallel
3/4 pizza
2/4 pizza

ShapeIf we take away two slice, we have 2 out of 4 slices remaining. 

1/4 pizza

ShapeIf we take away three slices, we have 1 out of 4 slices, remaining. 

In the above examples, we can understand that the same number is used as denominator. 

4 pizza

Equivalent fractions and common denominators 

Let us learn how to estimate the sum of two fractions. 

Example 1:  

parallel

Julie planted two 1-acre gardens. One had three sections of flowers, and the other had four sections of flowers. She plans to divide both gardens into more sections in order that they need an equivalent number of equal-sized sections. How many sections will each garden have? 

Solution: 

If you represent the gardens with pictures, they will be like, 

garden 1 and 2

Garden 1 Garden 2 

Divide each 1/3 into fourths

Divide each 1/3 into fourths

Divide each 1/4 into thirds

Divide each 1/4 into thirds

Each of the wholes will be divided into the same size parts, twelfths. 

  • Garden 1
Garden 1
  • Garden 2
Garden 2

So, both garden will have 12 sections. 

Finding common denominators 

Let us learn how to determine a common denominator? 

Example 1:  

  1. Determine a common denominator for 2/3 and 1/2. 
  1. Determine equivalent fractions for 2/3 and 1/2 using the common denominator from a). 

Solution: 

Method 1: Use Paper Folding or Diagrams 

a) Divide a rectangle into 3 equal parts. Either fold a piece of paper or draw a rectangle. 

Fold the paper or divide the rectangle into 2 equal parts the other way. 

There are 6 parts in the rectangle. 

A common denominator for 2/3 and 1/2 is 6. 

Use Paper Folding or Diagrams 

b) Shade 2/3 of the rectangle red. 

4 of the 6 parts are red.

2/3 = 4/6

4 of the 6 parts are red

Turn the paper over, or draw another rectangle and divide it as in step a). 

Shade 1/2 of this rectangle blue. 

3 of the 6 parts are blue.

1/2 = 3/6

3 of the 6 parts are blue

Method 2: Use multiples 

a) The denominator of 1/2 is 2. 

Multiples of 2 are 2, 4, 6, 8, 10, 12, … 

The denominator of 2/3 is 3. 

Multiples of 3 are 3, 6, 9, 12, 15, … 

The first multiple divisible by both 2 and 3 is 6. 

A common denominator is 6. 

b) Write equivalent fractions using 6 as the denominator. 

Use multiples

To determine equivalent fractions, multiply the numerator and denominator by the same number. This process does not change the value of the fraction. 

Use multiples

Exercise

  • Ian says, “A common denominator for and 3 is 12”, Mike says,“ agree with lan or Mike? Why?
  • Tina wanted to find a common denominator and equivalent fractions for 2 and 2. This is
    what she did
exercise 2

a) Was she correct? If not, what was her error?
b) Draw diagrams to show what she should have done.

  • Use multiples to find a common denominator for the fractions 2,2, and 2?
  • Use the folded papers shown to determine a common denominator and equivalent fractions for the given pair of fractions.
exercise 4
  • Use the folded papers shown to determine a common denominator and equivalent fractions for the given pair of fractions.
exercise 5
  • Look at the diagrams to determine a common denominator and equivalent fractions for the given pair of fractions
exercise 6
  • Look at the diagrams to determine a common denominator and equivalent fractions for
    the given pair of fractions.
exercise 7
  • Fill in the blanks to make equivalent fractions.
  • 1/4 = ?/8 =?/12 = ?/16 = ?/20 = ?/24 = ?/28
  • Fill in the blanks to make equivalent fractions
  • 24/56 = 12/? = 6/? = 3/? = 48/? = 9/?
  • A cookie recipe calls for > cup of brown sugar and = cup of walnuts. Find the least
    common denominator of the fractions used in the recipe.

Concept Map

Concept Map

What have we learned

  • Understand common denominator
  • Find equivalent fractions
  • Find common denominator for two or more fractions

Comments:

Related topics

area of square

How to Find the Area of Square?

The area of a square can be understood by how much space a square covers inside it. In simple terms, the space present within the boundary of a square is known as the area of the square. In this article, you shall learn the fundamental parameters of a square. Also, you will study how to […]

Read More >>
number sequences

Number sequences: Definition and Types

Number sequences is a crucial mathematical tool for assessing someone’s IQ. The majority of management aptitude tests frequently include number series questions.  Have you ever noticed a pattern in the numbers allotted to houses in a row, the page numbers of a book, or the salary increment an employee receives every year? If yes, you […]

Read More >>
Coordinate Grid

What is Meant by Coordinate Grid? – A Complete Guide

A plane is a flat surface. Just like a floor or a wall, it is a smooth and flat surface. However, a grid is something different. Have you wondered how metropolitan cities are laid out with a consistent, easy-to-follow grid plan? It is an ultimate example of a coordinate plane. Cities with well-planned street layouts […]

Read More >>
Subtraction with regrouping

Subtraction with Regrouping

No one wondered if math could be so easy to use by grouping the numbers to make the calculations go easier. The methodology becomes easier when the numbers are grouped in multiples of 10s or 100s. Subtraction with regrouping is one of those easiest methods that will help to quicken your numerical calculations and enhance […]

Read More >>

Other topics