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Meaning Of Fraction Equivalence And Comparison Grade

Key Concepts

Compare fractions: Use Benchmarks
Compare fractions: Use the Number Lines
Whole Numbers and Fractions

Prior Knowledge:

Answer the following questions 

  1. How can we compare different fractions? 
  1. How many thirds are there in 2 wholes? 
  1. Use the number line to help order the fractions from least to greatest. 

Answers: 

  1. If the denominators are different and the numerators are the same, then we can easily compare fractions by looking at their denominators. 
  1. We can use a number line or fraction strips to find a fraction name for two using thirds. 

Here, from the figure we get, 2 = 6/3

∴ The whole number 2 can also be written as the fraction 6/3

  1. Given number line would be 

Fractions from least to greatest are shown as below: 

The fractions from least to greatest are 0/4, 6/8, 1/4, 1/2 and 1.

Definition: 

Benchmark fractions are common fractions that we compare with other fractions. 

What benchmark fractions look like: 

  • Benchmark fractions are especially helpful on number lines 
  • The most famous number line used is a ruler 
  • Rulers use halves, fourths and eighths as benchmarks 
Benchmark Fractions

Benchmark Fractions Chart: 

Use the following benchmark chart for reference to compare fractions. 

Benchmark Fraction Chart

Example: 

Keri wants to buy 2/6 of a container of roasted nuts. Alan wants to buy 2/3 of a container of roasted nuts. The containers are of the same size. Who will buy more nuts? 

Roasted Nuts Example

Comparing each fraction to the benchmark number 1/2

Roasted Nuts Example

From the above figure, 2/6 is less than 2/3

Therefore,

2/3 is greater than 1/2. 

Using symbols: 

2/6 < 2/3. 

13.6 Compare Fractions: Use the Number Line  

Fractions on a Number Line 

Consider the whole shape, split the whole into 5 equal parts. 

Whole shape

Select 1/5 part of the whole and represent on a number line. 

Look at this number line. It starts at 0 and ends at 1, which represents the whole. 

Do you notice how it is split into 5 parts? 

That means our denominator must be 5. The numerators should go up in consecutive order. 

What the fractions would look like when marked on the number line is: 

Now we can easily compare the fractions. 

Note: 

A fraction is larger if it is farther from 0 on the number line 

A fraction is smaller if it is closer to 0 on the number line 

Example: 

Compare the fractions 2/3  and 2/3  and 3/4 using <, >, or = with the help of number lines 

First, draw a number line model for 

2/3

Next, draw the number line model for

3/4. Place it under the number line model for 2/3.

Which fraction is farther from 0? 

Here, 3/4 is farther from 0 than 2/3.

This means that 3/4 is greater than 2/3

∴ 3/ 4 > 2/3

13.7 Whole Numbers and Fractions 

  • Whole numbers are numbers that do not have fractions. Examples as 1, 2, and 10 
  • Every whole number can be written as a fraction too 

Writing Whole Numbers as Fractions: 

You can write any whole number into an equivalent fraction. Just divide it by 1. 

Can we write the whole number 1 into a fraction? 

Yes, we can write 1 into a fraction just by dividing 1 by 1, i.e., 1/1.

Fractions Equivalent to Whole Numbers: 

If the numerator is divisible by the denominator, the fraction is equivalent to a whole number. 

In other words, if you can divide the numerator by the denominator without any remainder, the fraction is equivalent to a whole number. 

Consider the improper fraction 2/2

Is it equivalent to a whole number?  

Yes, we can divide the numerator (2) by the denominator (2) without any remainder. 

So 2/2  is equivalent to a whole number. 

∴2/2 is equal to the whole number 1. 

Example: 

Write the equivalent fractions for the whole number 4. Use fraction strips to name whole numbers. 

Here, we use fractions strips to name whole numbers. 

Twelve 1/3 fraction strips are equal to 4 whole fraction strips. 

All whole numbers have fraction names. 

We can write 4 = 12/3

We also know 4 = 4/1

So, we write 4 = 4/1 = 12/3. 

Exercise:

  1. A mural is divided into 3 equal parts. What fraction represents the entire mural?
  2. A small cake is cut into 4 equal pieces. What fraction represents the entire cake?
  3. Write the equivalent fraction to the whole number 3.
  4. Compare with the help of a number line, which is greater  
  5. Use fraction strips to compare
  6. Riley says the library is  of a mile from their house. Sydney says it is  of a mile. Use the number lines to find who is correct.
  7. Compare  to the benchmark
  8. What fraction is equal to 65?
  9. What fraction is equal to 7?
  10. Mike had  of a candy bar. Sally had  of a candy bar. Whose fraction of a candy bar was closer to 1? Whose fraction of a candy bar was closer to 0?

What we have learnt:

  • Compare fractions by using concrete models
  • Compare fractions by using benchmarks
  • Order fractions by using concrete models, benchmarks and number lines
  • Use symbols (>, <, =) to compare fractions with benchmarks and number lines
  • Use representations to find fraction names for whole numbers

Concept Map :

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