Equivalent Fractions

Fractions can be a little tricky to understand at first, but once you get the hang of them, they're not so bad. In grade 5, students learn about "equivalent fractions." This is an important concept because it helps you understand how different fractions can actually be the same, even though they look different.

What is fraction?

Before we learn about equivalent fractions, let's recap what fractions are. A fraction represents a part of a whole. It is made up of two numbers: the numerator and the denominator. The numerator is the number on the top and it tells us how many parts we have. The denominator is the number on the bottom and it tells us how many parts the whole is divided into.

For example, the fraction 3/4 has a numerator of 3 and a denominator of 4. This fraction means that we have 3 parts out of a total of 4.

Understanding equivalent fractions

Equivalent fractions are fractions that look different but represent the same part of a whole. Think of it as different ways of expressing the same quantity.

For example, 1/2 means 2/4, 3/6, 4/8, and so on. All these fractions represent an amount that is half of the whole amount.

How to find equivalent fractions

To find equivalent fractions, both the numerator and denominator need to be multiplied or divided by the same number. Let's take a look at both methods:

Multiplying to find equivalent fractions

Suppose you have a fraction 1/2. If we multiply both the numerator and denominator by 2, the result will be 2/4.

        1/2 = (1×2)/(2×2) = 2/4
    

As another example, consider 3/5. Multiply by 3:

        3/5 = (3×3)/(5×3) = 9/15
    

Dividing to find equivalent fractions

Suppose you have a fraction 4/8. If we divide both the numerator and denominator by 2, the result will be 2/4.

        4/8 = (4÷2)/(8÷2) = 2/4
    

As another example, consider 10/15. Divide by 5:

        10/15 = (10÷5)/(15÷5) = 2/3
    

Why equivalent fractions are important

Understanding equivalent fractions is important because it helps you in many areas of math, such as simplifying fractions, comparing fractions, and even adding and subtracting fractions.

Simplifying fractions

Simplifying fractions means writing the fraction in its simplest form. To simplify a fraction, you need to find an equivalent fraction with the simplest terms. For example, 4/8 can be simplified to 1/2.

        4/8 = (4÷4)/(8÷4) = 1/2
    

Comparing fractions

Sometimes you will need to figure out which of two fractions is larger or smaller. To do this, you may need to convert them into equivalent fractions with the same denominator.

If you're comparing 1/3 and 1/4, you can convert them into equivalent fractions with the same denominator, such as 12:

        1/3 = (1×4)/(3×4) = 4/12
        1/4 = (1×3)/(4×3) = 3/12
    

Now, it is easy to see that 4/12 is greater than 3/12, so 1/3 is greater than 1/4.

Adding and subtracting fractions

To add or subtract fractions, they must have the same denominator. You can do this by finding equivalent fractions.

Consider 1/4 and 1/6. To add them, find a common denominator. The common denominator of 4 and 6 is 12:

        1/4 = (1×3)/(4×3) = 3/12
        1/6 = (1×2)/(6×2) = 2/12
    

Now you can add these:

        3/12 + 2/12 = 5/12
    

Practice problems

1. Find the equivalent fraction for 2/3 by multiplying both the numerator and denominator by 2, 3, and 4.
2. Simplify the fraction 24/36.
3. Are the fractions 4/9 and 8/18 the same? Show your work.
4. Which fraction is larger: 5/8 or 3/5? Use equivalent fractions to compare them.
5. Add the fractions 2/5 and 3/10 using equivalent fractions.

Solving practice problems

1. 2/3 Multiplying by 2, 3, and 4 gives you:

                   2/3 = (2×2)/(3×2) = 4/6
                   2/3 = (2×3)/(3×3) = 6/9
                   2/3 = (2×4)/(3×4) = 8/12
               

2. 24/36 Simplification:

                   24/36 = (24÷12)/(36÷12) = 2/3
               

3. Are 4/9 and 8/18 the same?

                   4/9 = (4×2)/(9×2) = 8/18
               

   Yes, they are equivalent.

4. Comparison of 5/8 and 3/5:

                   5/8 = (5×5)/(8×5) = 25/40
                   3/5 = (3×8)/(5×8) = 24/40
               

   25/40 is greater than 24/40, so 5/8 is greater than 3/5.

5. Adding 2/5 and 3/10:

                   2/5 = (2×2)/(5×2) = 4/10
                   4/10 + 3/10 = 7/10
               

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