Equivalent Fractions: Is It Fair?

Equivalent Fractions: Units

English: Stacks of US quarters and pennies
Stacks of US quarters and pennies (Photo credit: Wikipedia)

Equivalent fractions are fractions that are equal in value to each other. As a knife is used in this activity, an adult should supervise or cut the food. A common practice for deciding if something is fairly divided or not is to offer the other party, the one that did not divide it, first choice of whatever has been divided. Let’s see if we can show when parts of a whole equal parts of another whole divided a different way.


  • 4 apples
  • Knife
  • Cutting board
  • Optional: anything that can be cut into eight even pieces, like a doughnut, a slice of bread, a whole pizza or a pan of brownies.


  • Cut an apple in half, giving two halves
  • Cut another apple in half, then each half in half, giving four quarters
  • Cut another apple in half, then each half in half, then each quarter in half again, giving eight eighths
  • Ask your grandchild to take all of one apple, or any number of slices of one of the other apples, either halves, quarters or eighths.
  • Ask them how many slices of apple you can take to be fair, to have the same amount of apple they have. If they take a whole apple, for instance, you would have to take all eight slices of the apple cut in eighths to have the same amount, or all four slices of the apple cut in quarters
  • Reverse the question, taking, say, four quarters of one apple, and ask your grandchild how many slices of which apple they could take to have the same amount of apple you have.

What Should Happen?

As your grandchild sees and compares the apple slices that you have compared to the ones they have, it will start to become clear which pieces of the apple are the same.

  • One whole apple is equal to two halves, four quarters, and eight eighths.
  • One half apple is equal to two quarters and four eighth slices.
  • One quarter apple is equal to two eighth slices.
  • Optional: Ask your grandchild if it would be fair for them to have one half of an apple and you to have three eighths? For them to have three quarters and you to have one half? For you to have one half and them to have two quarters? For you to have three eighths and them to have one quarter?

Why Is This Useful?

Making change with money is a good example of how we compare equivalent fractions in every day life, with coins being a fraction of a dollar or 100 cents. We even call a 25-cent coin a quarter, for one-quarter of a dollar. One dollar is 100 cents. One dollar has the same value as 100 pennies . One quarter has the value of one-quarter of a dollar or 25 pennies. One dollar also has the same value as four quarters. Four quarters together have the value of 100 pennies. One quarter has the same value as two dimes and a nickel. So, two dimes and a nickel have the same value as (10 + 10 + 5) 25 pennies, or a quarter. One dollar also has the same value as two dimes and a nickel and three quarters (10 + 10 + 5 + 25 + 25 + 25 = 100 = $1).

If you split your savings into four slots in a piggy bank for Saving, Spending, Investing and Donating, every time you earn some money, you have to figure out how to divide it equally into four pots. Let’s say you earn one dollar from Grandma for writing her a nice thank-you letter. I pay my grandchildren one dollar every time they write me a nice letter. How do you divide one dollar equally among the four piggy bank slots?

You can’t cut up the dollar, but you can exchange the dollar for an equivalent or equal amount of money if you ask Grandma for change that can be divided into four slots. One dollar has the same value as 100 cents or pennies. Grandma could give you 100 pennies or four quarters, or four dimes, two nickels and two quarters. So, if you put one quarter or 25 pennies or two dimes and a nickel into each of the four slots of the piggy bank, each slot gets an equal amount of money. Are there any other combinations of coins that equal one dollar and can be divided by four?

Now, write your Grandma a nice thank-you note, whether she pays you for it or not.

Thanks to letslassothemoon.com for inspiring this activity


Carol Covin, Granny-Guru

Author, “Who Gets to Name Grandma? The Wisdom of Mothers and Grandmothers”



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Comments (15)

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  1. This is such a cool way to teach fractions. Anytime we can find a way to show children the importance and why fraction are necessary, it is a good thing. When we can make it fun, that is even better.

    • carolcovin says:

      Thanks, Susan! And, if food is involved, even better!

  2. This reminds me of my kids when they were younger and every coin was a nickel.

    • carolcovin says:

      You have a good memory, Jon. We sometimes forget that coins only have different values because we have assigned them different values, with the different metals and sizes memory aids to help us remember.

  3. JeriWB says:

    I remember having such a hard time learning fractions. My parents weren't much help with my homework, and concrete examples like this would have saved the day in the classroom!

    • carolcovin says:

      Thanks, Jeri, Now, as a grandparent, it seems easy to find concrete examples to help with what i know my grandchildren will need. As a parent, I was busy with so many other things.

  4. Susan Oakes says:

    Great way to show how to learn fractions Cheryl.

  5. carolcovin says:

    Thanks, Susan!

  6. Dan Meyers says:

    Oh yes, I remember how to do this stuff! It also made me hungry with all of this talk of pizza, doughnuts, and brownies!

  7. carolcovin says:

    So, maybe you could split up pieces of buffalo meat in Nepal!

  8. Wish someone would have taught me this when I was a kid. I am keeping a copy of this for future reference! I have so much trouble giving change OR figuring out if I have been given the right change!

  9. carolcovin says:

    Happy to help, Nancy! Sometimes things seem a lot easier when someone just sits down and explains them.

  10. Arleen says:

    That is a great way to introduce fractions. I plan to try that on my grandson. I think fractions are difficult to explain, but I love your idea.

    • carolcovin says:

      Thanks, Arleen. Anything we can do to make life easier for our grandchildren!

  11. Jeannette Paladino says:

    If my teachers had used your methods I would have been much better at fractions today!