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Different Fractions That Are Equal · Fractions and Decimals · CCSS.MATH.CONTENT.4.NF.A.1 · equivalent fractions

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Different Fractions That Are Equal

with Lumi

Lumi stands at a wooden picnic table outdoors, carefully slicing a rectangular pan of cornbread into equal pieces. Two identical pans sit side by side — one cut into 2 large pieces, one cut into 4 smaller pieces. Lumi holds up 1 piece from the first pan in one hand and 2 pieces from the second pan in the other hand, showing that both handfuls cover exactly the same amount of cornbread.

Explain why cutting each piece of a fraction into the same number of smaller pieces does not change the total amount.
Identify equivalent fractions by comparing fraction bars or area models.
Calculate an equivalent fraction by multiplying both the numerator and denominator by the same number.
Compare two fractions and determine whether they name the same amount.
Verify whether two fractions are equivalent by reading a visual fraction bar model and confirming the shaded lengths match.

Key terms

Equivalent fractions: Different fractions that name the same amount.
Numerator: The top number of a fraction.
Denominator: The bottom number of a fraction.
Equal parts: Pieces that are all the same size.

Same Amount, New Name

Some fractions look different but mean the same thing. One half and two fourths are the same amount of pie! When you cut every piece into more equal pieces, the total you have does not change. You just have more, smaller pieces. Fractions that mean the same amount are called equivalent fractions. They are like two different names for the very same snack.

The Multiply Trick

Here is the secret to making equivalent fractions. Take the top number and the bottom number, and multiply both of them by the same number. If you multiply top and bottom of 1/2 by 2, you get 2/4. They are equal! It works because you cut each piece into the same number of smaller pieces. Always use the same number for top and bottom, or it will not work.

Worked examples

Make a fraction equal to 1/3.

Pick a number to multiply by, like 2.
Multiply the top: 1 times 2 equals 2.
Multiply the bottom: 3 times 2 equals 6, so 1/3 equals 2/6.

Answer: 2/6

Imagine you and a friend each get a pan of cornbread that is exactly the same size. Your pan is cut into 2 equal pieces, and you take 1 piece. That is one-half of the pan — we write it as 1/2. Your friend's pan is cut into 4 equal pieces, and your friend takes 2 pieces. That is two-fourths of the pan — we write it as 2/4. Now put the two servings side by side. They are exactly the same size! One-half and two-fourths are equivalent fractions — different names for the same amount. Here is the secret: when you cut every piece into the same number of smaller pieces, you are multiplying the top number (numerator) AND the bottom number (denominator) by the same value. Multiplying top and bottom by 2 turns 1/2 into 2/4. The size of your portion never changes — it is like cutting a sandwich into more pieces: more cuts, same sandwich. Try it yourself: start with 1/3. Cut each of the 3 pieces into 2 equal parts. Now you have 6 pieces total, and your share is 2 of them — so 1/3 = 2/6. The amount is identical! Remember: multiply both numbers by the SAME value, and you always get an equivalent fraction.

Activity

Drag each fraction bar piece to the matching equivalent fraction on the right side.

Practice

Make a fraction that is equal to 2/4 using bigger numbers.

Is 3/4 the same amount as 6/8? Explain why or why not.

Common mistakes to avoid

Add the same number to top and bottom.No. You must multiply both, not add. Adding changes the amount.
More pieces always means more snack.No. More, smaller pieces can still be the same total amount.

Check your understanding

A pizza is cut into 3 equal slices and you eat 1 slice. Your friend has the same-size pizza cut into 6 equal slices and eats 2 slices. Which statement is true?

Which multiplication turns 2/3 into an equivalent fraction?

Look at these two fraction bars, each the same length. The first bar has 1 out of 4 parts shaded. The second bar has 2 out of 8 parts shaded. Are the shaded amounts equal?

Recap

Equivalent fractions are different names for the same amount. To make one, multiply the top number and the bottom number by the same value. The size of your share never changes.

Reflect

Can you think of two ways to share the same amount of pizza?