Equivalent fractions: same snack, new pieces

Same snack, new pieces

Imagine two identical snack bars. Each whole bar is the same size. Half of the top bar is shaded. Two quarters of the bottom bar are shaded. Compare the shaded lengths. They match, even though one bar has more pieces.

Count parts of the whole

The bottom number tells how many equal parts make one whole. The top number tells how many of those parts we count. One half counts one of two equal parts. Two quarters counts two of four equal parts. The pieces are equal within each bar.

Split every part in two

Split each half into two smaller equal parts. The whole now has four parts, and the shaded section has two. Multiply the top and bottom by two. We have not added more snack. Cutting it smaller is not a secret recipe for extra lunch.

Try thirds and sixths

Here are two thirds shaded. Split every third into two equal pieces. The whole now has six parts, and four are shaded. Two thirds equals four sixths. Equivalent fractions are different names for the same amount of the same whole.

Pause and try

Pause the video. The top bar has three quarters shaded. The equal-sized bottom bar is divided into eight parts. How many eighths should you shade to match three quarters? Picture splitting each quarter in two. Count the shaded pieces.

Six eighths matches

Shade six eighths. Each shaded quarter becomes two shaded eighths, so three becomes six. Four parts become eight parts in the whole. Multiplying both numbers by two preserves the fraction. Multiplying only the top number would change the amount.

More names, same amount

Fun fact: this shaded half has many fraction names. One half, two quarters, and four eighths all describe it. The bottom number gets bigger because the pieces get smaller. A bigger bottom number alone does not mean a bigger snack.

Check the picture and numbers

For equal-sized wholes, matching shaded amounts show equivalent fractions. In our whole-number examples, multiply or divide both numbers by the same nonzero number. On the worksheet, try this with thirds and ninths. Draw a bar when you want to check your thinking.