Modeling and Finding Equivalent Fractions
Learning Outcomes
- Use fraction tiles or visual aids to create equivalent fractions
- Find an equivalent fraction given a fraction
Equivalent Fractions
Equivalent fractions are fractions that have the same value.

Example
Use fraction tiles to find equivalent fractions. Show your result with a figure.- How many eighths() equal one-half()?
- How many tenths() equal one-half()?
- How many twelfths() equal one-half()?



Try it
#146001 [ohm_question height="270"]146001[/ohm_question]Find Equivalent Fractions
We used fraction tiles to show that there are many fractions equivalent to . For example, , and are all equivalent to . When we lined up the fraction tiles, it took four of the tiles to make the same length as a tile. This showed that . See the previous example. We can show this with pizzas, too. Image (a) shows a single pizza, cut into two equal pieces with shaded. Image (b) shows a second pizza of the same size, cut into eight pieces with shaded.
Equivalent Fractions Property
If , and are numbers where and , thenExample
Find three fractions equivalent to .Answer: Solution To find a fraction equivalent to , we multiply the numerator and denominator by the same number (but not zero). Let us multiply them by , and . So, , and are equivalent to .
Try it
Find three fractions equivalent to .Answer: Correct answers include .
Find three fractions equivalent to .Answer: Correct answers include .
Example
Find a fraction with a denominator of that is equivalent to .Answer: Solution To find equivalent fractions, we multiply the numerator and denominator by the same number. In this case, we need to multiply the denominator by a number that will result in . Since we can multiply by to get , we can find the equivalent fraction by multiplying both the numerator and denominator by .