Attention Getting Question:
Have you ever found equivalent fractions?
When something is equivalent, we can say that what is being compared has the same value. For instance, eight minus three is equivalent to five. Even though eight minus three looks different from five, we know that after performing the operation of subtraction, our answer will be five.
Remember, fractions tell us the number of equal parts that make a whole. Fractions are equivalent when they represent the same amount of the whole. We can find an equivalent fraction by either dividing or multiplying both the numerator (the number above the fraction bar) and denominator (the number below the fraction bar) by the same number. When dividing by the same number, it is important to divide the numerator and denominator by a number that will not leave any remainder.
Imagine that you are in a park with your friend eating a chocolate bar. Your friend asks for one-fourth of the chocolate bar, but it is cut into eight sections. Equivalent fractions help you determine how many sections of the chocolate bar your friend is asking for. The fraction of the chocolate your friend is asking for (one-fourth) has a four as the denominator. Since there are eight sections of the chocolate bar, the equivalent fraction will have an eight as the denominator. In order to get the denominator from four to eight, we must multiply by two. Because we are multiplying the denominator by two, we also multiply the numerator by two. This tells us that one-fourth and two-eighths are equivalent fractions, which means that your friend is asking for two of the eight sections of the chocolate bar. Now it is up to you to decide whether you are feeling nice enough to share those two sections.
Remember, multiplying or dividing the numerator and denominator by the same number finds equivalent fractions.
Pretend you are piloting a spaceship to get a closer look at the majestic rings of Neptune. Neptune is about thirty astronomical units away from Earth. Your mission leader on Earth contacts you and wants to know how much of the journey you have completed. You look down at your course map and see that you have travelled ten astronomical units of the thirty you have to travel altogether. Since you have gone ten astronomical units out of the thirty, we can represent this as the fraction ten over thirty. In order to tell him the most simple fraction of the trip you have travelled, we can use equivalent fractions to simplify. Both ten (the numerator) and thirty (the denominator) can be divided by ten without any remainders. By using this division with both the numerator and denominator, we can determine that one-third is an equivalent fraction to ten over thirty. Now you can tell your mission leader that you have completed one-third of your expedition.
In summary, determining equivalent fractions can help us to simplify fractions into terms that are more understandable or establish how many parts of a whole a simple fraction is referring to. By using multiplication or division by the same number with both the numerator and denominator of the fraction, we can identify equivalent fractions. If you are multiplying, you multiply both the numerator and the denominator by the same number. If you are dividing, determine a number that will divide into both the numerator and denominator without any remainder. Then divide both the numerator and denominator by that number. As you can see, it is easy to determine equivalent fractions that represent the same value.