Recognizing Equivalent Fractions Recognizing Equivalent Fractions Equivalent fractions are fractions that have the same value or represent the same part of an object. If a pie is cut into two pieces, each piece is also one-half of the pie. If a pie is cut into 4 pieces, then two pieces represent the same amount of pie that 1/2 did. We say that 1/2 is equivalent to 2/4. Fractions are determined to be equivalent by multiplying the numerator and denominator of one fraction by the same number. This number should be such that the numerators will be equal after the multiplication. For example if we compare 1/2 and 2/4, we would multiply 1/2 by 2/2 which would result in 2/4 so they are equivalent. To compare 1/2 and 3/7 we would multiply 1/2 by 3/3 to produce 3/6. Since 3/6 is not the same as 3/7, the fractions are not equivalent. Fractions equivalent to 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12 ... Fractions equivalent to 1/3 are 2/6, 3/9, 4/12, 5/15, ...
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Fractions equivalent to 1/4 are 2/8, 3/12, 4/16, 5/20, ... Fractions equivalent to 1/5 are 2/10, 3/15, 4/20, 5/25, ... Fractions equivalent to 2/5 are 4/10, 6/15, 8/20, 10/25, ... Equivalent fractions are fractions that may look different, but are equal to each other. Two equivalent fractions may have a different numerator and a different denominator. (A fraction is also equivalent to itself. In this case, the numerator and denominator would be the same.) Let's take a moment to demonstrate the concept of equivalent fractions. Follow the steps below. Take a sheet of paper and fold it twice, creating three equal sections. Now shade two of them. This shaded portion represents 2/3. Fold the paper again, in the other direction, but down the center of the paper. The shaded portion is now 4/6. The shaded portion of the paper does not change, so the fraction of the paper shaded does not change. The fractions 2/3 and 4/6 are equivalent. Equivalent fractions can be created by multiplying or dividing both the numerator and denominator by the same number. This number is referred to as a multiplier. We can do this because, if you multiply both the numerator and denominator of a fraction by the same non-zero number, the fraction remains unchanged in value.
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In the demonstration above, we could get the fraction 4/6 by multiplying both the top and bottom of 2/3 by 2. Example Show that the fraction 8/12 is equivalent to the fraction 2/3. If you multiply both the numerator and denominator of 2/3 by 4, you get the fraction 8/12. Therefore, the two are equivalent. A factor of a number is a number that can be divided into the original number evenly (meaning there is no remainder). For example, 4 is a factor of 8. That means 8 can be divided by 4 and there is no remainder (8 ÷ 4 = 2). This means that 2 is also a factor of 8. A prime number is a number that has only two factors, 1 and itself. For example, the number 2 can be divided evenly only by itself and 1, therefore, it is a prime number. The five smallest prime numbers are 2, 3, 5, 7, 11, and 13. Numbers that are not prime numbers are referred to as composite numbers. The number 8 is a composite number since it has factors of 2 and 4. Finding the prime factors of a composite number is done by dividing out the prime factors. For example, if we wish to find the prime factors of 24, we can start by dividing 24 by 2: When we divide 24 by 2 we get a result of 12. Since 2 goes into 24 evenly, it is a factor of 24. It is also a prime factor since it can only be divided by itself and 1. So, 24 has 2 as a prime factor and 12 as a composite factor.
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