Math Lessons for 1-9-12 Di Todd Fifth Grade 2012

Steps for Addition of Fractions Find the needed information. Using lowest common multiple of the denominators, find the least common denominator. Change addends to equivalent fractions with the least common denominator. Add the numerators (denominator stay the same). Then reduce the sum to the lowest terms.

To add two fractions that do not have the same denominators, First convert the fractions being added into equivalent fractions with the same denominator. Then add the numerators. Use you fraction bars to show ½ + ¼ Questions: Can we combine ½ and ¼ and talk about the answer in terms of halves?

For ½ + ¼ = n, we divide ½ in half. A half of a half is a quarter For ½ + ¼ = n, we divide ½ in half. A half of a half is a quarter. Two quarters is equivalent to one half. Prove this statement is true using your fraction bars. So if 2/4 = ½, for ½ + ¼, we convert ½ to 2/4 : 2/4 + ¼. Now the denominators are the same, so we can add the numerators. 2/4 + ¼ = 3/4

Often we cannot convert the larger denominator into an equivalent fraction with same denominator as the other fraction. Example: ½ + 1/3 = x We can’t add these two fractions in terms of halves or thirds, because neither divides equally into the other. (There aren’t an even number of thirds in a half, and half is larger than a third.) Prove this statement using your fraction bars.

We must divide both fractions into the same size pieces We must divide both fractions into the same size pieces. If the fractions are divided into the same size pieces, then the denominators are the same, or common denominators. The number of pieces will be different, because the original fractions were not the same size. A common denominator is a number that can be divided evenly by the other denominators. To find the common denominator of two or more denominators, we use the least common multiple.

Least Common Multiple The least common multiple is the smallest number that is a product in the multiplication tables of the original denominators. Example: LCM of ½ and 1/3 Multiples of 2: Multiples of 3: 2 x 1= 2 2x 5=10 3 x 1= 3 2x2=4 2 x 6= 12 3 x 2= 6 2 x3=6 3 x 3= 9 2 x 4= 8 3 x 4 = 12 Common multiples of 2 and 3 are 6, 12, and so on. The least, or lowest common multiple is 6, so 6 is the least common denominator.

Finally, the original fractions are converted into equivalent fractions with the least common denominator (LCD). ½ = 3/6 ; 1/3= 2/6 To find the numerator for these equivalent fractions, divide the LCD by each of the original denominator, and multiply that number by the original numerator. ½ = 3/6 because 6÷2=3 and 3x1=3 1/3 = 2/6 because 6÷3=2 and 2x1=2

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