Unit 5 - Operations with Fractions. Selection File type icon File name Description Size Revision Time User. Welcome to The Mixed Operations with Three Fractions Including Negatives and Improper Fractions (A) Math Worksheet from the Fractions Worksheets Page at Math-Drills.com. This math worksheet was created on 2016-02-03 and has been viewed 74 times this week and 195 times this month. It may be printed, downloaded or saved and used in your classroom, home school.
Unit 4: Operations with Fractions. How are equivalent fractions helpful when solving problems?. How can a fraction be greater than 1?. How can a fraction model help us make sense of a problem?. How can comparing factor size to 1 help us predict what will happen to the product? Unit 4: Use Estimation, Strategies, and Algorithms to Solve Divison Problems with Whole Numbers. Students will use strategies and algorithms, including the standard algorithm, to solve whole number division problems. Unit 4: Operations with Fractions How are improper fractions and mixed numbers alike and different? How can you use fractions to solve addition and subtraction problems? How do we add fractions with like denominators? How do we apply our understanding of fractions in everyday life?
We can only add or subtract fractions when they have the same denominator. Pictures. Therefore, the first step in adding or subtracting fractions is writing them as fractions with the same denominator (see Reducing Fractions and the Least Common Denominator). Once the denominators have been equalized, adding or subtracting the fractions is easy--simply add or subtract the numerators, while keeping the denominator the same. The numerator of the answer is this result, and the denominator of the answer is the common denominator.
It is often useful to write the answer in lowest terms, using the steps learned in Reducing Fractions and the Least Common Denominator.
Example 1: 1/12 + 5/42 = ?
I. Find the LCD.
1. Factor the denominators. 12 = 2×2×3 and 42 = 2×3×72. Find the LCM of the denominators. 2×2×3×7 = 843. The LCD is 84.II. Write each fraction as an equivalent fraction with the LCD (84) as the new denominator.
(a) 12×7 = 84. 1×7 = 7Thus, 1/12 = 7/84 and 5/42 = 10/84
(b) 42×2 = 84. 5×2 = 10
7/84 + 10/84 = 17/84.BR>IV. Reduce. Since 17 and 84 have no common factors, the fraction cannot be reduced further.
1/12 + 5/42 = 17/84
Example 2: 13/20 - 3/70 = ?
I. Find the LCD
1. 20 = 2×2×5 and 70 = 2×5×7II. Write as equivalent fractions with the LCD as the denominator.
2. 2×2×5×7 = 140
3. The LCD is 140
(a) 20×7 = 140. 13×7 = 91
(b) 70×2 = 140. 3×2 = 6
91/140 - 6/140 = 85/140IV. Reduce.
1. Factor the numerator and the denominator. 85 = 5×17 and 140 = 2×2×5×713/20 - 3/70 = 17/28.
2. Find the GCF. The GCF is 5.BR>3. Divide. 85/5 = 17 and 140/5 = 28. Thus, 85/140 = 17/28
Example 3: 9/8 - 5/12 - 2/5 = ?
I and II. As we have already learned,these three fractions with common denominators are:
9/8 = 135/120III. Subtract. 135 - 50 - 48 = 37
5/12 = 50/120
2/5 = 48/120
135/120 - 50/120 - 48/120 = 37/120IV. Reduce. Since 37 and 120 have no common factors, the fraction cannot be reduced further.
9/8 - 5/12 - 2/5 = 37/120
To add and subtract mixed numbers, first add or subtract the whole numbers and then add or subtract the fractions as above. If the fractional part is improper, convert it to a mixed number (see converting mixed fractions).
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Unit 5 - Fractions