Find the value of each expression in lowest terms.
1. $2 \frac{1}{5}+1 \frac{3}{4}$
2. $3 \frac{1}{2}-2 \frac{2}{3}$
3. $3 \frac{1}{2} - (\frac{1}{2})$
4. $1 \frac{1}{2}+2 \frac{3}{3}$
5. $3 \frac{1}{2}-2 \frac{5}{9}$
6. $5 \frac{1}{2}+5 \frac{1}{4}$
Answer (2)
After converting mixed numbers to improper fractions and performing the calculations, the results are: 3 \frac{19}{20}, \frac{5}{6}, 3, 4 \frac{1}{2}, \frac{17}{18}, and 10 \frac{3}{4}.
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Convert mixed fractions to improper fractions.
Add or subtract the improper fractions.
Simplify the resulting fraction.
Convert the simplified improper fraction back to a mixed fraction.
The answers are: 3 20 19 , 6 5 , 4 2 1 , 18 17 , 10 4 3 .
Explanation
Problem Analysis We need to find the value of the given expressions involving mixed fractions. We will convert each mixed fraction to an improper fraction, perform the indicated operation (addition or subtraction), simplify the result, and convert it back to a mixed fraction.
Solving Expression 1 Let's evaluate the first expression: 2 5 1 + 1 4 3 .
First, convert the mixed fractions to improper fractions: 2 5 1 = 5 2 × 5 + 1 = 5 11 1 4 3 = 4 1 × 4 + 3 = 4 7 Now, add the improper fractions: 5 11 + 4 7 = 5 × 4 11 × 4 + 4 × 5 7 × 5 = 20 44 + 20 35 = 20 44 + 35 = 20 79 Convert the improper fraction back to a mixed fraction: 20 79 = 3 20 19
Solving Expression 2 Now, let's evaluate the second expression: 3 2 1 − 2 3 2 .
Convert the mixed fractions to improper fractions: 3 2 1 = 2 3 × 2 + 1 = 2 7 2 3 2 = 3 2 × 3 + 2 = 3 8 Subtract the improper fractions: 2 7 − 3 8 = 2 × 3 7 × 3 − 3 × 2 8 × 2 = 6 21 − 6 16 = 6 21 − 16 = 6 5
Solving Expression 3 Next, let's evaluate the third expression: 1 2 1 + 2 3 3 .
Convert the mixed fractions to improper fractions: 1 2 1 = 2 1 × 2 + 1 = 2 3 2 3 3 = 2 + 3 3 = 2 + 1 = 3 = 1 3 Add the fractions: 2 3 + 1 3 = 2 3 + 1 × 2 3 × 2 = 2 3 + 2 6 = 2 3 + 6 = 2 9 Convert the improper fraction back to a mixed fraction: 2 9 = 4 2 1
Solving Expression 4 Now, let's evaluate the fourth expression: 3 2 1 − 2 9 5 .
Convert the mixed fractions to improper fractions: 3 2 1 = 2 3 × 2 + 1 = 2 7 2 9 5 = 9 2 × 9 + 5 = 9 23 Subtract the improper fractions: 2 7 − 9 23 = 2 × 9 7 × 9 − 9 × 2 23 × 2 = 18 63 − 18 46 = 18 63 − 46 = 18 17
Solving Expression 5 Finally, let's evaluate the fifth expression: 5 2 1 + 5 4 1 .
Convert the mixed fractions to improper fractions: 5 2 1 = 2 5 × 2 + 1 = 2 11 5 4 1 = 4 5 × 4 + 1 = 4 21 Add the improper fractions: 2 11 + 4 21 = 2 × 2 11 × 2 + 4 21 = 4 22 + 4 21 = 4 22 + 21 = 4 43 Convert the improper fraction back to a mixed fraction: 4 43 = 10 4 3
Examples
Mixed fractions are commonly used in everyday life, such as in cooking and baking. For example, a recipe might call for 2 2 1 cups of flour and 1 4 1 cups of sugar. To determine the total amount of dry ingredients, you would need to add these mixed fractions. Understanding how to add and subtract mixed fractions is essential for accurate measurements and successful cooking.
