Subtract and simplify if necessary.
[tex]
\begin{array}{l}
1. 1 \frac{3}{10}-\frac{9}{10}= \\
2. 7 \frac{4}{9}-\frac{7}{9}= \\
3. 8 \frac{2}{5}-2 \frac{3}{5}= \\
4. 11 \frac{2}{7}-6=
\end{array}
[/tex]
Answer (2)
Convert mixed numbers to improper fractions.
Perform the subtraction.
Simplify the resulting fraction to a mixed number or a whole number if possible.
The solutions are: 5 2 , 6 3 2 , 5 5 4 , 5 7 2 .
Explanation
Understanding the Problem We are given four subtraction problems involving mixed numbers and fractions. We need to solve each one and simplify the result if necessary.
Solving the first problem Let's solve the first problem: 1 10 3 − 10 9 . First, convert the mixed number to an improper fraction: 1 10 3 = 10 10 + 10 3 = 10 13 . Now, subtract the fractions: 10 13 − 10 9 = 10 13 − 9 = 10 4 . Simplify the fraction: 10 4 = 5 2 .
Solving the second problem Now, let's solve the second problem: 7 9 4 − 9 7 . First, convert the mixed number to an improper fraction: 7 9 4 = 9 7 × 9 + 9 4 = 9 63 + 9 4 = 9 67 . Now, subtract the fractions: 9 67 − 9 7 = 9 67 − 7 = 9 60 . Simplify the fraction: 9 60 = 3 20 . Convert the improper fraction to a mixed number: 3 20 = 6 3 2 .
Solving the third problem Now, let's solve the third problem: 8 5 2 − 2 5 3 . First, convert the mixed numbers to improper fractions: 8 5 2 = 5 8 × 5 + 5 2 = 5 40 + 5 2 = 5 42 and 2 5 3 = 5 2 × 5 + 5 3 = 5 10 + 5 3 = 5 13 . Now, subtract the fractions: 5 42 − 5 13 = 5 42 − 13 = 5 29 . Convert the improper fraction to a mixed number: 5 29 = 5 5 4 .
Solving the fourth problem Now, let's solve the fourth problem: 11 7 2 − 6 . First, convert the mixed number to an improper fraction: 11 7 2 = 7 11 × 7 + 7 2 = 7 77 + 7 2 = 7 79 . Convert the whole number to a fraction with the same denominator: 6 = 7 6 × 7 = 7 42 . Now, subtract the fractions: 7 79 − 7 42 = 7 79 − 42 = 7 37 . Convert the improper fraction to a mixed number: 7 37 = 5 7 2 .
Final Answer So, the solutions are:
1 10 3 − 10 9 = 5 2
7 9 4 − 9 7 = 6 3 2
8 5 2 − 2 5 3 = 5 5 4
11 7 2 − 6 = 5 7 2
Examples
Understanding how to subtract fractions and mixed numbers is essential in everyday life. For example, if you are baking a cake and need to measure ingredients, you might need to subtract fractions to get the correct amount. Also, when calculating time differences or working with measurements in construction or carpentry, subtracting fractions becomes a necessary skill. Mastering these operations allows for accurate calculations and problem-solving in various practical situations.
To solve subtraction problems with mixed numbers, first convert them to improper fractions, perform the subtraction, and simplify the result if possible. The answers are: 5 2 , 6 3 2 , 5 5 4 , and 5 7 2 . This method helps to accurately subtract mixed numbers and fractions.
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