Subtract and simplify if necessary.
$\begin{array}{l}
1 \frac{3}{10}-\frac{9}{10}=N \quad 2-7 \frac{4}{9}-\frac{7}{9}=N \quad 3 \cdot \frac{3}{4}-1 \frac{3}{4}=N \\
8 \frac{2}{5}-2 \frac{3}{5}=N \quad \text { s. } 11 \frac{2}{7}-6 \frac{5}{7}=N
\end{array}$
Answer (1)
Convert mixed numbers to improper fractions.
Perform the subtraction.
Simplify the resulting fraction.
The answers are: 5 2 , 6 3 2 , − 1 , 5 5 4 , 4 7 4 .
The final answers are: 5 2 , 6 3 2 , − 1 , 5 5 4 , 4 7 4
Explanation
Introduction We are given five subtraction problems involving fractions and mixed numbers. Our goal is to solve each problem and simplify the result if necessary. Let's tackle them one by one!
Solving Problem 1 Problem 1: 1 10 3 − 10 9 = N
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 .
So, N = 5 2 .
Solving Problem 2 Problem 2: 7 9 4 − 9 7 = N 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 back to a mixed number: 3 20 = 6 3 2 .
So, N = 6 3 2 .
Solving Problem 3 Problem 3: 4 3 − 1 4 3 = N First, convert the mixed number to an improper fraction: 1 4 3 = 4 4 + 4 3 = 4 7 .
Now, subtract the fractions: 4 3 − 4 7 = 4 3 − 7 = 4 − 4 .
Simplify the fraction: 4 − 4 = − 1 .
So, N = − 1 .
Solving Problem 4 Problem 4: 8 5 2 − 2 5 3 = N 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 back to a mixed number: 5 29 = 5 5 4 .
So, N = 5 5 4 .
Solving Problem 5 Problem 5: 11 7 2 − 6 7 5 = N First, convert the mixed numbers to improper fractions: 11 7 2 = 7 11 × 7 + 7 2 = 7 77 + 7 2 = 7 79 and 6 7 5 = 7 6 × 7 + 7 5 = 7 42 + 7 5 = 7 47 .
Now, subtract the fractions: 7 79 − 7 47 = 7 79 − 47 = 7 32 .
Convert back to a mixed number: 7 32 = 4 7 4 .
So, N = 4 7 4 .
Final Answers In summary:
1 10 3 − 10 9 = 5 2
7 9 4 − 9 7 = 6 3 2
4 3 − 1 4 3 = − 1
8 5 2 − 2 5 3 = 5 5 4
11 7 2 − 6 7 5 = 4 7 4
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to subtract fractions is essential for accurately calculating quantities and ensuring fair distribution. For example, if you have 2 2 1 cups of flour and a recipe calls for 1 4 1 cups, subtracting these fractions will tell you how much flour you'll have left after baking: 2 2 1 − 1 4 1 = 1 4 1 cups.
