Work out and simplify where possible:
a) $\frac{1}{5}+\frac{3}{10}$
b) $\frac{7}{8}-\frac{1}{4}$
Answer (1)
To add 5 1 and 10 3 , find a common denominator of 10, convert 5 1 to 10 2 , and add to get 10 5 . Simplify to 2 1 .
To subtract 4 1 from 8 7 , find a common denominator of 8, convert 4 1 to 8 2 , and subtract to get 8 5 .
The result of a) is 2 1 .
The result of b) is 8 5 .
Explanation
Problem Analysis We are given two expressions involving fractions that we need to simplify: a) 5 1 + 10 3 b) 8 7 − 4 1
Solving a) For part a), we need to add two fractions. To do this, we first need to find a common denominator. The least common multiple of 5 and 10 is 10. We can rewrite 5 1 as an equivalent fraction with a denominator of 10: 5 1 = 5 × 2 1 × 2 = 10 2 Now we can add the two fractions: 10 2 + 10 3 = 10 2 + 3 = 10 5 Finally, we simplify the resulting fraction: 10 5 = 2 1
Solving b) For part b), we need to subtract two fractions. To do this, we first need to find a common denominator. The least common multiple of 8 and 4 is 8. We can rewrite 4 1 as an equivalent fraction with a denominator of 8: 4 1 = 4 × 2 1 × 2 = 8 2 Now we can subtract the two fractions: 8 7 − 8 2 = 8 7 − 2 = 8 5 The fraction 8 5 is already in its simplest form.
Final Answer Therefore, the simplified expressions are: a) 2 1 b) 8 5
Examples
Fractions are a fundamental concept in mathematics and are used in various real-life situations. For example, when baking, you often need to measure ingredients using fractions. If a recipe calls for 2 1 cup of flour and you only have a 4 1 cup measuring spoon, you need to use it twice to get the correct amount. Understanding how to add and subtract fractions is crucial for accurately following recipes and achieving the desired results in cooking and baking.
