Subtract.
$\frac{-3}{10}-\frac{-4}{5}=$
$\square$
Answer (1)
Rewrite the second fraction with a common denominator: 5 − 4 = 10 − 8 .
Rewrite the subtraction as an addition: 10 − 3 − 10 − 8 = 10 − 3 + 10 8 .
Combine the fractions: 10 − 3 + 8 = 10 5 .
Simplify the fraction: 10 5 = 2 1 . The final answer is 2 1 .
Explanation
Understanding the Problem We are asked to subtract two negative fractions: 10 − 3 − 5 − 4 .
Finding a Common Denominator To subtract the fractions, we need to have a common denominator. The least common denominator of 10 and 5 is 10. We can rewrite the second fraction with a denominator of 10: 5 − 4 = 5 × 2 − 4 × 2 = 10 − 8
Rewriting the Expression Now we can rewrite the original expression as: 10 − 3 − 10 − 8
Simplifying the Subtraction Subtracting a negative number is the same as adding its positive counterpart. So we have: 10 − 3 − 10 − 8 = 10 − 3 + 10 8
Combining the Fractions Now, combine the fractions: 10 − 3 + 8 = 10 5
Simplifying the Fraction Finally, simplify the fraction: 10 5 = 2 1
Final Answer Therefore, the result of the subtraction is 2 1 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to add and subtract fractions, especially negative fractions, is essential for accurate calculations in these situations. For example, if you are following a recipe that calls for 2 1 cup of flour, but you only want to make half the recipe, you need to calculate 2 1 × 2 1 = 4 1 cup of flour. Similarly, if you are tracking your expenses and you spent $3.50 (represented as − $3.50 ) and then received $5.00 , you need to calculate − $3.50 + $5.00 = $1.50 to determine your current balance.
