Adding and Subtracting Mixed Numbers

Front

What is a mixed number?

Back

A mixed number is a whole number combined with a fraction, such as 2 \frac{1}{2}.

Front

How do you convert a mixed number to an improper fraction?

Back

Multiply the whole number by the denominator, add the numerator, and place that over the original denominator. For example, 2 \frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{11}{4}.

Front

What is the first step in adding mixed numbers?

Back

Convert each mixed number to an improper fraction.

Front

How do you find a common denominator for fractions?

Back

Identify the least common multiple (LCM) of the denominators.

Front

What is the sum of 2 \frac{1}{3} and 1 \frac{2}{5}?

Back

First convert to improper fractions: 2 \frac{1}{3} = \frac{7}{3}, 1 \frac{2}{5} = \frac{7}{5}. Find a common denominator (15), then add: \frac{35}{15} + \frac{21}{15} = \frac{56}{15} = 3 \frac{11}{15}.

Front

What is the difference between 5 \frac{1}{2} and 2 \frac{3}{4}?

Back

Convert to improper fractions: 5 \frac{1}{2} = \frac{11}{2}, 2 \frac{3}{4} = \frac{11}{4}. Find a common denominator (4), then subtract: \frac{22}{4} - \frac{11}{4} = \frac{11}{4} = 2 \frac{3}{4}.

Front

What do you do if the result of adding mixed numbers is an improper fraction?

Back

Convert the improper fraction back to a mixed number.

Front

What is the importance of having common denominators when adding or subtracting fractions?

Back

Common denominators allow you to combine the fractions easily by ensuring they represent the same size parts.

Front

What is the result of 3 \frac{2}{5} + 4 \frac{1}{10}?

Back

Convert to improper fractions: 3 \frac{2}{5} = \frac{17}{5}, 4 \frac{1}{10} = \frac{41}{10}. Find a common denominator (10), then add: \frac{34}{10} + \frac{41}{10} = \frac{75}{10} = 7 \frac{5}{10} = 7 \frac{1}{2}.

Front

What is the result of 6 \frac{1}{4} - 2 \frac{2}{3}?

Back

Convert to improper fractions: 6 \frac{1}{4} = \frac{25}{4}, 2 \frac{2}{3} = \frac{8}{3}. Find a common denominator (12), then subtract: \frac{75}{12} - \frac{32}{12} = \frac{43}{12} = 3 \frac{7}{12}.