Adding Fractions!

Front

What is the process for adding fractions with the same denominator?

Back

To add fractions with the same denominator, keep the denominator the same and add the numerators. For example, \( \frac{a}{c} + \frac{b}{c} = \frac{a+b}{c} \).

Front

How do you add fractions with different denominators?

Back

To add fractions with different denominators, first find a common denominator, convert each fraction to an equivalent fraction with that denominator, and then add the numerators. For example, to add \( \frac{1}{2} + \frac{1}{3} \), the common denominator is 6, so it becomes \( \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \).

Front

What is a mixed number?

Back

A mixed number is a whole number combined with a proper fraction. For example, \( 1 \frac{2}{3} \) is a mixed number, consisting of the whole number 1 and the fraction \( \frac{2}{3} \).

Front

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

Back

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. The result becomes the new numerator, and the denominator remains the same. For example, \( 1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3} \).

Front

What is the first step in adding mixed numbers?

Back

The first step in adding mixed numbers is to convert them to improper fractions. This makes it easier to perform the addition.

Front

How do you simplify a fraction?

Back

To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify \( \frac{8}{12} \), the GCD is 4, so it simplifies to \( \frac{2}{3} \).

Front

What is the result of adding \( 1 \frac{2}{5} + \frac{3}{5} \)?

Back

The result is 2. First, convert \( 1 \frac{2}{5} \) to an improper fraction: \( \frac{7}{5} \). Then add: \( \frac{7}{5} + \frac{3}{5} = \frac{10}{5} = 2 \).

Front

What is the result of adding \( 36 \frac{3}{4} + 7 \frac{1}{2} \)?

Back

The result is \( 44 \frac{1}{4} \). Convert both mixed numbers to improper fractions, add them, and convert back to a mixed number.

Front

How do you handle fractions when adding a whole number?

Back

When adding a whole number to a fraction, convert the whole number to a fraction with the same denominator as the fraction, then add. For example, to add 3 to \( \frac{1}{4} \), convert 3 to \( \frac{12}{4} \) and add: \( \frac{12}{4} + \frac{1}{4} = \frac{13}{4} \).

Front

What is the result of adding \( 1 \frac{1}{2} + \frac{8}{12} \)?

Back

The result is \( 2 \frac{2}{12} \), which simplifies to \( 2 \frac{1}{6} \). Convert \( 1 \frac{1}{2} \) to \( \frac{3}{2} \), convert \( \frac{8}{12} \) to \( \frac{2}{3} \), find a common denominator, and add.