Math Help: Mixed Fraction Problems and Solutions

Mixed Fraction Help

Fractions represent parts of a whole, like 1/2 of a pizza or 3/4 of an orange. But what if you have two and 1/2 pizzas, or three and 3/4 oranges? When you have an integer amount, like two or three, and a fractional amount left over, you represent this using a mixed fraction, like 2 1/2 or 3 3/4.

Division

One important use of mixed fractions is writing the answers to division problems that have remainders. For instance, if you divide 25 by 12, you'll get an answer of two with a remainder of one. This means that 12 went into 25 two times, but you have 1/12 left over, so you could write this answer as the mixed fraction 2 1/12. The numerator of the fraction is the remainder, and the denominator is the divisor.

Tip: Sometimes, you'll need to simplify the fractional part of the mixed fraction. For example, 5 2/6 would be simplified to 5 1/3.

Mixed Numbers to Improper Fractions

If you want to add, subtract, multiply or divide mixed fractions, you have to turn them into improper fractions first. An improper fraction is a fraction which has a numerator that's larger than the denominator. For instance, 11/5 and 21/8 are improper fractions. Just like mixed fractions, they represent amounts that are greater than one. To turn a mixed fraction into an improper fraction, there are three steps to follow:

1. Multiply the denominator of the fraction by the integer.
2. Add the numerator of the fraction to that answer.
3. The answer becomes the numerator of the improper fraction, and the denominator remains the same.

For example, the first step toward converting 5 1/3 into an improper fraction is to multiply three and five to get 15 (3 x 5 = 15). Next, add 15 to one to get 16 (15 + 1 = 16). Last, 16 becomes the numerator and three remains the denominator: 16/3.

Improper Fractions to Mixed Numbers

If you have an improper fraction and you need to change it to a mixed number, you reverse the steps described earlier for changing a mixed number to a fraction. Here's the process:

1. Divide the numerator of the improper fraction by the denominator. The result becomes the integer part of the mixed number.
2. The remainder, if any, becomes the numerator of the new mixed fraction.
3. The denominator of the mixed fraction is the denominator from the improper fraction. Reduce the fractional part of the mixed number if necessary.

As an example, let's change 15/6 into a mixed number. First, divide 15 by six to get two with a remainder of three. Two will become the integer in the mixed number, and three will become the numerator of the fraction in the mixed number. The denominator will still be six. The entire mixed number will look like this: 2 3/6. Since 3/6 can be simplified to 1/2, the final answer will be 2 1/2.

Practice Problems

1. Nina has four whole watermelons and one quarter of a watermelon. Express this as a mixed fraction.

2. Change 4 1/3 to an improper fraction.

3. Write the improper fraction 18/7 as a mixed number.

Solutions

1. Four and one quarter is written as a mixed fraction like this: 4 1/4.

2. First, multiply three by four to get 12 (3 x 4 = 12). Add one to 12 to get 13 (1 + 12 = 13), which becomes the numerator of the improper fraction. The denominator will still be three, so the improper fraction will be 13/3.

3. To write 18/7 as a mixed number, first divide 18 by seven to get two with a remainder of four. Two will become the integer in the mixed number. The numerator will be the remainder, four, and the denominator will still be seven. The mixed number will be 2 4/7.