Subtract Mixed Numbers
Subtracting mixed numbers can be tricky, but you can do it in just a few easy steps if you follow a few basic rules. If you want to know how, just read on.
Steps
- Change the mixed numbers into improper fractions. You can covert a mixed number into an improper fraction in just three easy steps:
- First, multiply the whole number by the denominator of the fraction.
- If you are converting the number 3 3/4 to an improper fraction, you would first multiply the whole number 3 by the denominator of the fraction, 4. 3 * 4 = 12.
- Add this number to the numerator of the fraction.
- Add your previous answer 12 to the numerator, 3. 3 + 12 = 15.
- Place this new number over the original denominator of the fraction.
- The new number is 15, so you can place it over 4, the original denominator. The mixed number 3 3/4 converts to the improper fraction 15/4.
- To convert the second number, 1 1/2, to an improper fraction, you should first multiply the whole number by the denominator of the fraction.
- Multiply 1 by 2 to get 2.
- Then, add 2 to the numerator of the fraction. 2 + 1 = 3.
- Put the new number, 3, over the original denominator, 2, to get 3/2.
- First, multiply the whole number by the denominator of the fraction.
- Find the least common denominator (LCD).The least common denominator is the smallest number that is evenly divisible by both denominators.
- The denominators are 4 and 2, and the LCD is 4 because 4 is evenly divisible by both 4 and 2.
- The LCD is often a number that is greater than both numbers. For example, the LCD of 3 and 6 is 12, because that is the lowest number that is divisible by both 3 and 6. The LCD can never be smaller than either number.
- Divide the LCD by the denominators of the fractions. 4/4 = 1, so 15/4 becomes 15/1. 4/2 = 2 so 3/2 remains 3/2.
- Make the fractions have the same base. Before you can subtract the fractions, they need to have the same base. To give them the same base, 4, you need to multiply the numerator of each fraction by the numbers you got from dividing their numerators into the LCD in the previous step. This will keep the numerators of the fractions proportional with their new denominator, 4.
- 15/1 : since your answer was 1 when you divided the LCD by the denominator (4/4 = 1), you should multiply the numerator by 1. Since 15 * 1 = 1, the fraction 15/1 will be converted into 15/4.
- 3/2 : since your answer was 2 when you divided the LCD by the denominator (4/2 = 2), you should multiply the numerator by 2. 3 * 2 = 6, so the fraction 3/2 will be changed into 6/4.
- Subtract. Now that you've converted the numbers to have the same denominator, you can subtract them. To subtract numbers with the same denominator, you only need to subtract the numerators.
- 15/4 - 6/4 = 9/4.
- Convert the improper fraction into a mixed number. Since the question is in mixed number form, the final answer should be a mixed number. You have to work backwards to convert the improper fraction back into a mixed number. Here's how you do it:
- First, divide the top number by the bottom number. Do long division to divide 4 into 9. 4 goes into 9 2 times. This means that the quotient is 2. The remainder, or the number that is left over, is 1.
- Make your quotient the new whole number. Take your remainder and place it over the original denominator to finish converting the improper fraction into a mixed number. The quotient is 2, the remainder is 1, and the original denominator was 4, so the final answer is 2 1/4.
Tips
- Remember that you can only add and subtract fractions that have the same denominator.
- If it's a question for homework or an exam make sure to show your work.
