Fractions problems may seem difficult at first, but they become easier with practice and knowing how to do them. Start by learning terms and fundamentals, then practice addition, subtraction, multiplication, and division of fractions. If you already understand the meaning and how to process fractions, the problems faced will be able to be done easily.
Step
Method 1 of 2: Practice the Basics
Step 1. Know that the numerator is at the top and the denominator is at the bottom
A fraction is part of a whole, and the number above the fraction is called the numerator, which indicates the number of parts of the unit it has. The number below the fraction is the denominator, which indicates the number of parts that make up the whole.
For example, in 3/5, 3 is the numerator which means we have 3 parts, and 5 is the denominator, which means there are a total of 5 parts that make up the whole. In, 7 is the numerator and 8 is the denominator
Step 2. Convert a whole number to a fraction by placing it above the number 1
If you have a whole number and want to convert it to a fraction, use the whole number as the numerator. For the denominator, you should always use the number 1 because every number divided by 1 is the number itself.
If you want to convert 7 to a fraction, write 7/1
Step 3. Shrink the fraction if it needs to be simplified
Start by finding the Greatest Common Factor (GCF) of the numerator and denominator. GCF is the largest number that can evenly divide the numerator and denominator (the result of the division is an integer). Then, simply divide the numerator and denominator by the GCF to reduce the fraction.
For example, if the fraction in the problem is 15/45, the greatest common factor is 15 because 15 and 45 are divisible by 15. Divide 15 by 15 to make 1, and write the new numerator. Divide 45 by 15, which makes 3, and write it down as the new denominator. Thus, 15/45 is reduced to 1/3
Step 4. Learn how to convert mixed fractions into improper fractions
Mixed fractions have whole numbers and fractions. To solve certain fraction problems easily, you need to convert mixed fractions into improper fractions (i.e. fractions whose numerator is greater than the denominator). The trick, multiply the whole number by the denominator of the fraction, then add the result with the numerator. Write the result as the new numerator.
Let's say you have a mixed number 1 2/3. Start by multiplying 1 by 3 to get 3. Add 3 to the numerator, which is 2. The result is a new numerator, which in this case is 5 so the fraction is not usually 5/3
Tip:
Usually, you need to convert mixed numbers to improper fractions if you want to multiply or divide them.
Step 5. Learn how to convert an unusual fraction to a mixed number
Sometimes, questions ask you to do the opposite, which is to convert an unusual fraction to a mixed number. Start by knowing how many times the numerator can enter the denominator using division. The result is a whole number in the mixed number. Continue by multiplying the whole number by the divisor (the number used to divide) and dividing the result by the division (the number that was divided). Write the remainder over the initial denominator.
Let's say you have the unusual fraction 17/4. Change the problem to 17 4. The number 4 can go into 17 4 times so that the whole number is 4. Then, multiply 4 by 4, which equals 16. Subtract 17 by 16 to get 1; this is the remainder in mixed numbers. Thus, 17/4 is equal to 4 1/4
Method 2 of 2: Counting Fractions
Step 1. Add up the fractions that have the same denominator by adding the numerators
Fractions can only be added if the denominators are the same. If so, simply add up all the numerators.
For example, to calculate 5/9 + 1/9, simply add 5 + 1, which equals 6. Thus, the answer is 6/9 which can be reduced to 2/3
Step 2. Subtract fractions that have the same denominator by subtracting the numerator
Like addition, fractions can only be subtracted if the denominators are the same. In that case, you just need to subtract the numerator of the fractions in the order in which they were calculated.
For example, to solve problems 6/8 - 2/8, you just need to subtract 6 by 2. The answer is 4/8, which can be reduced to 1/2. Conversely, if the calculation is 2/8-6/8, you subtract 2 by 6 which results in -4/8, which can be reduced to -½
Step 3. Find Least Common Multiple (LCM) to add or subtract fractions that do not have the same denominator
If the denominators of the fractions you want to calculate are not the same, you need to find the Least Common Multiple of the denominators of the related fractions to equalize. To do this, multiply the numerator and denominator by a number that turns the fractions into their least common multiple. Then add or subtract the numerators to find the answer.
- For example, if you want to add 1/2 and 2/3, start by determining the least common multiple. In this case, the common multiple is 6 because 2 and 3 can be converted into 6. To convert 1/2 to a fraction with a denominator of 6, multiply the numerator and denominator by 3:1 x 3 = 3 and 2 x 3 = 6 so the new fraction is 3 /6. To convert 2/3 to a fraction with a denominator of 6, multiply both denominators by 2: 2 x 2 = 4 and 3 x 2 = 6 so that the new fraction is now 4/6. Now, you can add up the numerators: 3/6 + 4/6 = 7/6. Since the result is an unusual fraction, you can convert it to a mixed number 1 1/6.
- On the other hand, say your problem is 7/10 - 1/5. The common multiple is 10 because 1/5 can be converted into a fraction with a denominator of 10 by multiplying by 22:1 x 2 = 2 and 5 x 2 = 10 so the new fraction is 2/10. You don't need to change any other fractions. So, simply subtract 7 by 2 and get 5. The answer is 5/10, which can also be reduced to 1/2.
Step 4. Multiply fractions directly
Fortunately, multiplying multiple fractions is fairly easy to do. Shrink the fraction not yet to its lowest term. Then, you just need to multiply the numerator by the numerator, and the divisor by the divisor.
For example, multiplying 2/3 and 7/8, find the new numerator by multiplying 2 and 7, which equals 14. Then, multiply 3 by 8, which gives 24. Thus, the answer is 14/24, which can be reduced to 7 /12 by dividing the numerator and denominator by 2
Step 5. Divide fractions by inverting the second fraction, then multiplying directly
To divide a fraction, start by converting the divisor to its reciprocal. The trick is to turn the numerator of the fraction into the denominator, and the denominator into the numerator. After that, multiply the numerator and denominator of the two fractions to get the division result.
For example, to solve the problem 1/2 1/6, flip 1/6 to make it 6/1. Then, simply multiply the numerator 1 x 6 to get the answer's numerator (which is 6), and the denominator 2 x 1 to find the answer's denominator (which is 2). Thus, the result of dividing the two fractions is 6/2, which is equal to 3
Tips
- Take the time to read the questions carefully at least twice so that you understand exactly what the questions are asking for.
- Check with the teacher to see if you need to convert an unusual fraction to a mixed number and/or reduce the fraction to its smallest term to get full marks
- To get a reciprocal integer, just put the number 1 above it. For example, 5 becomes 1/5.
- Fractions never have a denominator of 0. The denominator of zero is undefined because dividing by zero is illegal.
