Fraction problems may seem difficult, but a little practice and knowledge will make it easier. Here's how to solve exercises with fractions.
Steps
Method 1 of 4: Multiplying fractions
Step 1. You need to work with two fractions
These instructions only work in the case of two fractions. If you have mixed numbers, first turn them into improper fractions.
Step 2. Multiply numerator x numerator, then denominator x denominator
Having 1/2 x 3/4, multiply 1 x 3 and 2 x 4. The answer is 3/8
Method 2 of 4: Divide fractions
Step 1. You need to work with two fractions
Again, the procedure will ONLY work if you have already converted any mixed numbers into improper fractions.
Step 2. Reverse the second fraction
It doesn't matter which fraction you choose as the second.
Step 3. Change the sign of division to the sign of multiplication
If you started from 8/15 ÷ 3/4, then it will become 8/15 x 4/3
Step 4. Multiply above x above and below x below
8 x 4 is 32 and 15 x 3 is 45, hence the result is 32/45
Method 3 of 4: Convert mixed numbers into improper fractions
Step 1. Convert mixed numbers into improper fractions
Improper fractions are fractions where the numerator is greater than the denominator. (For example, 5/17.) If you are multiplying or dividing, before doing the other calculations, you need to convert the mixed numbers into improper fractions.
Suppose the mixed number is 3 2/5 (three and two fifths)
Step 2. Take the whole number and multiply it by the denominator
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In our case, 3 x 5 gives 15.
Solve Fraction Questions in Math Step 5
Step 3. Add the result to the numerator
In our case, we add 15 + 2 to get 17
Step 4. Write this sum above the original denominator and you will get an improper fraction
In our case, we will get 17/5
Method 4 of 4: Adding and subtracting fractions
Step 1. Find the lowest common denominator (the bottom number)
For both addition and subtraction, we start in the same way. Find the smallest common fraction that contains both denominators.
For example, between 1/4 and 1/6, the least common denominator is 12. (4x3 = 12, 6x2 = 12)
Step 2. Multiply the fractions to match the lowest common denominator
Remember that in doing this, you are not really changing the value, only the terms in which it is expressed. Think of a pizza: 1/2 of pizza and 2/4 of pizza are the same amount.
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Calculate how many times the current denominator is contained in the lowest common denominator.
For 1/4, 4 multiplied by 3 gives 12. For 1/6, 6 multiplied by 2 gives 12.
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Multiply the numerator and denominator of the fraction by that number.
In the case of 1/4, multiply both 1 and 4 by 3 to get 3/12. 1/6 multiplied by 2 gives 2/12. Now the problem will be: 3/12 + 2/12 or 3/12 - 2/12.
Step 3. Add or subtract the two numerators (top numbers) but NOT the denominators
This is because you want to determine how many fractions of that type are in total. If you add up the denominators as well, you will change the type of fractions.
For 3/12 + 2/12, the final result is 5/12. For 3/12 - 2/12, it's 1/12
Advice
- To get the reciprocal of an integer, simply write a 1 over it. For example, 5 becomes 1/5.
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Another way to say "invert the fraction" is to say "find the reciprocal". However, it is the same as swapping the numerator and denominator. Ex.
2/4 will be 4/2
- Basic knowledge of the four operations (multiplication, division, addition and subtraction) will make the calculations quick and easy.
- You can multiply and divide mixed numbers without converting them to improper fractions first. But this involves using the distributive property in a method that can be complex. It is therefore better to make use of the improper fractions.
- When you write the reciprocal of a negative number, the sign does not change.
Warnings
- Convert mixed numbers into improper fractions before starting.
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Ask your teacher if you have to give the results in minimum terms or not.
For example, 2/5 is the minimum term, but 16/40 is not
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Ask your teacher if you need to convert results from improper fractions to mixed numbers.
For example, 3 1/4 instead of 13/4
