- 1 What you need to know about fractions:
- 2 How to add fractions with a common denominator:
- 3 How to add fractions with different denominators:
- 4 How to subtract fractions with a common denominator:
- 5 How to subtract fractions with different denominators:
- 6 How to multiply fractions:
- 7 How to divide fractions:
- 8 Fraction Operations Task
Fraction operations are taught in the 6th grade. In the initial lessons of this topic, children learn to add and subtract fractions with a common denominator. Later, they move on to multiplication and division. In future grades, this skill is necessary for solving more complex equations and problems in algebra and geometry. Mathema has prepared an article that will quickly teach you how to add, subtract, divide, and multiply fractions.
What you need to know about fractions:
- The top number of a fraction is called the numerator.
- The bottom number of a fraction is called the denominator.
- If the numerator is greater than the denominator, the fraction is improper.
- Improper fractions can be simplified and written as proper fractions.
How to add fractions with a common denominator:
Adding is one of the simplest operations with fractions. First, pay attention to the denominators of both fractions. If they are the same, you can simply add the numerators and write the result as one fraction.
\[\frac26+\frac36=\;\frac{2+3}6=\frac56\]If there are whole numbers next to the fraction, they also need to be added, and then the operations with the fractions should be performed.
\[2\frac5{12}+3\frac4{12}=(2+3)\;\frac{5+4}{12}=5\frac9{12}\]Sometimes, improper fractions are obtained when adding fractions. In this case, they need to be reduced by dividing the numerator by the denominator.
\[\frac9{20}+\frac{15}{20}=\;\frac{9+15}{20}=\frac{24}{20}=\frac65=1\frac15\]
Math tutors for 6th grade working at Mathema will help the student understand fractions. Follow the link and book your first diagnostic lesson.
How to add fractions with different denominators:
To add fractions with different denominators, first find their common denominator. The common denominator is the least common multiple of both numbers, i.e., the number that is divisible by both numbers without a remainder. For example, for 10 and 5, the least common multiple will be 10: 10÷10 = 1, 10÷5 = 2.
Then you need to find additional multipliers for the numerator and denominator. An additional multiplier is formed when the common denominator is divided by the denominators of the first and second fractions. Consider the calculation:
\[\frac7{10}+\frac58\]- Find the least common denominator. It is 40, which is divisible by 10 and 8.
- Now find the additional multipliers. Divide 40 by the denominators: 40÷10 = 4 and 40÷8 = 5. Therefore, the additional common multipliers are 4 for the first fraction and 5 for the second fraction.
- Multiply the additional multiplier by the numerator.
\[\frac7{10}+\frac58=\frac{7\times4+5\times5}{40}=\frac{28+25}{40}=\frac{53}{40}=1\frac{13}{40}\]
How to subtract fractions with a common denominator:
If the denominators of the fractions are the same, simply perform the operation on the numerators. The bottom part of the fraction can be left unchanged.
\[\frac{11}{15}-\frac6{15}=\frac{11-6}{15}=\frac5{15}=\frac13\]How to subtract fractions with different denominators:
The principle of subtracting fractions with different denominators is no different from addition. Consider the calculation:
\[\frac7{12}-\frac38\]- Find the common denominator. It is 24.
- Find additional multipliers: 24÷12 = 2, 24÷8 = 3. Therefore, the additional multiplier for the first fraction is 2, and for the second fraction, it is 3.
- Multiply the additional multiplier by the numerators.
How to multiply fractions:
The principle of multiplying fractions does not depend on a common denominator. To perform the operation correctly, simply multiply the numerators and denominators of the fractions, and then reduce them to a simple fraction. Consider the calculation:
\[\frac{12}{25}\times\frac5{18}=\frac{12\times5}{25\times18}=\frac{12\times5}{25\times18}=\frac{2\times1}{3\times3}\;=\frac2{15}\]If there is a whole number before the fraction and it needs to be multiplied by another fraction, this is called an example with mixed numbers. In this case, the mixed number should be written as an improper fraction and then the fractions should be multiplied. Consider the calculation:
\[1\frac13\times\frac13=\frac43\times\frac13=\frac49\]How to divide fractions:
To divide two fractions, replace the division operation between them with multiplication. Remember that this operation is like “turning” the second fraction upside down. This is called the reciprocal. Consider the calculation:
\[\frac23\div\frac45=\frac23\times\frac54=\frac{10}{12}=\frac56\]Fraction Operations Task
Mathema teachers have prepared several examples of fraction operations that are taught in the 6th grade. The answers and solutions are below.
Task 1. Calculate the expression:
\[\frac9{15}-\frac6{15}=\]Task 2. Calculate the expression:
\[\frac47+\frac8{21}=\]Task 3. Calculate the expression:
\[2\frac35\times\frac47\]Task 4. Calculate the expression:
\[1\frac35\div2\frac12=\]
