If you forgot how to multiply the fractional numbers with different denominators, what fractions are, then read the article. You will recall the rules for multiplying fractions and some of their properties that were taught at school.
Content
Fractionsthe parts of the whole number are called. They consist of a single share. With fractions, you can perform different actions: divide, multiply, add, subtract. Next, consider the multiplication of fractions with different denominators. We will learn how to multiply simple fractions with the right, wrong, mixed, how to find a work of two, three or more fractions.
Multiplication of fractions with different denominators: types of fractions
The rule of multiplication of fractions with different denominators and the same ones do not vary. The numerators and denominators of fractional numbers change separately from each other. When it is necessary to find a work of mixed fractional numbers, they should first be translated into the wrong ones, and then perform actions with them. Further more about what fractional numbers are.
There are several types of fractional numbers with different denominators:
- Correct- These are the fractional numbers that have less than the denominator.
- The wrong- Those whose denominator is less than the numerator or is equal to him.
- Mixed- Those numbers that have an integer.
Examples:
Correct fractions:2/3, 3/5, 9/8, 11/12, 23/30, 123/145.
Incorrect fractions:12/5, 11/3, 5/5, 34/11, 122/7, 151/76.
Mixed fractions:these are the same irregular fractional numbers with the allocated whole number: 5/5 \u003d 1, 12/5 \u003d 2 2/5; 57/9 \u003d 6 3/9 \u003d 6 1/3.
Multiplication of fractions with different denominators - grade 5
Already from the fifth grade, the school has been studying the multiplication of fractions. It is important at this age not to miss the opportunity to deal with this topic, because in life such knowledge can be useful in reality. It all starts with the examination of the share. Objects are often divided into equal parts, it is they are called shares. Indeed, in practice, it is not always permissible to express the size of objects, the length or volume by an entire number.
The science of fractions first arose in the Arab Emirates. In Russia, they began to study fractions in the eighth century. Previously, mathematicians believed that section: Frops are the most difficult topic. After the first books on arithmetic in the 17th century, the fractional numbers were called - broken.
It was difficult for students to understand the section of fractional numbers, and actions with fractions for a long time considered the most difficult theme of arithmetic. Great mathematician scientists wrote articles to describe actions with fractions as easier. Read the rule of multiplication of fractions with different denominators below and see examples of actions with them:
Rule of multiplication: To multiply fractions with different denominators, you will first change the numbers of fractions, and then denominators. Sometimes it is required to reduce the fractional number in order to make it convenient to make further calculations with it. A clearly example of multiplication is as follows: b/s • d/m \u003d (b • D)/(C • M).
Reducing fractions - means the division of both the numerator and the denominator into a common multiple number, if any. Before starting the division, check whether it is possible to reduce the fractions so to alleviate multiplication. After all, it is much more convenient to change unambiguous or two -digit numbers than bulky three -digit, etc. Below are examples of fractions reduction that are studied in the fifth grade.
Interesting fact: Frops and now remain difficult to understand people with a non -mathematical warehouse of the mind who are prone to the humanities. The Germans came up with their proverb on this subject: he hit the fractions. It means that a person was in a difficult position.
The fractional number reduction occurs due to the property of this fraction.
After the fractional number has been reduced by multiplication of fractions. It is interesting that, in contrast to the addition and subtraction of fractions with different denominators, multiplication and division of fractional numbers is carried out the same with the same denominators, even with different ones. Fractional expressions are not necessary to lead to a common denominator, but just change the upper and lower values \u200b\u200band all.
Multiplication of fractions with different denominators Grade 6 - examples
New topics of multiplication of fractions with different denominators in the sixth grade are studied in sufficient detail. Children are ready to learn how to carry out such actions with fractional numbers. Moreover, they have already learned to reduce them in the fifth grade.
Example: multiplication of fractions with different denominators.
- It should be multiplied by 3/27 by 5/15. To solve, you will first reduce the presented fractional numbers.
- At the output you will turn out: 3/27 \u003d 1/9 (the upper and lower parts of the fraction were divided into three), divide the second shot by: 5, it turns out: 5/15 \u003d 1/3.
- Next, we change the fractions: 1/9 • 1/3 \u003d 1/27.
Result: 1/27.
IMPORTANT: In the event that fractional numbers have a minus in front of brackets, then the finished work will have the same sign as when multiplying ordinary numbers. More precisely, if the minuses are an odd amount in the expression, then the fractional work will have a minus sign.
Multiplication of several fractions with different denominators:
Change three, four, etc. Frops - it will not be difficult if you know all the rules described above. For the convenience of the account, it is allowed to move numerical values \u200b\u200bseparately in the numerator, and separately in the denominator. The resulting numerical values \u200b\u200bin this work will not change. If it is convenient for you, you can put brackets - this can easily easier an account.
In order not to be mistaken in calculations, follow the following rules:
- Describe the numbers in the numerator separately, and separately in the denominator. Look what happens, maybe the fraction can be reduced.
- If large numbers can be divided into multipliers, it is easier to reduce the fraction.
- When you carry out the reduction process, perform the multiplication of fractions at first in the numerator, and then in the denominator.
- The improper fraction obtained as a result, transform into mixed, highlighting the whole number in front of the fraction.
Examples:
- 4/9 • 14/28 • 1/3 \u003d (4 • 14 • 1)/(9 • 28 • 3) \u003d (2 • 1 • 1)/(9 • 1 • 3) \u003d 2/27;
- 25/3 • 21/5 • 4/3 \u003d (25 • 21 • 4)/(3 • 5 • 3) \u003d (5 • 7 • 4)/(1 • 1 • 3) \u003d 140/3 \u003d 46 2 /3.
Explanation to the notes: Three fractions with different denominators were given to us to change them, first, write down for convenience under a common line, all the values \u200b\u200bof numerators in the form of a work of multipliers, and under the line all the numerical values \u200b\u200bof the denominators, if there are common multipliers, reduce the fractions. For example, in the first example fractions were reduced on 14 and 2. More precisely, both the numerator and the denominator of the fraction were divided into these common multiple. As a result, a fractional work came out 2/27.
The second expression was reduced to 5 and 3,the result was the wrong fraction, which was recorded in the form of a mixed fraction: 46 2/3
Multiplication of mixed fractions with different denominators:
As you can see, at first the fraction is translated into the wrong one, after reducing it and the numbers, denominators are reduced and shifted: 3/1 • 16/7 = 48/7. Now it remains to highlight the whole number 6 6/7 - This is the result.
Video: Multiplication of ordinary fractions with different denominators
