Calculate a fraction from a number. To find a fraction of a number, the rule is

Mathematics is the queen of sciences. Her greatness is limitless, and her strength is great. All other sciences are based on mathematical results. Be it physics, chemistry, biology, and even philology.

Just as a house is made of bricks, every task has small subtasks. And by learning to solve small ones, you can learn to solve more complex problems.

Today we will look at how to find fractions. The concept of a fraction originated in Ancient Greece, after the Greeks introduced the concept of length, equivalent to integers. Next, a concept was needed that expresses part of the length, for example, half, one third of the length. This is how the concept of a fraction appeared.

The set of rational numbers Q is a set of numbers represented in the form m/n, where m, n are integers. The number m/n is called an ordinary fraction, where m is the numerator and n is the denominator, n≠0.

If n=〖10〗^k, k=1,2,.. , then such a fraction is called a decimal and is written as 0,0..0m, and the number of zeros after the decimal point is k-1.

A number is called composite if it has divisors other than 1 and itself.

Basic Operations

We will move from simple to complex, showing with examples exactly how certain operations are performed.

How to reduce a fraction

To do this, you need to factor the numerator and denominator into simple factors, if they are composite. And then, if these prime factors coincide, then remove them.

If there are no prime factors, the fraction is called irreducible. For example, 85/65=(17*5)/(13*5)=17/13

How to find a fraction from a number

Let the number be a certain length. And a fraction is essentially a part of this length, which means to find the integer part you need to multiply the fraction by the number. For example, 2/3 of 27=27*2/3=27/3*2=18

How to find a fraction from a fraction

It's essentially a simple multiplication process; to find a fraction from a fraction, you just multiply the 2 fractions together. For example, 2/3 and 13/17: 2/3*13/17=26/51

Division of fractions

When dividing fractions a/b,c/d, the divisor c/d can be represented as d/c and multiplied, and then reduced. For example, 27/17?9/34=27/17*34/9=2*3=6.

It is also necessary to remember that when solving complex examples, it is necessary to come up with a solution algorithm. You may have to change division to multiplication with a change in fraction; it is possible to perform multiplication and division by the same number. Such fairly simple instructions will help in solving examples.

Let's take a classic word problem as an example. From a warehouse in which there were 150 tons of fuel oil, 2/3 was stolen. The stolen parts were distributed in parts in the ratio of 5/17 and 12/17, the last one was taken for processing. The remaining fuel oil in the warehouse was taken for processing. How much fuel oil was processed?

150*2/3*12/17+150*(1-2/3)=150*41/51

Fraction problems are the basis of school arithmetic. They are not inherently difficult, but require perseverance and attentiveness to complete. If these conditions are met, the result will not take long to arrive.

For solutions of this assignment, let’s remember what a fraction of a number is equal to and use an example to show how to find a fraction of a number.

Finding a fraction from a number

Fractions in mathematics are used to denote part of a quantity. This value is the whole number from which the part was taken. Knowing what a whole quantity is equal to, you can find its part. In order to find a fraction, that is, a part of a number, you need to multiply this number by this fraction.

Finding a fraction from a number using an example

Problem: There are 30 students in the class. 1/3 of all students are girls. Calculate the number of girls in the class.

In this problem, the integer value is the number of students in the class - 30, and the fraction, that is, the part - 1/3. In order to calculate the number of girls in a class, we must multiply the fraction 1/3 by the total value - 30.

30 * 1/3 = 30/1 * 1/3 = 30 * 1 / 1 * 3 = 30 / 3 = 10 students.

To multiply a whole number by a fraction:

• represent an integer as a fraction (30 = 30/1).
• Multiply the numerator of the first fraction by the numerator of the second fraction.
• multiply the denominator of the first fraction by the denominator of the second fraction.
• Write the first product in the numerator of the new fraction, and the second in the denominator.

The rule for finding a number by its fraction:

To find a number from a given value of its fraction, you need to divide this value by the fraction.

Let's look at how to find a number by its fraction, using specific examples.

Examples.

1) Find a number whose 3/4 are equal to 12.

To find a number by its fraction, divide the number by that fraction. To do this, you need to multiply this number by the inverse of the fraction (that is, by an inverted fraction). To do this, you need to multiply the numerator by this number and leave the denominator unchanged. 12 and 3 by 3. Since we got one in the denominator, the answer is an integer.

2) Find a number if 9/10 of it equals 3/5.

To find a number given the value of its fraction, divide this value by this fraction. To divide a fraction by a fraction, multiply the first fraction by the inverse of the second (inverted). To multiply a fraction by a fraction, multiply the numerator by the numerator, and the denominator by the denominator. We reduce 10 and 5 by 5, 3 and 9 by 3. As a result, we get the correct irreducible fraction, which means this is the final result.

3) Find a number whose 9/7 are equal

To find a number by the value of its fraction, divide that value by that fraction. Mixed number and multiply it by the inverse of the second number (inverted fraction). We reduce 99 and 9 by 9, 7 and 14 by 7. Since we received an improper fraction, we need to separate the whole part from it.