Тема: Правильні та неправильні дроби. Мішані числа
In this lesson we will learn about mixed numbers, proper and improper
fractions.
Mixed Numbers and Improper Fractions
A mixed number is a combination of a
whole number and a fraction. For example, if you have two whole apples and one
half apple, you could describe this as 2 + 1/2 apples, or 21/2 apples.
Writing Mixed Numbers as Fractions
This mixed number can also be expressed
as a fraction. Each whole apple contains two half apples. Your two whole apples
are also four half apples. Four half apples plus one half apple is five half
apples. So you have 5/2 apples.
To put this other way: to turn a
mixed number into a fraction, multiply the whole number by the denominator (the
bottom part), and add the result to the numerator (the top part).
21/2 = ?
Multiply the whole number by the
denominator.
The whole number is 2.
The denominator is 2.
2 x 2 = 4.
Add the result to the numerator:
The numerator is 1.
4 + 1 = 5
The numerator is 5. The denominator
remains 2.
21/2 = 5/2
Let's try another example:
52/3 = ?
Multiply the whole number by the
denominator.
The whole number is 5.
The denominator is 3.
5 x 3 = 15.
Add the result to the numerator:
The numerator is 2.
15 + 2 = 17
The numerator is 17. The
denominator remains 3.
52/3 = 17/3
Proper and Improper Fractions
A fraction in which the
numerator is smaller than the denominator, like 1/3 or 2/5 is called a proper
fraction. A fraction in which the numerator is larger than or equal to the
denominator, like 5/2, 17/3, or 6/6 is called an improper fraction. (To put it
another way, a fraction with a value less than 1 is a proper fraction. A
fraction with a value greater than or equal to 1 is an improper fraction.)
As we have shown above, mixed
numbers can be written as improper fractions. Similarly, improper fractions can
be written as mixed numbers.
Writing Improper Fractions as Mixed Numbers
To write an improper fraction as
a mixed number, divide the numerator (top part) by the denominator (bottom
part). The quotient is the whole number, and the remainder is the numerator.
How would you express 17/4 as a mixed number?
Divide the numerator by the
denominator:
17 ÷ 4 = 4, with a remainder of 1
The quotient, 4, is the whole
number. The remainder, 1, is the numerator. The denominator remains 4.
17/4 = 41/4
Let's try another couple of examples:
14/9 = ?
Divide the numerator by the
denominator:
14 ÷ 9 = 1, with a remainder of 5
The quotient, 1, is the whole
number. The remainder, 5, is the numerator. The denominator remains 9.
14/9 = 15/9
If there is no remainder, just take
the quotient as the whole number:
20/5 = ?
Divide the numerator by the
denominator:
20 ÷ 5 = 4
The quotient, 4, is the whole
number. There is no remainder.
20/5 = 4
Follow the link and review the theory: https://www.ipracticemath.com/learn/fraction/fractions_proper_improper_and_mixed_numbers
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