Respuesta :
Answer:
[tex]\frac{21}{8}=2\frac{5}{8}[/tex]
Decimal result:
[tex]2.625[/tex]
Step-by-step explanation:
Method: Operations with fractions
1. Simplify the expression
[tex]33/8+-3/2[/tex]
Find the lowest common denominator:
[tex]\frac{33}{8}+\frac{\left(-3\cdot 4\right)}{\left(2\cdot 4\right)}[/tex]
Multiply the denominators:
[tex]\frac{33}{8}+\frac{\left(-3\cdot 4\right)}{8}[/tex]
Multiply the numerators:
[tex]\frac{33}{8}+\frac{-12}{8}[/tex]
Combine the fractions:
[tex]\frac{\left(33+-12\right)}{8}[/tex]
Combine the numerators:
[tex]\frac{21}{8}[/tex]
21/8 in mixed number form is equal to 2 5/8.
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Why learn this:
Let's say you invite ten friends over for movie night and order four pizzas to split. How do you divide the pizza evenly so everyone gets the same amount of pizza? If each section of the couch can fit 1+1/5 people, how many sections would there need to be to accommodate all of your friends? The whole world is made up of little bits and pieces that are part of something larger, and the key to understanding them is fractions.
Fractions are the mathematical representation of any whole thing that is made up of multiple parts. Knowing how to manipulate them using operations like addition, subtraction, multiplication, and division is one of the most widely applicable math skills in everyday situations and provides an important foundation for other math concepts you will encounter.
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Terms and topics
- Operations with fractions
A fraction represents a smaller part of a whole and is usually written as a numerator, which represents the smaller part, written over a denominator, which represents the whole. To express the fraction as a single number, the quotient, we divide the numerator by the denominator.
There are three main kinds of fractions:
Proper fractions
- The numerator is smaller than the denominator.
Improper fractions
- The numerator is larger than the denominator.
Mixed fractions
- A whole number combined with a proper fraction
It is important to note that improper fractions and mixed fractions can be used to express the same values.
When doing operations with fractions, it is usually easier to first convert any integers and/or mixed fractions into improper fractions:
To convert an integer into an improper fraction, simply place the integer over 1.
To convert a mixed fraction into an improper fraction, multiply the denominator (bottom number) by the whole number (number in front or to the left of the fraction), add the product to the numerator (top number), and write the sum over the original numerator.
Adding and subtracting fractions
The general rule for adding fractions is: [tex]\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{bc}{bd}=\frac{ad+bc}{bd}[/tex]
The general rule for subtracting fractions is: [tex]\frac{a}{b}-\frac{c}{d}=\frac{ad}{bd}-\frac{bc}{bd}=\frac{ad-bc}{bd}[/tex]
There are 4 steps to adding and subtracting fractions:
1. Simplify the fractions by reducing them, if possible. Divide the numerator (top number) and the denominator (bottom number) by their greatest common factor (gcf). The gcf of a set of numbers is the highest number that can divide evenly into all numbers in the set with no remainder.
2. Find the fractions' common denominator. There are two ways to find the common denominator:
1. Multiply the top and bottom of each fraction by the denominator of the other fraction.
2. Find the least common denominator. To do this, we find the least common multiple (lcm) of the denominators and use it as the common denominator. There are two ways to find the lcm: listing numbers' multiples (solver coming soon!) and by prime factorization.
3.Add or subtract the numerators. At this point, the fractions should have the same denominator, meaning we can simply add or subtract the numerators and write the result over the denominator we found in the previous steps.
Simplify the resulting fraction by reducing, if possible, as described above in step 1.
Multiplying fractions
The general rule for multiplying fractions is: [tex]\frac{a}{b}*\frac{c}{d}=\frac{a*c}{b*d}[/tex]
There are 4 steps to multiplying fractions:
1. Simplify the fractions by reducing them, if possible. Divide the numerator (top number) and the denominator (bottom number) by their greatest common factor (gcf). The gcf of a set of numbers is the highest number that can divide evenly into all numbers in the set with no remainder.
2. Multiply the numerators (top numbers).
3. Multiply the denominators (bottom numbers).
4. Simplify the resulting fraction by reducing, if possible, as described above in step 1.
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