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Questions and Answers
What is the decimal equivalent of the fraction 3/4?
0.75
How is the fraction 1/3 of a pizza with six slices expressed as a decimal?
0.333
What does the decimal 0.666 represent in the ratio 2 : 3?
2
Explain the relationship between fractions, ratios, and decimals.
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How can decimals be used to compare quantities similar to ratios?
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Study Notes
Fractions, Ratios, Decimals
Fractions, ratios, and decimals are essential concepts in mathematics used to describe quantities and relationships between them. In this article, we will explore these three related mathematical ideas.
Fractions
A fraction is a way of expressing parts of a whole that are equal. For example, if a pizza is divided into six parts, and we eat three of those pieces, the fraction to describe this would be 3/6, which can also be written as 1/2. Fractions have two main components: the top number, called the numerator, and the bottom number, called the denominator. The denominator represents the total number of equal parts, while the numerator tells how many of those parts you want. For instance, when dividing a pizza into four equal slices, one slice is 1/4 of the whole pizza.
Ratios
A ratio compares quantities by measuring how many units there are for every unit of another quantity. Ratios use symbols with a colon, such as "2 : 3" or "4 / 5," indicating how many times one value appears compared to another value. For example, if your brother is 3 inches shorter than you, and he weighs half your weight, you could say he is "3 inches : 1 inch" tall and "half : 1" weight. Ratios are often used to compare related quantities that have different units of measurement.
Decimals
Decimals represent fractions just like fractions do, but they use digits instead of lines and numbers over lines. For example, the fraction 3/4 can also be written as the decimal 0.75. In this case, the whole number part is 0, while the fraction part is 0.75, which tells you how many parts out of ten there are remaining after the whole number part has been removed.
For instance, if you eat one-third (1/3) of a pizza with six slices (or 1/6 of a pizza with four slices), you would write it as the decimal 0.333, meaning three-thirds of the pizza. The same idea applies when comparing ratios using decimals; for example, "2 : 3" is equivalent to "0.666 : 1.000".
In summary, fractions, ratios, and decimals are closely related mathematical concepts. Fractions describe parts of a whole, while ratios compare quantities using the same units of measurement. Decimals represent fractions numerically and can be used to compare quantities in the same way as ratios.
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Description
Explore the fundamental concepts of fractions, ratios, and decimals in mathematics. Learn how fractions represent parts of a whole, ratios compare quantities, and decimals numerically represent fractions. Discover the relationships between these mathematical ideas.
