Fractions and Decimals
Multiply, Divide, Subtract and Add
Multiply, Divide, Subtract and Add
Fractions and decimals are fundamental mathematical concepts that play a crucial role in representing and manipulating parts of a whole or values between whole numbers. Understanding how to perform operations such as addition, subtraction, multiplication, and division with fractions and decimals is essential for solving a wide range of mathematical problems.
Fractions: A fraction is a way of expressing a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). The numerator represents the part we have, and the denominator represents the total number of equal parts that make up a whole. Operations with Fractions:
Addition and Subtraction: To add or subtract fractions, ensure they have a common denominator. Add or subtract the numerators and keep the common denominator.
Example: 2/3 + 1/4 = 8/12 + 3/12 = 11/12 or 3/2 + 4/1 = 12/8
Multiplication: Multiply the numerators together to get the new numerator. Multiply the denominators together to get the new denominator.
Example: 3/5 × 2/3 = 6/15 or 5/3 × 3/2 = 15/6
Division: Invert the second fraction (reciprocal) and then multiply.
Example: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 or 4/3 ÷ 2/1 = 4/3 × 1/2 = 4/6 = 2/3
Decimals: Decimals represent parts of a whole and are based on powers of 10. Each digit in a decimal has a place value, such as units, tenths, hundredths, and so on. Operations with Decimals:
Addition and Subtraction: Align the decimal points and add or subtract as if dealing with whole numbers. Adjust the decimal point in the result accordingly.
Example: 0.6 + 0.25 = 0.85 0.6+0.25 = 0.85
Multiplication: Multiply as if dealing with whole numbers. Count the total decimal places in the factors and place the decimal point in the result accordingly.
Example: 1.5 × 0.2 = 0.3 1.5×0.2=0.3
Division: Divide as if dealing with whole numbers. Count the total decimal places in the dividend and divisor and place the decimal point in the quotient accordingly.
Example: 2.4 ÷ 0.6 = 4 2.4÷0.6=4 Understanding the principles of
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