Multiplying and dividing fractions
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To multiply fractions, multiply the top numbers together and the bottom numbers together, cancelling common factors if possible. To divide fractions, flip the second fraction upside down, change the division sign to multiplication, and then multiply the tops and bottoms together. The document provides instructions for multiplying and dividing fractions by explaining the rules to multiply the numerators and denominators, and to flip the second fraction when dividing.
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2) Key steps for adding fractions include finding a common denominator and then adding the numerators. For subtraction, the steps are the same but taking away the second numerator from the first.
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Operations with rational numbers
This document discusses rational numbers and different types of fractions including mixed numbers, improper fractions, adding, subtracting, multiplying, and dividing fractions. It explains that rational numbers are numbers that can be made by dividing one integer by another. Fractions have a numerator and denominator and can be added or subtracted by finding a common denominator. To multiply fractions, you multiply the numerators and denominators. To divide fractions, you keep the first fraction the same, change the operation to divide, and flip the second fraction to its inverse.
Jason Solves Inequalities
The document provides step-by-step instructions for solving different types of inequalities involving multiplication, division, addition, and subtraction. It explains that to isolate the variable, the same steps are followed as with equations but the sign of the inequality must be preserved. Examples shown include subtracting, dividing, and multiplying both sides of the inequality as needed to isolate the variable.
Chapter 3. linear equation and linear equalities in one variables
Here are the steps to solve this inequality problem:
1) Write an expression for the perimeter in terms of x
2) Set the perimeter expression ≤ 40
3) Isolate x by undoing the operations
4) Write the solution set
The solution is 0 ≤ x ≤ 7
Converting Improper Fraction to Mixed Number
Improper fractions have a numerator that is greater than or equal to the denominator and can be converted to mixed numbers. To do so, divide the numerator by the denominator and write the whole number result with the remainder over the denominator. For example, an improper fraction of 15/4 would convert to a mixed number of 3 7/4 by dividing 15 by 4 to get 3 with a remainder of 3, written with the 3 and remainder over the original denominator.
Chapter 6 pharmacy calculation
The document provides an outline of topics covered in Chapter 6 of The Pharmacy Technician 4E including basic pharmaceutical measurements, calculations, and conversions. Key areas discussed include numbers, fractions, decimals, ratios, proportions, percents, and metric and household conversions. Examples are provided for calculating common denominators, multiplying fractions, setting up and solving proportions, and converting between ratios, percents, and fractions.
Cross Reducing
This document describes a shortcut method called cross-division for simplifying fractions. The method involves dividing the numerator and denominator of a fraction by common factors across the multiplication problem, rather than multiplying fully first. Two examples are provided where the fractions 15/10 and 6/2 are simplified using this cross-division approach.
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Multiplying and dividing fractions
- 1. Multiplying and Dividing Fractions
- 2. You may like to take some notes!
- 3. Multiplying fractions is the easy one! x
- 4. Because you just multiply the top numbers together and multiply the bottom numbers together x
- 5. Because you just multiply the top numbers together and multiply the bottom numbers together x =
- 6. Because you just multiply the top numbers together and multiply the bottom numbers together x =
- 7. Don’t forget to cancel down. In this case we can divide both numbers by 6 x =
- 8. Don’t forget to cancel down. In this case we can divide both numbers by 6 x =
- 9. Don’t forget to cancel down. In this case we can divide both numbers by 6 x =
- 11. The rule is
- 12. Turn the SECOND fraction upside down
- 13. Turn the SECOND fraction upside down
- 14. and change the divide sign to a multiply
- 16. then multiply the top numbers together
- 17. then multiply the top numbers together and multiply the bottom numbers together
- 18. and multiply the bottom numbers together
- 19. and that’s it for multiplying and dividing fractions