Curriculum Outcomes
Number: Develop number sense. 3. Demonstrate an understanding of rational numbers by: • comparing and ordering rational numbers • solving problems that involve arithmetic operations on rational numbers. [C, CN, PS, R, T, V] [ICT: P2–3.4] 4. Explain and apply the order of operations, including exponents, with and without technology. [PS, T] [ICT: P2–3.4] 5. Determine the square root of positive rational numbers that are perfect squares. [C, CN, PS, R, T] [ICT: P2–3.4] 6. Determine an approximate square root of positive rational numbers that are non-perfect squares. [C, CN, PS, R, T] |
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Things You Need to Know
- All real numbers can be categorized in the following ways:
- Natural numbers: these are the "counting numbers". 1, 2, 3, 4, ....
- Whole numbers: same as natural numbers, but 0 is included, too.
- Integers: ..., -3, -2, -1, 0, 1 , 2, 3, ....
- Rational numbers: any number that can be expressed as a fraction with integers as the numerator/denominator
- These can take the shape of decimals, fractions, or mixed numbers. For decimals, if the decimal ends, or continues infinitely in a repeating pattern, then you know it is a rational number.
- Irrational numbers: any non-repeating and non-terminating decimal number that can't be expressed as an fraction using integers (the most famous irrational number is pi).
- Order of Operations:
- BEDMAS
- Brackets
- Exponents
- Division and Multiplication (same step)
- Addition and Subtraction (same step)
- BEDMAS
- Multiplying/Dividing Integers:
- Same sign = positive answer.
- Different sign = negative answer.
- Adding Integers:
- Same sign = add normally (if both positive, positive answer. If both negative, negative answer)
- Different sign:
- Put the "bigger" number in front.
- Subtract the numbers, pretending both are positive.
- The sign of the answer is the sign of that "bigger" number.
- Subtracting Integers:
- Change the - to a + and then change the sign of the second number.
- Then follow the addition steps.
- Multiplying Rational Numbers (Decimals)
- Line the numbers up on the right (don't line up decimals).
- Perform long multiplication, ignoring the decimals.
- Put the decimal in the answer the number of places from the right equal to the total number of decimal places the numbers you were multiplying had.
- Dividing Rational Numbers (Decimals)
- Change the number you're dividing by to a whole number.
- Move the decimal in the number that's being divided over the same number of places.
- Do long division as usual.
- Change the number you're dividing by to a whole number.
- Multiplying Fractions
- Multiply the numerators together and multiply the denominators together.
- Multiply the numerators together and multiply the denominators together.
- Dividing Fractions
- Change the division to a multiplication, and take the reciprocal of the second fraction (i.e. flip the second fraction upside down).
- Do multiplication of fractions as usual.
- Change the division to a multiplication, and take the reciprocal of the second fraction (i.e. flip the second fraction upside down).
- Adding/Subtracting Fractions
- Ensure both fractions have the same denominator by multiplying the numerator/denominator of each fraction by the other fraction's denominator.
- Once they have the same denominator, add/subtract the numerators as usual.
- Ensure both fractions have the same denominator by multiplying the numerator/denominator of each fraction by the other fraction's denominator.