Unit 1 review
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This document reviews key concepts from Unit 1 including: adding, subtracting, multiplying, and dividing integers; order of operations with expressions containing multiple operations; evaluating expressions by substituting values for variables; combining like terms using the distributive property; and determining if proportions are true or false and solving proportions. It provides examples of each concept to practice, with expressions containing integers, variables, operations, and evaluating expressions by substituting numeric values for variables.
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Solving by factoring remediation notes
Here are the key steps to factoring when a ≠ 1:
1. Check for GCF. If there is a GCF, factor it out.
2. If no GCF, find two numbers whose product is ac and sum is b. These will be the coefficients of the factors.
3. Split the middle term into two terms using the factors.
4. Factor using the box method, finding the GCF of each row and column.
Some examples:
2x2 + 11x + 5
ac = 10, factors are 2, 5
(2x + 1)(x + 5)
3x2 - 5x - 2
ac = -
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2) Simplifying rational expressions by factoring numerators and denominators and cancelling common factors.
3) Multiplying, dividing, adding, and subtracting rational expressions by finding common denominators.
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3) Divide the factored numerator and denominator, simplifying the expression.
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Solving by factoring remediation notes
Here are the key steps to factoring when a ≠ 1:
1. Check for GCF. If there is a GCF, factor it out.
2. If no GCF, find two numbers whose product is ac and sum is b. These will be the coefficients of the factors.
3. Split the middle term into two terms using the factors.
4. Factor using the box method, finding the GCF of each row and column.
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3x2 - 5x - 2
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This document provides examples of how to solve one-step equations by adding, subtracting, multiplying, and dividing. It includes 3 examples for each operation: adding by isolating the variable term on one side of the equation and adding its opposite to both sides; subtracting by isolating the variable term and subtracting its opposite from both sides; multiplying by isolating the variable term and dividing both sides by its coefficient; and dividing by isolating the variable term and multiplying both sides by the reciprocal of its coefficient.
Solving equations
This document discusses solving two-step equations and provides examples of solving equations such as 2x + 1 = 4, X - 2 = 3 + 3, X + 2x = 6, and -x + 4 = 10. The solutions to these example equations are provided as x = 3/2, x = 8, x = 2, and x = -6, respectively.
Ratio powerpoint
The document discusses ratios and provides examples using Lucky Charms cereal. It states there are 287 marshmallow pieces and 2,583 oat pieces in one box of Lucky Charms. This ratio of marshmallows to oats can be written in three ways: as a fraction, using the word "to", or using a colon. The document also discusses writing ratios in simplest form and explaining their meanings.
Ratio slideshow
The document discusses ratios and how to express them in different formats. Ratios can be expressed using a colon, "to", or as a fraction. They can compare parts to parts (part-to-part ratios) or parts to the whole (part-to-whole ratios). Examples are given of simplifying ratios by finding the greatest common factor and converting ratios to their simplest form.
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