In this Grade 9 Saxon Algebra 1 lesson from Chapter 3, students learn to solve decimal equations using two methods: multiplying each term by a power of 10 to convert decimals to integers, and applying inverse operations directly using the Subtraction and Division Properties of Equality. Students also practice finding decimal parts of numbers and setting up equations from real-world contexts, such as a zoology word problem involving linear relationships.
Section 1
📘 Solving Decimal Equations
Algebra is the study of mathematical symbols and the rules for manipulating them. Its central goal is solving equations to find an unknown value, turning real-world questions into solvable puzzles.
Now, let's apply these powerful algebraic principles. We'll dive into specific strategies for solving decimal equations through worked examples and real-world applications.
Section 2
Clearing Decimals With Powers Of 10
To write decimals as integers, multiply the entire equation by a power of 10. Hint: Multiply by a power of 10 that will make the decimal with the most decimal places an integer, for example .
Decimal points slowing you down? Just zap them! By multiplying every single term in an equation by a power of 10 (like 100 or 1000), you can magically turn all those tricky decimals into friendly whole numbers. This makes solving the equation much easier, so you can avoid messy decimal calculations and get to the answer faster.
Section 3
Solving Decimal Equations Directly
A decimal equation can also be solved by using inverse operations without multiplying by a power of 10 first.
If you're comfortable with decimals, you don't have to clear them. You can solve the equation directly using the same inverse operations you already know, like subtracting a decimal from both sides or dividing by a decimal. It’s the same process as with integers; you just need to be extra careful where that decimal point lands in your final answer!
Section 4
Finding a Part of a Number
Finding a decimal part of a number is the same as finding a fraction or percent of a number. The word 'of' means to multiply.
Whenever you spot the word 'of' between two numbers, it’s a secret code that means 'multiply!' This little trick helps you translate word problems into math equations. So, when a question asks for ' of ', you can immediately rewrite it as an equation like and solve for the answer.
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Section 1
📘 Solving Decimal Equations
Algebra is the study of mathematical symbols and the rules for manipulating them. Its central goal is solving equations to find an unknown value, turning real-world questions into solvable puzzles.
Now, let's apply these powerful algebraic principles. We'll dive into specific strategies for solving decimal equations through worked examples and real-world applications.
Section 2
Clearing Decimals With Powers Of 10
To write decimals as integers, multiply the entire equation by a power of 10. Hint: Multiply by a power of 10 that will make the decimal with the most decimal places an integer, for example .
Decimal points slowing you down? Just zap them! By multiplying every single term in an equation by a power of 10 (like 100 or 1000), you can magically turn all those tricky decimals into friendly whole numbers. This makes solving the equation much easier, so you can avoid messy decimal calculations and get to the answer faster.
Section 3
Solving Decimal Equations Directly
A decimal equation can also be solved by using inverse operations without multiplying by a power of 10 first.
If you're comfortable with decimals, you don't have to clear them. You can solve the equation directly using the same inverse operations you already know, like subtracting a decimal from both sides or dividing by a decimal. It’s the same process as with integers; you just need to be extra careful where that decimal point lands in your final answer!
Section 4
Finding a Part of a Number
Finding a decimal part of a number is the same as finding a fraction or percent of a number. The word 'of' means to multiply.
Whenever you spot the word 'of' between two numbers, it’s a secret code that means 'multiply!' This little trick helps you translate word problems into math equations. So, when a question asks for ' of ', you can immediately rewrite it as an equation like and solve for the answer.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter