Pre-Algebra - Ch. 7.4 Extension Repeating Decimals Page 316-317

Mathematical Equivalence

ON

Mathematical Equivalence

ON

Mathematical Equivalence

ON

Mathematical Equivalence

ON

Problem #5

STRUCTURE: In Example 1, why can you subtract the original equation from the new equation after multiplying by 10? Explain why these two steps are performed.

• Multiply by 10 so that when you add the original equation, the repeating part is removed.

• Multiply by 10 so that when you subtract the original equation, the repeating part is removed.

Problem #5

STRUCTURE: In Example 1, why can you subtract the original equation from the new equation after multiplying by 10? Explain why these two steps are performed.

• Because the solution does not change when adding/subtracting two equivalent equations.

• Because the solution does change when adding/subtracting two equivalent equations.

Problem #6

REPEATED REASONING: Compare the repeating decimals and their equivalent fractions in Exercises 1-4. Describe the pattern.

• In Exercises 1-4, the common pattern was the denominator of 9.

• In Exercises 1-4, the common pattern was the numerator of 9.

Problem #6

REPEATED REASONING: Compare the repeating decimals and their equivalent fractions in Exercises 1-4. Describe the pattern. Use the pattern to explain how to write a repeating decimal as a fraction when only the tenths digit repeats.

• Write the digit that repeats in the denominator and use 9 in the numerator.

• Write the digit that repeats in the numerator and use 9 in the denominator.

Mathematical Equivalence

ON

Mathematical Equivalence

ON