Chapter 3: Q16. (page 108)

For each exercise, write the equation you think should come next. Check your prediction with a calculator.
$\begin{array}{l} 9 \times 9 + 7 = 88 \\ 98 \times 9 + 6 = 888 \\ 987 \times 9 + 5 = 8888 \end{array}$

Short Answer

Expert verified

The next equation must be $9876 \times 9 + 4 = 88888$ .

Step by step solution

Step 1. Define deductive and inductive reasoning.

Deductive reasoning is conclusions based on accepted statements like a theorem, postulate, facts etc.

Inductive reasoning is conclusions based on several past observations.

Step 2. Look for a pattern.

While looking for a pattern in the sequence

$\begin{array}{l} 9 \times 9 + 7 = 88 \\ 98 \times 9 + 6 = 888 \\ 987 \times 9 + 5 = 8888 \end{array}$

reason inductively that is., we can conclude based on past observations

As,

$\begin{array}{r} 9 \to 98 \to 987 \\ 7 \overset{- 1}{\to} 6 \overset{- 1}{\to} 5 \\ 88 \to 888 \to 8888 \end{array}$

And 9 is fixed.

Step 3. Predict the next equation.

So, as per the pattern of the sequence, next terms in the equation will be:

$\begin{array}{r} 9 \to 98 \to 987 \to \underline{9876} \\ 7 \overset{- 1}{\to} 6 \overset{- 1}{\to} 5 \overset{- 1}{\to} \underline{4} \\ 88 \to 888 \to 8888 \to \underline{88888} \end{array}$

Therefore, the next equation must be $9876 \times 9 + 4 = 88888$ .

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For each exercise, write the equation you think should come next. Check your prediction with a calculator.
$\begin{array}{l} 9 \times 9 + 7 = 88 \\ 98 \times 9 + 6 = 888 \\ 987 \times 9 + 5 = 8888 \end{array}$

Short Answer

Step by step solution

Step 1. Define deductive and inductive reasoning.

Step 2. Look for a pattern.

Step 3. Predict the next equation.

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For each exercise, write the equation you think should come next. Check your prediction with a calculator.9×9+7=8898×9+6=888987×9+5=8888

Short Answer

Step by step solution

Step 1. Define deductive and inductive reasoning.

Step 2. Look for a pattern.

Step 3. Predict the next equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Discrete Mathematics

Theoretical and Mathematical Physics

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

For each exercise, write the equation you think should come next. Check your prediction with a calculator.
$\begin{array}{l} 9 \times 9 + 7 = 88 \\ 98 \times 9 + 6 = 888 \\ 987 \times 9 + 5 = 8888 \end{array}$