Math Problem Statement

Complete each ratio table by filling in the missing values.

Solution

Let's go through the ratio tables one by one and fill in the missing values.

Table 1:

  • The ratio pattern is increasing by a factor of 3.
  • First column: 1361 \to 3 \to 6.
  • Second column: 39183 \to 9 \to 18.
  • Since 1 multiplied by 3 gives 3, and 3 multiplied by 3 gives 9, we expect 6×3=186 \times 3 = 18. So, the missing value in the last box of the first column is 6.

Table 2:

  • The ratio pattern shows an increase by a factor of 3.
  • First row: 11335416211 \to 33 \to 54 \to 162.
  • Second row: 61830426 \to 18 \to 30 \to 42.
  • The missing value in the third box is already filled as 54.

Table 3:

  • The ratio seems to involve multiplication by a factor of 5.
  • First row: 2135missing21 \to 35 \to \text{missing}.
  • Second row: 840728 \to 40 \to 72.
  • Let's find the missing value: 35÷5=735 \div 5 = 7, and similarly 8×9=728 \times 9 = 72, so 8×5=408 \times 5 = 40.
  • The missing value would be the one corresponding to 35×2=7035 \times 2 = 70.

Table 4:

  • Incomplete, seems to follow the ratio rule of 2.
  • First row: 3912missing3 \to 9 \to 12 \to \text{missing}.
  • Second row: (7 \to 14 \to \textul.... %@helpers

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Multiplication Patterns

Formulas

a / b = c / d
Ratio scaling

Theorems

Proportionality Theorem
Multiplication Factor Rule

Suitable Grade Level

Grades 5-6