Math Problem Statement

Evaluate the following expressions: -5 × (-2.4), -7.4 ÷ 10, (-4/7) ÷ (-2), 4 × (-3/8).

Solution

Let's evaluate each expression step by step:

  1. First expression: 5×(2.4)-5 \times (-2.4) Multiplying two negative numbers results in a positive number: 5×(2.4)=12-5 \times (-2.4) = 12

  2. Second expression: 7.4÷10-7.4 \div 10 Dividing a negative number by a positive number results in a negative number: 7.4÷10=0.74-7.4 \div 10 = -0.74

  3. Third expression: 47÷(2)\frac{-4}{7} \div (-2) Dividing two negative numbers results in a positive result. First, rewrite the division as multiplication by the reciprocal: 47×12=414=27\frac{-4}{7} \times \frac{-1}{2} = \frac{4}{14} = \frac{2}{7}

  4. Fourth expression: 4×(38)4 \times \left(-\frac{3}{8}\right) Multiplying a positive number by a negative fraction results in a negative value: 4×(38)=128=1.54 \times \left(-\frac{3}{8}\right) = -\frac{12}{8} = -1.5

The final results for each expression are:

  1. 1212
  2. 0.74-0.74
  3. 27\frac{2}{7}
  4. 1.5-1.5

Would you like any more details on these steps, or do you have any questions?

Here are 5 related questions:

  1. What happens when you multiply a positive number by a negative number?
  2. How do you divide fractions, and why is the reciprocal used?
  3. What is the result of dividing a number by 10?
  4. Why does the product of two negative numbers result in a positive number?
  5. Can you convert a decimal into a fraction?

Tip: When dividing fractions, always remember to multiply by the reciprocal of the divisor.

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Math Problem Analysis

Mathematical Concepts

Multiplication
Division
Fractions
Positive and Negative Numbers

Formulas

Multiplication of numbers: a × b
Division of numbers: a ÷ b
Reciprocal of a fraction: 1/a

Theorems

The product of two negative numbers is positive
Dividing by a fraction is equivalent to multiplying by the reciprocal

Suitable Grade Level

Grades 6-8