Math Problem Statement

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Various math problems including algebraic equations, percentage calculations, sequence identification, and logic puzzles.

Solution

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Problem 1:

22÷2×312÷3×2=?22 \div 2 \times 3 - 12 \div 3 \times 2 = ?

Solution: We solve this using the order of operations (BODMAS/PEMDAS):

  • First, division and multiplication from left to right.

22÷2=11,12÷3=422 \div 2 = 11, \quad 12 \div 3 = 4 So, we now have: 11×34×211 \times 3 - 4 \times 2 Next, solve multiplication: 11×3=33,4×2=811 \times 3 = 33, \quad 4 \times 2 = 8 Now subtract: 338=2533 - 8 = 25 Thus, the answer is 25.


Problem 2:

(a) How many degrees is 25%25 \% of 360°360 \degree?

Solution: 25%×360=25100×360=90°25\% \times 360 = \frac{25}{100} \times 360 = 90 \degree Thus, the answer is 90 degrees.

(b) What is 0.4×0.050.4 \times 0.05?

Solution: 0.4×0.05=0.020.4 \times 0.05 = 0.02 Thus, the answer is 0.02.


Problem 3:

Find the third term of the sequence 1,3,9,11,131, 3, 9, 11, 13.

Solution: The third term is simply 9.


Problem 4:

Calculate 6x=2x×7x6^x = 2^x \times 7^x, solve for xx.

Solution: We simplify the equation: 6x=(2×7)x6^x = (2 \times 7)^x This implies 6x=14x6^x = 14^x, which is only possible if x=0x = 0.

Thus, the answer is x = 0.


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Math Problem Analysis

Mathematical Concepts

Order of Operations (BODMAS)
Percentage Calculations
Multiplication of Decimals
Arithmetic Sequences
Basic Algebra

Formulas

BODMAS: Brackets, Order, Division, Multiplication, Addition, Subtraction
Percentage Formula: (part/whole) * 100
Basic Multiplication: a * b
Arithmetic Sequence: a_n = a_1 + (n-1)d

Theorems

Order of Operations
Rules of Arithmetic Sequences
Exponent Laws

Suitable Grade Level

Grade 8-10