Math Problem Statement

Solve the given exercises including geometry, division, arithmetic sequences, mixed fractions multiplication, multiples, and factors.

Solution

I see the image you've uploaded contains several math exercises in Arabic, ranging from geometry to arithmetic and fractions. I will help solve the exercises and provide clear explanations.

Here's a breakdown of the tasks and solutions:


1. Geometry:

  • The first two diagrams ask for completing the shapes based on given dimensions:
    • (a) Triangle Construction:

      • Given: BAC=50\angle BAC = 50^\circ, AC=1.5cmAC = 1.5 \, \text{cm}, AB=2cmAB = 2 \, \text{cm}.
      • Task: Draw the triangle following these conditions.
    • (b) Rectangle Construction:

      • Given: Width =5cm= 5 \, \text{cm}.
      • Task: Complete the rectangle on the graph paper.

2. Division Problem:

  • Complete the division 61.5÷561.5 \div 5.
    • Solution: 61.5÷5=12.361.5 \div 5 = 12.3.

3. Arithmetic Sequences:

  • Find the median (middle) of these numbers: 45.5,46.3,45.7,46.05,46.2345.5, 46.3, 45.7, 46.05, 46.23.
    • Solution: Arrange them in increasing order: 45.5,45.7,46.05,46.23,46.345.5, 45.7, 46.05, 46.23, 46.3.
    • Median =46.05= 46.05 (the middle value).

4. Mixed Fractions Multiplication:

  • The question asks to write the product of 13×23\frac{1}{3} \times \frac{2}{3} and 23×43\frac{2}{3} \times \frac{4}{3}.
    • Solution: 13×23=29,23×43=89\frac{1}{3} \times \frac{2}{3} = \frac{2}{9}, \quad \frac{2}{3} \times \frac{4}{3} = \frac{8}{9}

5. Multiples and Factors:

  • Find multiples of 7 between 20 and 45:

    • Multiples: 21,28,35,4221, 28, 35, 42.
  • Find the divisors of 18:

    • Divisors: 1,2,3,6,9,181, 2, 3, 6, 9, 18.

Would you like a detailed explanation for any specific problem? Here are some related questions you can explore:

  1. How can I construct a triangle using specific angle and side measurements?
  2. What is the median, and how do we calculate it for a set of numbers?
  3. What is the process for dividing decimals manually?
  4. How do you multiply mixed fractions and simplify the results?
  5. How do you identify multiples and divisors of a number?

Tip: To find the median of any set of numbers, first arrange them in increasing order, then choose the middle value. If there are two middle values, take their average.

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Math Problem Analysis

Mathematical Concepts

Geometry
Division
Arithmetic Sequences
Fractions Multiplication
Multiples
Factors

Formulas

Area of a rectangle: A = length × width
Division: dividend ÷ divisor = quotient
Finding the median: arrange numbers in ascending order and select the middle value
Multiplication of fractions: (a/b) × (c/d) = (a×c)/(b×d)

Theorems

Median calculation theorem
Properties of multiplication and division of fractions

Suitable Grade Level

Grades 5-7