https://file.aiquickdraw.com/mathbot/file/1725985089247pwhaz5kv.jpg

Let's work through the questions on the provided image:

1. **(a) Workout \(28 - 16 \div 2\):**

   According to the order of operations (BIDMAS/BODMAS):
   \[
   28 - 16 \div 2 = 28 - 8 = 20
   \]
   **Answer: 20**

2. **(b) Find the reciprocal of \(\frac{4}{5}\):**

   The reciprocal of a fraction is obtained by flipping the numerator and denominator.
   \[
   \text{Reciprocal of } \frac{4}{5} = \frac{5}{4}
   \]
   **Answer: \(\frac{5}{4}\)**

3. **(c) A square number greater than 10:**

   The square numbers are \(1, 4, 9, 16, 25, \dots\). The first square number greater than 10 is 16.
   **Answer: 16**

4. **Factorize \(3x^2 - 7xy\):**

   Factor out the common factor \(x\):
   \[
   3x^2 - 7xy = x(3x - 7y)
   \]
   **Answer: \(x(3x - 7y)\)**

5. **The temperature on Monday is \(-27^\circ C\). The temperature on Tuesday is \(15^\circ C\) higher than on Monday. Work out the temperature on Tuesday.**

   Add 15 to \(-27\):
   \[
   \text{Temperature on Tuesday} = -27^\circ C + 15^\circ C = -12^\circ C
   \]
   **Answer: \(-12^\circ C\)**

6. **(a) Find the value of \(13^9\):**

   \(13^9\) is a large number, so it’s usually calculated using a calculator:
   \[
   13^9 = 106,044,993,730,963
   \]
   **Answer: 106,044,993,730,963**

7. **(b) Simplify \(56^{12} = 7^?\):**

   Express \(56\) as a power of 7:
   \[
   56 = 7 \times 8
   \]
   Simplifying further requires additional steps and is typically more complex than directly simplified forms. Let's focus on powers and conversions.

   Since \(56^{12}\) isn't directly expressible in simpler terms as \(7^?\), this might require interpretation or rechecking.

   **Answer:** (Typically \(7^x\) can't simplify in this way. Needs re-examination.)

8. **Write the number 31,072,000 in words:**

   The number 31,072,000 in words is:
   **Answer: Thirty-one million seventy-two thousand**

---

If you need more details on any specific step, or have any questions, feel free to ask!

### Related Questions:
1. How do you determine the order of operations in mathematical expressions?
2. What is the importance of finding reciprocals in mathematics?
3. Can you list more examples of square numbers?
4. How do you factorize polynomials with more complex terms?
5. How would you calculate very large powers like \(13^9\) by hand or calculator?

**Tip:** Remember to always follow the order of operations (BIDMAS/BODMAS) when solving arithmetic problems!

Solve the following math problems:
(a) Workout 28 - 16 ÷ 2
(b) Find the reciprocal of 4/5
(c) Find a square number greater than 10
Factorize 3x^2 - 7xy
Find the temperature on Tuesday if Monday is -27°C and Tuesday is 15°C higher
Find the value of 13^9
Simplify 56^12 = 7^?
Write the number 31,072,000 in words.

Learn how to solve arithmetic expressions with BIDMAS, find reciprocals, identify square numbers, factorize expressions, and calculate powers. This guide walks through key concepts like 28 - 16 ÷ 2, the reciprocal of 4/5, and factorizing 3x^2 - 7xy. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation