Math Problems: Number Systems, Calculations, and Algebra

Published on May 24, 2026

Pre-Algebra

Solve a variety of math problems including number system conversions, arithmetic calculations, algebraic expressions, and ordering numbers.

Question

Answer

Here are the step-by-step solutions to the math problems presented in the image:

1. Write the number name in Hindu-Arabic number system:

In the Indian (Hindu-Arabic) numbering system, commas are placed after the first three digits from the right, and then after every two digits.
  • Number with commas: (Wait, let’s re-group correctly: )
  • Place values:
    • is in the Arab (ten-thousand crore/billion) place? No, let’s use the standard Indian system:
    • Arab, Crore, Lakh, Thousand, .
  • Number Name: Eighty-seven Arab, sixty-four crore, thirty-four lakh, sixty-eight thousand, nine hundred twenty-one.

2. Write the number name in International number system:

In the International system, commas are placed after every three digits from the right.
  • Number with commas:
  • Place values:
    • is in the Billions place.
    • is in the Millions place.
    • is in the Thousands place.
    • is the remainder.
  • Number Name: Fifty-three billion, eight hundred ninety-six million, four hundred sixty thousand, two hundred sixteen.

3. Give three different ways of showing using buttons and .

We need to find combinations of these buttons that sum to .
  • Way 1 (Standard): buttons of , buttons of , and buttons of .
  • Way 2 (Using more tens): buttons of , buttons of , and buttons of .
  • Way 3 (Using more hundreds): buttons of , buttons of , and buttons of .

4. Calculate using quick method:

A quick method is to treat as of .

5. Arrange in descending order of their values:

First, calculate the value of each expression:
Descending order (largest to smallest):

In original form:

6. Find the value:

Follow the order of operations (BODMAS/PEMDAS):
  1. Parentheses first:
  2. Substitute back into expression:
  3. Multiplication:
  4. Addition and Subtraction (left to right):



7. Find the value of when

  1. Substitute into the expression:
  2. Solve inside the parentheses:

  3. Multiply by :