Math Problem Statement

What is place value? Write the number 2,348 in expanded form (break down the value of each digit).

What is commutative property of multiplication? Give me one example. If you multiply 18 × 6, then add 12, what’s the result? a) 24 cookies are shared equally among 6 children. How many cookies does each child get?

b) If the time is 3:30 PM now, what will the time be 2 hours later? a) Define what a fraction is and what the numerator and denominator represent.

b) A square has 4 equal sides. If one side is 5 cm, what is the total length of all the sides (perimeter) of the square?

a) If you go to bed at 8:00 PM and wake up at 6:30 AM, how many hours did you sleep?

b) Subtract 12 from the product of 4 × 5. What do you get? make another 3 sets of question like above

Solution

Explanation of Place Value

Place value refers to the value of each digit in a number based on its position. In the number 2,348:

  • The digit 2 is in the thousands place, so its value is 2,000.
  • The digit 3 is in the hundreds place, so its value is 300.
  • The digit 4 is in the tens place, so its value is 40.
  • The digit 8 is in the ones place, so its value is 8.

Expanded Form of 2,348

The number 2,348 can be written in expanded form as: 2,348=2,000+300+40+82,348 = 2,000 + 300 + 40 + 8

Commutative Property of Multiplication

The commutative property of multiplication states that changing the order of the factors does not change the product. In other words, for any two numbers aa and bb: a×b=b×aa \times b = b \times a Example: 4×5=5×4=204 \times 5 = 5 \times 4 = 20

Multiplication and Addition

If you multiply 18×618 \times 6 and then add 12: 18×6=10818 \times 6 = 108 108+12=120108 + 12 = 120

Questions:

  1. a) Division Problem: 24 cookies are shared equally among 6 children. How many cookies does each child get? 246=4 cookies per child\frac{24}{6} = 4 \text{ cookies per child}

b) Time Addition: If the time is 3:30 PM now, what will the time be 2 hours later? 3:30PM+2hours=5:30PM3:30 \, \text{PM} + 2 \, \text{hours} = 5:30 \, \text{PM}

Fraction Definition

A fraction represents a part of a whole. It has two parts:

  • The numerator (top number) represents how many parts we have.
  • The denominator (bottom number) represents the total number of equal parts the whole is divided into.

Square and Perimeter

A square has 4 equal sides. If one side is 5 cm, the total length of all sides (perimeter) is: Perimeter=4×5=20cm\text{Perimeter} = 4 \times 5 = 20 \, \text{cm}

Sleeping Hours Calculation

If you go to bed at 8:00 PM and wake up at 6:30 AM, the number of hours slept is: 8:00PMto6:30AM=10hours and30minutes8:00 \, \text{PM} \, \text{to} \, 6:30 \, \text{AM} = 10 \, \text{hours and} \, 30 \, \text{minutes}

Subtraction and Multiplication Problem

Subtract 12 from the product of 4×54 \times 5: 4×5=204 \times 5 = 20 2012=820 - 12 = 8

Additional Problem Sets

  1. a) A pizza is cut into 8 equal slices. If you eat 3 slices, what fraction of the pizza did you eat?

b) You have 5 dimes. How much money do you have in total?

  1. a) If a rectangle has a length of 7 cm and a width of 3 cm, what is its area?

b) What is the result of subtracting 15 from the sum of 9+129 + 12?

  1. a) If you walk at a speed of 4 km/h for 3 hours, how far will you have walked?

b) What is 25% of 80?

Tip:

When working with fractions, always remember that the denominator represents the number of equal parts the whole is divided into, while the numerator tells you how many of those parts you're focusing on.

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Math Problem Analysis

Mathematical Concepts

Place Value
Expanded Form
Commutative Property of Multiplication
Division
Time Calculation
Fractions
Perimeter
Multiplication
Subtraction

Formulas

Expanded form: 2,000 + 300 + 40 + 8
Commutative Property: a × b = b × a
Perimeter of a Square: P = 4 × side
Product and Subtraction: (4 × 5) - 12

Theorems

Commutative Property of Multiplication

Suitable Grade Level

Grades 4-6