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Math for Grade 5
1 Number Sense
1-1 Place Value
1-1 1 Understanding place value up to millions
1-1 2 Reading and writing numbers in standard and expanded form
1-1 3 Comparing and ordering numbers
1-2 Rounding
1-2 1 Rounding numbers to the nearest 10, 100, and 1000
1-2 2 Estimating sums and differences
1-3 Number Patterns
1-3 1 Identifying and extending number patterns
1-3 2 Using patterns to solve problems
2 Operations
2-1 Addition and Subtraction
2-1 1 Adding and subtracting multi-digit numbers
2-1 2 Solving word problems involving addition and subtraction
2-2 Multiplication
2-2 1 Multiplication facts up to 12x12
2-2 2 Multiplying multi-digit numbers by one-digit numbers
2-2 3 Multiplying multi-digit numbers by two-digit numbers
2-2 4 Solving word problems involving multiplication
2-3 Division
2-3 1 Division facts up to 12x12
2-3 2 Dividing multi-digit numbers by one-digit numbers
2-3 3 Dividing multi-digit numbers by two-digit numbers
2-3 4 Solving word problems involving division
2-4 Order of Operations
2-4 1 Understanding and applying the order of operations (PEMDAS)
2-4 2 Solving problems with multiple operations
3 Fractions
3-1 Understanding Fractions
3-1 1 Identifying parts of a whole and parts of a set
3-1 2 Equivalent fractions
3-1 3 Comparing and ordering fractions
3-2 Operations with Fractions
3-2 1 Adding and subtracting fractions with like denominators
3-2 2 Adding and subtracting fractions with unlike denominators
3-2 3 Multiplying fractions by whole numbers
3-2 4 Solving word problems involving fractions
4 Decimals
4-1 Understanding Decimals
4-1 1 Reading and writing decimals
4-1 2 Comparing and ordering decimals
4-1 3 Converting between fractions and decimals
4-2 Operations with Decimals
4-2 1 Adding and subtracting decimals
4-2 2 Multiplying decimals
4-2 3 Dividing decimals
4-2 4 Solving word problems involving decimals
5 Measurement
5-1 Units of Measurement
5-1 1 Understanding customary and metric units of length, weight, and capacity
5-1 2 Converting between units of measurement
5-2 Time
5-2 1 Telling time to the minute
5-2 2 Calculating elapsed time
5-2 3 Solving word problems involving time
5-3 Area and Perimeter
5-3 1 Finding the area and perimeter of rectangles and squares
5-3 2 Solving word problems involving area and perimeter
6 Geometry
6-1 Shapes
6-1 1 Identifying and classifying 2D shapes (triangles, quadrilaterals, etc )
6-1 2 Identifying and classifying 3D shapes (cubes, pyramids, etc )
6-2 Angles
6-2 1 Identifying and measuring angles
6-2 2 Classifying angles as acute, obtuse, right, or straight
6-3 Symmetry
6-3 1 Identifying lines of symmetry
6-3 2 Creating symmetrical shapes
7 Data and Probability
7-1 Data Representation
7-1 1 Reading and interpreting bar graphs, line graphs, and pie charts
7-1 2 Creating graphs to represent data
7-2 Probability
7-2 1 Understanding probability as a measure of likelihood
7-2 2 Predicting outcomes based on probability
7-2 3 Solving simple probability problems
Dividing Decimals Explained

Dividing Decimals Explained

Key Concepts

1. **Understanding Division**: Division is the process of splitting a number into equal parts. When dividing decimals, the goal is to find how many times one number (the divisor) can fit into another (the dividend).

2. **Moving the Decimal Point**: To make division easier, you can move the decimal point in both the divisor and the dividend the same number of places to the right, turning the divisor into a whole number.

3. **Long Division with Decimals**: Once the divisor is a whole number, you can use the long division method to find the quotient.

4. **Placing the Decimal Point in the Quotient**: The decimal point in the quotient should be placed directly above the decimal point in the dividend.

Detailed Explanation

Understanding Division

Division involves finding how many times one number (divisor) can fit into another (dividend). For example, dividing 6.4 by 2 means finding how many times 2 can fit into 6.4.

Moving the Decimal Point

To simplify division, move the decimal point in both the divisor and the dividend the same number of places to the right. For example, to divide 6.4 by 0.2, move the decimal point one place to the right in both numbers, turning it into 64 divided by 2.

Long Division with Decimals

Once the divisor is a whole number, use the long division method. For example, to divide 64 by 2:

  1. Divide 6 by 2 to get 3.
  2. Bring down the next digit (4) and divide 4 by 2 to get 2.
  3. The quotient is 32.

Placing the Decimal Point in the Quotient

When dividing decimals, the decimal point in the quotient should be placed directly above the decimal point in the dividend. For example, in 6.4 divided by 0.2, the quotient is 32.0, with the decimal point directly above the one in the dividend.

Examples

Example 1: Dividing Decimals

Divide 4.8 by 0.4:

Step 1: Move the decimal point one place to the right in both numbers (48 divided by 4).

Step 2: Perform long division: 48 ÷ 4 = 12.

Final Answer: 12.

Example 2: Long Division with Decimals

Divide 7.2 by 0.6:

Step 1: Move the decimal point one place to the right in both numbers (72 divided by 6).

Step 2: Perform long division: 72 ÷ 6 = 12.

Final Answer: 12.

Analogies

Think of dividing decimals as sharing a large number of items equally among a smaller group. For example, dividing 4.8 liters of water among 0.4 people is like sharing 48 liters among 4 people, which results in each person getting 12 liters.

Practical Application

Understanding how to divide decimals is essential for various real-life tasks such as:

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