Lattice multiplication
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This document provides examples of multiplying multi-digit numbers. It shows step-by-step workings for 46 x 56, 67 x 48, 435 x 53, 684 x 37 and 4.562 x 3.45. The examples range from multiplying 2-digit by 2-digit numbers to 3-digit by 2-digit and decimal numbers.
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![46 x 56 4 6 2 3 ,[object Object],5 2 0 ,[object Object],0 ,[object Object],3 2 6 ,[object Object],6 4 5 Add each section. 7 6 Answer: 2,576](https://image.slidesharecdn.com/latticemultiplication-101005200141-phpapp01/85/Lattice-multiplication-1-320.jpg)
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The document presents the steps of lattice multiplication to multiply whole numbers, decimals, and polynomials. It begins by explaining that lattice multiplication breaks down the traditional long multiplication method into smaller steps by using a grid. For whole number multiplication, the steps are to draw a grid with rows and columns equal to the number of digits in the factors, write the factors in the grid, multiply pairs of digits and record partial products in the grid, and sum the products along the diagonals. The same process is used for decimal multiplication. For polynomial multiplication, the coefficients of the factors determine the grid size, each term is multiplied out, and the results are combined into a polynomial. Examples are provided to demonstrate the lattice multiplication process.
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The document provides step-by-step instructions for multiplying 356 by 25 using the lattice method. It instructs the reader to make a 2x3 grid, place the numbers in the grid by multiplying vertically, add the diagonals and carry numbers to get the final answer of 8,900.
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I found this on the net and really found it useful This free teaching resource is from Innovative Teaching Resources. You can access hundreds of their excellent resources here. https://www.teacherspayteachers.com/Store/Innovative-Teaching-Ideas
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The document provides step-by-step instructions for performing lattice multiplication with decimals. It demonstrates multiplying 3.42 by 6.9 using a lattice method. The steps include drawing a grid, placing the numbers in the grid with decimals aligned, multiplying the numbers and placing results in the grid, adding the diagonals while carrying numbers, and finally placing the decimal point to get the final answer of 23.598.
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The document provides step-by-step instructions for performing lattice multiplication with decimals. It demonstrates multiplying 3.42 by 6.9 using a lattice method. The steps include drawing a grid, placing the numbers in the grid with decimals aligned, multiplying the numbers and placing results in the grid, adding the diagonals while carrying numbers, and finally placing the decimal point to get the final answer of 23.598.
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Lattice multiplication is a method for multiplying multi-digit numbers by drawing a grid and placing the numbers to be multiplied along the sides. For each box in the grid, the number above is multiplied by the number to the right and the products are written in the boxes. The numbers are then added along the diagonals, with carries as needed, and the final sum is the answer. Two examples of lattice multiplication problems are worked out step-by-step to demonstrate the method.
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The document provides step-by-step instructions for multiplying 356 by 25 using the lattice method. It explains how to set up a 2x3 grid based on the numbers, fill in the grid by multiplying the digits and placing them in the intersecting lines, then adding the diagonals and carrying numbers to get the final solution of 8,900.
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- The ones pattern states that any number multiplied by 1 equals itself.
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I. Objectives:
Cognitive: Order fractions in simple and mixed forms in ascending or ascending order using different methods
Psychomotor: Write in ascending or descending order fractions in simple and mixed forms
Affective: Prepare a budget
II. Learning Content
Skill: Ordering fractions in simple and mixed forms in ascending or descending order using different methods
Reference: BEC PELC G.10
Materials: ICT Integration
III. Learning Experiences:
A. Preparatory Activities
1. Mental Computation
2. Review
(ICT Integration)
3. Motivation
B. Developmental Activities
1. Presentation
(ICT Integration)
2. Fixing Skills
(ICT Integration)
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What are the different ways of ordering fraction?
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2) One trick for multiplying a two-digit number by 11 is to split the number into digits, add the digits, and place the sum in the middle.
3) To divide a number by 27 or 37, split it into triplets from the ones place, sum the triplets, and take the remainder of dividing the sum by 27 or 37.
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This document explains how to multiply two digit numbers using lattice multiplication. Lattice multiplication involves setting up a grid with the digits of the first number written vertically and the second number written horizontally. Each digit is then multiplied together and written in the boxes, with the partial products added down the diagonals. The final answer is obtained by adding across the bottom row and down the left column, ignoring an initial zero if it occurs.
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The document describes the lattice method for multiplying two-digit numbers. It involves creating a grid with the factors along the top and side and filling in the cells by multiplying the corresponding digits and recording the partial products. The digits are then added along the diagonals, including carries to the next diagonal, and the final answer is written. Many students find the lattice method helpful for keeping track of partial products without extra zeros.
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The document discusses integers and rational numbers including:
- All integers are rational numbers because they can be written as fractions.
- Negative numbers are expressed with a negative sign such as -77 feet below sea level.
- When multiplying integers, a positive result occurs with an even number of negatives and a negative result with an odd number.
- Coordinates are plotted on a coordinate plane and basic operations are performed with integers and rational numbers.
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The document defines equivalent fractions as fractions that name the same amount. It then provides examples of equivalent fractions by showing how different fractions can represent the same portion of a whole through operations like multiplying or dividing the numerator and denominator by the same number. The key rule discussed is that to make fractions equivalent, the same operation must be performed on both the numerator and denominator.
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This document discusses comparing and ordering numbers. It explains how to compare numbers by lining them up based on place value and comparing the digits from left to right. Lower digits represent smaller values. It provides examples of comparing standard and word forms of numbers. The document also demonstrates how to order numbers from least to greatest or greatest to least by comparing place values from left to right and arranging the numbers in the appropriate order.
Inverse relationship of addition and subtraction
Addition and subtraction are inverse operations. The inverse of an operation undoes that operation. Specifically:
- Addition is the inverse of subtraction, and subtraction is the inverse of addition. Performing one operation and then its inverse returns to the original number.
- Examples show that equations like 6 - 4 = 2 and 6 = 4 + 2 are equivalent, as are 5 - 3 = 2 and 5 = 3 + 2, because subtraction and addition undo each other.
- Practicing inverse operations on number sentences helps demonstrate that the order of addends doesn't change the sum, so equations like 1 + 4 = 5 and 4 + 1 = 5 are also equivalent.
Simplifying basic radical expressions
This document provides instructions and examples for simplifying radical expressions. It defines a radical as a square root expression. It then provides 5 problems with step-by-step explanations and solutions for simplifying radical expressions by finding perfect squares under the radical signs. The problems cover simplifying radicals of variables, combining like radicals, and simplifying fractional radicals.
Order Of Operations
The document discusses order of operations, which is the order in which mathematical operations should be performed in a problem containing multiple operations. The standard order is: 1) operations within parentheses, 2) exponents, 3) multiplication and division from left to right, 4) addition and subtraction from left to right. It provides examples of solving problems using the proper order of operations and asks readers to try solving sample problems on their own.
Speed mathematics
Speed mathematics provides techniques to solve problems faster without extensive calculation. Some key methods described in the document include:
- Squaring numbers ending in 5 by multiplying the previous digit by one more than itself and adding the product of the last digits.
- Multiplying numbers by 9s or 1s by subtracting or adding to the digits from 9 or 1 respectively and placing the answer left to right.
- Mental calculation techniques like breaking numbers into place values to add, subtract or multiply mentally.
- The criss-cross system to multiply multi-digit numbers by working through place values vertically and cross-wise in steps.
Division
This document provides an explanation of the steps involved in one-digit division. It defines division as splitting into equal parts or groups, and identifies the key parts in a division problem: the dividend, divisor, quotient, and sometimes remainder. The document then outlines the 5 steps to perform one-digit division: 1) divide, 2) multiply, 3) subtract, 4) bring down, 5) repeat or give the remainder. It works through an example problem of 947 divided by 2 to demonstrate how to apply the steps.
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The document provides patterns for learning multiplication facts:
- The zero pattern states that any number multiplied by 0 equals 0.
- The ones pattern states that any number multiplied by 1 equals itself.
- Higher number patterns, such as the twos, fives, nines and sixes patterns, provide steps to derive the answer through doubling, halving, adding or relating the numbers. Knowing these patterns makes learning multiplication facts easier.
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The document provides patterns for learning multiplication facts:
- The zero pattern states that any number multiplied by 0 equals 0.
- The ones pattern states that any number multiplied by 1 equals itself.
- Higher number patterns, like the twos, fives, nines and sixes patterns, provide steps to derive the answer through doubling, halving, adding/subtracting numbers etc. Knowing these patterns makes learning multiplication facts easier.
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The document provides patterns for learning multiplication facts:
- The zero pattern states that any number multiplied by 0 equals 0.
- The ones pattern states that any number multiplied by 1 equals itself.
- Higher number patterns, like the twos, fives, nines and sixes patterns provide steps to derive the answer through doubling, halving, adding/subtracting numbers etc. Learning these patterns makes memorizing multiplication facts easier.
Comparing and ordering whole numbers and decimals
MATHEMATICS VI
I. Objectives:
Cognitive: Order fractions in simple and mixed forms in ascending or ascending order using different methods
Psychomotor: Write in ascending or descending order fractions in simple and mixed forms
Affective: Prepare a budget
II. Learning Content
Skill: Ordering fractions in simple and mixed forms in ascending or descending order using different methods
Reference: BEC PELC G.10
Materials: ICT Integration
III. Learning Experiences:
A. Preparatory Activities
1. Mental Computation
2. Review
(ICT Integration)
3. Motivation
B. Developmental Activities
1. Presentation
(ICT Integration)
2. Fixing Skills
(ICT Integration)
3. Generalization
What are the different ways of ordering fraction?
What should be the basis in ordering fractions in ascending order? Descending order?
4. Application
(ICT Integration)
5. Evaluation
(ICT Integration)
IV. Assignment
(ICT Integration)
Math 'e' Magic
Mathemagic is inspired from Vedic Mathematics and Smart Maths to develope a passion for quantitative section of various entrance exams especially for those who belongs to non mathematic streams.
Maths tricks -1
1) Vedic maths uses tricks and techniques to simplify math and make it more fun.
2) One trick for multiplying a two-digit number by 11 is to split the number into digits, add the digits, and place the sum in the middle.
3) To divide a number by 27 or 37, split it into triplets from the ones place, sum the triplets, and take the remainder of dividing the sum by 27 or 37.
Short Division: 3 Digit by 1 Digit (No Remainder)
The document provides step-by-step instructions for dividing a 3-digit number by a 1-digit number without remainder. It uses the example of dividing 741 by 3. The instructions are to place the larger number inside the division bar and the smaller number outside. Then divide the hundreds, tens, and ones columns sequentially, placing the quotients above and remainders beside the next column. Following these steps, the document arrives at the solution of 741 divided by 3 equals 247.
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- 2. Let’s Try 67 X 48 6 7 2 2 3 4 4 8 5 4 2 8 8 6 1 6
- 3. Let’s Try Without the Colors 2 8 1 4 1 5 0 0 5 1 5 7 4 6 9 6
- 4. 5 4 0 0 1 1 5 4 3 4 0 9 5 6 2 6
- 5. 5 4 0 0 1 1 5 4 3 4 0 9 5 6 2 6
- 6. 5 4 0 0 1 1 5 4 3 4 0 9 5 6 2 6
- 7. 5 4 0 0 1 1 5 4 3 4 0 9 5 6 2 6
- 8. What about 3 Digit by 2 digit? 435 x 53 =
- 9. 4 3 5 1 2 2 2 5 5 0 5 1 1 0 3 3 5 9 2 0 5 5
- 10. 684 x 37 =
- 11. 6 8 4 2 1 1 2 3 2 8 4 4 2 5 7 5 8 6 2 3 8 0
- 12. 4.562 x 3.45 =
- 13. Multiply 4562 x 345 4 5 6 2 1 1 1 0 3 1 2 8 6 5 1 2 2 0 4 5 0 6 4 8 2 2 3 1 7 5 5 0 0 0 3 8 9 0