Division with Remainder (Math 4)
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This document contains several math word problems and division problems with remainders. It asks the reader to find quotients, determine how many books or tickets are left over after equal distribution, and identify whether sample division equations with remainders are correct or incorrect.
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1) The document discusses ordering decimals from least to greatest using place value and number lines. It provides examples of ordering prices from a McDonald's menu and test scores.
2) Equivalent decimals have the same value even if they have a different number of decimal places. Annexing zeros by adding trailing zeros does not change a decimal's value.
3) To order decimals from least to greatest, decimals are first lined up and zeros are annexed to give each number the same number of decimal places. Then the decimals are compared using place value starting from the left.
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The document contains a list of numerical values expressed using different place value names such as thousandths, tenths, hundreths, and ten thousandths. The values range from single digit numbers like 2 to longer decimals like 29.0075 expressed in different place value notations.
Equivalent Fractions
Equivalent Fractions have the same value, even though they may look different.
You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.
You only multiply or divide, never add or subtract, to get an equivalent fraction.
Only divide when the top and bottom stay as whole numbers.
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The document reviews place value and place names for decimal numbers. It discusses how to read and write numbers with decimals, such as four and five tenths or five and sixty-seven hundredths. It has students practice comparing the value of decimal numbers, such as determining whether 0.3 or 0.03 is greater, by representing them with place value counters on a place value chart.
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This document provides steps for adding fractions with unlike denominators:
1) Find equivalent fractions with a common denominator
2) Add the numerators and use the sum as the new numerator
3) Keep the common denominator as the denominator
4) Simplify the resulting fraction if possible by reducing to lowest terms
Worked examples demonstrate applying the steps to add several pairs of fractions.
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1. The document explains the steps for long division with a 2 digit divisor through an example of dividing 418 by 21.
2. It breaks down the process into 5 steps - dividing, multiplying, subtracting, bringing down remaining digits, and repeating the steps or noting the remainder.
3. Following these steps, the example divides 418 by 21 and gets a quotient of 20 with a remainder of 3.
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Here are the steps to round each number as indicated in Exercise 3.2 on pages 105 and 106:
a. 4.231 to 2 decimal places is 4.23
b. 0.75 to 1 decimal place is 0.8
c. 2.076 to 2 decimal places is 2.08
d. 0.698 to 2 decimal places is 0.70
e. 23.357 to 1 decimal place is 23.4
f. 48.6929 to 3 decimal places is 48.693
g. 639.678 to the nearest hundred is 640
h. 12.364 to the nearest ten is 12.4
i. 95.89 to the nearest ten is 100
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This document provides instructions for comparing and ordering fractions using different methods:
- Drawing a picture or using the "butterfly" method to compare fractions less than, greater than, or equal to each other
- Finding the least common denominator (LCD) to order fractions from least to greatest, which involves expressing the fractions with the same denominator and then comparing their numerators
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This document provides instructions for comparing and ordering decimals. It explains how to:
1) Compare decimals by lining up the decimal points, finding the first differing digit, comparing that digit, and using <, >, or =.
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The document discusses comparing and ordering decimals. It explains that decimals can be compared using the symbols > or <, and that annexing zeros to the right of a decimal does not change its value, which is useful for ordering decimals from least to greatest. As an example, it lists the decimals 14.95, 15, 15.01, and 15.8 in order from least to greatest. It also provides additional decimal comparisons to use >, <, or = symbols.
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Dividing Decimals
This document discusses dividing decimals by whole numbers and decimals. It provides examples of dividing decimals by 1-digit and 2-digit whole numbers. Key steps include estimating the quotient, placing the decimal point in the quotient, and annexing zeros if needed. Examples are also given for dividing by decimals, which involves multiplying the divisor and dividend by the same power of 10 to clear the decimal. The document concludes with practice problems for the reader.
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1) The document provides instructions for rounding numbers to the nearest ten or hundred using a memorization poem.
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3) Examples show using the poem to round 978 to the nearest ten (980) and 327 to the nearest hundred (300).
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Division is one of the four basic mathematical operations. It involves splitting a number, called the dividend, into equal groups or parts using another number, called the divisor, to find the quotient. There are two forms of writing division - horizontal uses the division symbol ÷, while vertical stacks the dividend above the divisor with the answer below. Division is the opposite of multiplication, so if you know a multiplication fact you can derive the corresponding division fact.
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The document contains a list of numerical values expressed using different place value names such as thousandths, tenths, hundreths, and ten thousandths. The values range from single digit numbers like 2 to longer decimals like 29.0075 expressed in different place value notations.
Equivalent Fractions
Equivalent Fractions have the same value, even though they may look different.
You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.
You only multiply or divide, never add or subtract, to get an equivalent fraction.
Only divide when the top and bottom stay as whole numbers.
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The document reviews place value and place names for decimal numbers. It discusses how to read and write numbers with decimals, such as four and five tenths or five and sixty-seven hundredths. It has students practice comparing the value of decimal numbers, such as determining whether 0.3 or 0.03 is greater, by representing them with place value counters on a place value chart.
Add Fractions With Unlike Denominators
This document provides steps for adding fractions with unlike denominators:
1) Find equivalent fractions with a common denominator
2) Add the numerators and use the sum as the new numerator
3) Keep the common denominator as the denominator
4) Simplify the resulting fraction if possible by reducing to lowest terms
Worked examples demonstrate applying the steps to add several pairs of fractions.
Two-Digit Division
1. The document explains the steps for long division with a 2 digit divisor through an example of dividing 418 by 21.
2. It breaks down the process into 5 steps - dividing, multiplying, subtracting, bringing down remaining digits, and repeating the steps or noting the remainder.
3. Following these steps, the example divides 418 by 21 and gets a quotient of 20 with a remainder of 3.
Rounding Decimal Numbers
Here are the steps to round each number as indicated in Exercise 3.2 on pages 105 and 106:
a. 4.231 to 2 decimal places is 4.23
b. 0.75 to 1 decimal place is 0.8
c. 2.076 to 2 decimal places is 2.08
d. 0.698 to 2 decimal places is 0.70
e. 23.357 to 1 decimal place is 23.4
f. 48.6929 to 3 decimal places is 48.693
g. 639.678 to the nearest hundred is 640
h. 12.364 to the nearest ten is 12.4
i. 95.89 to the nearest ten is 100
j.
Multiplication
The document discusses learning multiplication facts through daily practice. It explains that multiplication is the process of adding equal sets or groups together. It provides examples of multiplying numbers like 2 x 3 and 3 x 2 by representing the numbers as groups of objects and counting the total objects. The document also demonstrates how to multiply two-digit numbers by multiplying the digits in the ones and tens places and regrouping or carrying numbers to the next place value.
2.1 comparing & ordering fractions
This document provides instructions for comparing and ordering fractions using different methods:
- Drawing a picture or using the "butterfly" method to compare fractions less than, greater than, or equal to each other
- Finding the least common denominator (LCD) to order fractions from least to greatest, which involves expressing the fractions with the same denominator and then comparing their numerators
- Using the LCD method involves finding the lowest common multiple of the denominators as the LCD, writing the fractions with this equivalent denominator, and then ordering the fractions by comparing their numerators from greatest to least
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This document provides instructions for comparing and ordering decimals. It explains how to:
1) Compare decimals by lining up the decimal points, finding the first differing digit, comparing that digit, and using <, >, or =.
2) Order decimals from least to greatest by lining up decimal points, annexing zeros, and comparing place values.
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Worked examples and practice problems are provided to demonstrate comparing and ordering decimals.
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This document discusses multiplying numbers by multiples of 10 and 100. It explains that to multiply a number by 10, you write down the number and add a zero, and to multiply by 100 you write down the number and add two zeros. It then provides examples of multiplying various numbers by 10, 100, 1000, and 10,000. It emphasizes that when multiplying numbers with zeros, you first multiply the digits ignoring the zeros, then add the appropriate number of zeros based on how many are in the original numbers.
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This document contains notes and instructions for dividing decimals. It includes:
1. A review of vocabulary terms like quotient, dividend and divisor.
2. Steps for dividing decimals that include placing the decimal point in the quotient directly above the decimal point in the dividend and dividing as with whole numbers.
3. Examples of dividing decimals with answers and worked out steps shown.
Comparing and ordering decimals
The document discusses comparing and ordering decimals. It explains that decimals can be compared using the symbols > or <, and that annexing zeros to the right of a decimal does not change its value, which is useful for ordering decimals from least to greatest. As an example, it lists the decimals 14.95, 15, 15.01, and 15.8 in order from least to greatest. It also provides additional decimal comparisons to use >, <, or = symbols.
Multiplying by two-and three times one-digit
The document provides step-by-step instructions for multiplying two- and three-digit numbers by a one-digit number. It explains that the process involves multiplying the ones place values first, carrying values to the next place if needed, and then multiplying each subsequent place value while accounting for any carried values. Two examples are shown working through multiplying 45 by 5 and 364 by 4 to arrive at the final answers of 225 and 1,456 respectively.
Dividing Decimals
This document discusses dividing decimals by whole numbers and decimals. It provides examples of dividing decimals by 1-digit and 2-digit whole numbers. Key steps include estimating the quotient, placing the decimal point in the quotient, and annexing zeros if needed. Examples are also given for dividing by decimals, which involves multiplying the divisor and dividend by the same power of 10 to clear the decimal. The document concludes with practice problems for the reader.
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1) The document provides instructions for rounding numbers to the nearest ten or hundred using a memorization poem.
2) The poem states to find the number, look at the digit in the place value being rounded to, and if it is 4 or less ignore it but if 5 or more add 1 to the preceding digit.
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The document discusses decimals and their relationship to fractions. It explains that decimals extend the place value system to include values less than one. The value of each place decreases by a factor of ten as you move to the right of the decimal point. Decimals can be added, subtracted, multiplied and divided using standard algorithms. Terminating decimals can be converted to fractions by writing the decimal as the numerator over an appropriate power of ten as the denominator. Repeating decimals can be converted to fractions by writing the repeating portion as the numerator over nines and zeros in the denominator.
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centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
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help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
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- 2. What is 32 divided by 4?
- 3. What number is half of 20?
- 4. What number will you multiply by 5 to get 50?
- 5. What number will you multiply to 8 to get 16?
- 6. What number will you divide by 10 to get 10?
- 7. What is 0 divided 6?
- 10. It is an excess or a leftover when a number is divided by another number.
- 11. Ana and Elsa helped each other put 167 books on different shelves. After putting the same number of books on 4 shelves, there was some book left. How many books were left?
- 12. There were 356 books distributed to everybody in our class. If each in our class received 8 books, how many learners were there in our class? How many books were left after the distribution?
- 13. At our school fair, 500 tickets are for sale to 8 Grade 4 sections. How many tickets will each section buy if they will get the same number of tickets? How many tickets will be left unsold?
- 14. Let’s Practice
- 15. Find the quotients using division with remainder.
- 16. 715 ÷ 9
- 17. 485 ÷ 45
- 18. 2 194 ÷ 19
- 19. Stand UP & face the monitor if the equation is correct. Stand Up & face at the back if the equation is incorrect.
- 20. 401 ÷ 9 = 44 r. 4 1 44 r. 5
- 21. 695 ÷ 8 = 86 r. 7 2
- 22. 2511 ÷ 32 = 78 r. 15 3
- 23. 7112 ÷ 34 = 209 r. 7 4 209 r. 6