Math things - Fractions
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This document provides definitions and examples of common math fraction terms including mixed numbers, improper fractions, and the parts of a fraction. Mixed numbers contain both a whole number and a fraction part, while improper fractions have a numerator larger than the denominator. The document explains how to convert a mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator. It also identifies the numerator and denominator as the key parts of any fraction.
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3.1
The document discusses positive and negative numbers on the number line. Positive numbers are to the right of zero, negative numbers are to the left of zero, and together they form the set of integers. Positive and negative numbers are used in everyday contexts like temperature, finances, and elevation. The document provides examples of writing positive and negative numbers for situations involving debt, deposits, elevation relative to sea level, profit, and temperature below zero degrees. Students are assigned practice problems related to comparing and writing positive and negative numbers.
Decimals
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.
Introduction to Fractions
Fractions represent equal parts of a whole or a collection.
Fraction of a whole: When we divide a whole into equal parts, each part is a fraction of the whole.
Proper; Improper & Mixed Number Fractions
This document discusses different types of fractions:
- Proper fractions have a numerator less than the denominator (e.g. 1/4).
- Improper fractions have a numerator greater than or equal to the denominator (e.g. 5/3).
- Mixed numbers are a combination of a whole number and a proper fraction (e.g. 2 1/4).
The document provides examples of converting between improper fractions and mixed numbers by dividing the numerator by the denominator to get the whole number part and remainder.
What is a fraction
A fraction represents an object divided into equal parts, with the numerator indicating how many parts are taken and the denominator indicating the total number of equal parts the whole was divided into. There are different types of fractions such as proper fractions where the numerator is smaller than the denominator, improper fractions where the numerator is greater than or equal to the denominator, and mixed fractions which represent a whole number plus a fraction.
Mixed and improper fraction
An improper fraction has a numerator that is greater than the denominator, while a mixed fraction is similar to an improper fraction where the numerator is divided by the denominator with the remainder written to the left of the fraction bar. Mixed fractions show the whole number part and fractional part of an amount or quantity.
fractions introduction
Fractions represent parts of a whole and can be used to describe amounts. They are not division problems but rather a way to express how much of something is being referred to, such as one slice out of a pizza cut into eight slices being written as 1/8. Proper fractions have a numerator smaller than the denominator, improper fractions have a numerator larger than the denominator, and mixed fractions contain a whole number and a fraction.
Decimalsppt.x
Decimals represent parts of whole numbers and are written with a decimal point separating the whole numbers from the fractional parts. Decimals can be compared by looking at the place values from tenths to thousandths. To multiply decimals, multiply the numbers as whole numbers and place the decimal in the answer by counting the total number of decimal places. To divide decimals, move the decimal points to make the divisor a whole number, then divide as usual and place the decimal in the quotient above the original decimal.
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3.1
The document discusses positive and negative numbers on the number line. Positive numbers are to the right of zero, negative numbers are to the left of zero, and together they form the set of integers. Positive and negative numbers are used in everyday contexts like temperature, finances, and elevation. The document provides examples of writing positive and negative numbers for situations involving debt, deposits, elevation relative to sea level, profit, and temperature below zero degrees. Students are assigned practice problems related to comparing and writing positive and negative numbers.
Decimals
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.
Introduction to Fractions
Fractions represent equal parts of a whole or a collection.
Fraction of a whole: When we divide a whole into equal parts, each part is a fraction of the whole.
Proper; Improper & Mixed Number Fractions
This document discusses different types of fractions:
- Proper fractions have a numerator less than the denominator (e.g. 1/4).
- Improper fractions have a numerator greater than or equal to the denominator (e.g. 5/3).
- Mixed numbers are a combination of a whole number and a proper fraction (e.g. 2 1/4).
The document provides examples of converting between improper fractions and mixed numbers by dividing the numerator by the denominator to get the whole number part and remainder.
What is a fraction
A fraction represents an object divided into equal parts, with the numerator indicating how many parts are taken and the denominator indicating the total number of equal parts the whole was divided into. There are different types of fractions such as proper fractions where the numerator is smaller than the denominator, improper fractions where the numerator is greater than or equal to the denominator, and mixed fractions which represent a whole number plus a fraction.
Mixed and improper fraction
An improper fraction has a numerator that is greater than the denominator, while a mixed fraction is similar to an improper fraction where the numerator is divided by the denominator with the remainder written to the left of the fraction bar. Mixed fractions show the whole number part and fractional part of an amount or quantity.
fractions introduction
Fractions represent parts of a whole and can be used to describe amounts. They are not division problems but rather a way to express how much of something is being referred to, such as one slice out of a pizza cut into eight slices being written as 1/8. Proper fractions have a numerator smaller than the denominator, improper fractions have a numerator larger than the denominator, and mixed fractions contain a whole number and a fraction.
Decimalsppt.x
Decimals represent parts of whole numbers and are written with a decimal point separating the whole numbers from the fractional parts. Decimals can be compared by looking at the place values from tenths to thousandths. To multiply decimals, multiply the numbers as whole numbers and place the decimal in the answer by counting the total number of decimal places. To divide decimals, move the decimal points to make the divisor a whole number, then divide as usual and place the decimal in the quotient above the original decimal.
Mixed Numbers & Equivalent Fractions
The document discusses fractions, including whole numbers, mixed numbers, and improper fractions. It explains that improper fractions are when the numerator is greater than the denominator, such as 7/4. The document provides examples of representing fractional amounts as mixed numbers and improper fractions, such as writing the number of slices in a picture as a mixed number or improper fraction.
Improper and mixed fractions
This document discusses improper and mixed fractions. Improper fractions have a numerator that is larger than the denominator. Mixed fractions are like improper fractions but where the numerator is larger than the denominator, the integer part is written before the fraction, such as 3 1/2 where 3 is the integer part and 1/2 is the fraction. Mixed fractions allow writing an improper fraction as a "normal" fraction by subtracting the denominator from the numerator until it fits in the denominator and writing the amount subtracted as the integer part.
Mathslidecast
This document provides an overview of decimals, including how to read, write, compare, order, add and subtract them. It defines decimals as any number in the base-ten number system that has one or more digits to the right of the decimal point. Decimals are used to provide more precision than whole numbers, such as representing amounts of money between whole dollar amounts. The whole number part of a decimal is to the left of the decimal point, while the fractional part is to the right.
Improper and mixed( fractions )
This document discusses mixed numbers and improper fractions. An improper fraction has a numerator greater than the denominator, while a mixed number is a whole number with a proper fraction. The document provides steps to convert between mixed numbers and improper fractions, such as multiplying the whole number by the denominator and adding it to the numerator to convert a mixed number to an improper fraction.
Fractions keynote for explaining
This document discusses improper fractions and mixed numbers. It defines improper fractions as fractions where the numerator is greater than the denominator. Mixed numbers are defined as numbers with both a whole number and fractional part. It provides instructions for converting between improper fractions and mixed numbers by multiplying or dividing the numerator and denominator.
Understanding Fractions
The document defines fractions and their classifications including proper, improper, and mixed numbers. It explains that a fraction is the quotient of two rational numbers with a numerator and denominator. Proper fractions have a numerator smaller than the denominator, improper fractions have a numerator greater than or equal to the denominator, and mixed numbers contain a whole number and an improper fraction. The document also discusses how to identify equivalent fractions and how to order fractions with the same denominator by comparing their numerators.
Sophie M
The document defines key fraction concepts such as the numerator, denominator, and converting fractions to decimals. It also explains how to perform operations with fractions such as addition, subtraction, multiplication, and division by finding common denominators or converting to improper fractions. Examples are provided to illustrate fraction conversions and the different steps for each mathematical operation.
Nats Decimal Keynote
A decimal is a number written in the base ten system, with a decimal point separating the ones place from the tenths place. Places to the right of the decimal point show parts of a whole, with tenths being the first place and hundredths, thousandths, etc following. When ordering decimals from least to greatest, zeros at the end do not change the value, and the number of digits does not matter - only the first digit in each number is compared. Decimals are rounded the same as whole numbers, rounding up if over 5 and down if under 5. Adding and subtracting decimals involves lining up the decimal points and performing the operation as with whole numbers, while multiplying requires multiplying as usual and placing the decimal point
Micah D
1) A fraction represents a part of a whole or group, with the numerator above the fraction bar indicating the parts and the denominator below indicating the whole.
2) To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a fraction, determine the place value and use that number as the denominator with the original number as the numerator.
3) When adding or subtracting fractions, find a common denominator to convert the fractions before adding or subtracting the numerators and writing the final fraction over the common denominator.
Integers
Integers are whole numbers that can be positive, negative, or zero, but not fractions or decimals. A negative number is less than zero and is represented by a minus sign (-). The number line is used to show integer operations and the relative positions of positive and negative numbers. In the place value system, the value of each digit in a number depends on its place, with ones, tens, hundreds, and so on. Integer rules state that adding or subtracting two numbers of the same sign results in a positive number, while opposite signs can result in a positive or negative number depending on the values.
Subtracting fractions using a number line
To subtract fractions using a number line, first create a number line with appropriate units like the denominator. Then plot the first fraction on the number line. Finally, subtract the fractions by moving to the left on the number line and simplify if needed.
Dylan M
A fraction represents a part of a whole number, with the numerator representing the number of parts and the denominator representing the whole number. To convert a fraction to a decimal, divide the numerator by the denominator. To add or subtract fractions, find a common denominator. When multiplying fractions, multiply the numerators and denominators, and when dividing fractions invert the second fraction and multiply.
Multiplication lesson
This document explains how to multiply fractions. It shows that when multiplying fractions, the sizes of the fractional parts change rather than staying the same size as with addition and subtraction. Examples are provided of multiplying different fractions like 1/2 x 1/2 = 1/4, 1/2 x 3/4 = 3/8, and 2/3 x 4/5 = 8/15. Practice problems are also given for the student to try multiplying different fractions.
KS2 Year 3 equivalent fractions power point
1) This document discusses equivalent fractions, which are fractions that represent the same amount or value even though they are written with different numerators and denominators.
2) It provides examples of how to make fractions equivalent by multiplying both the numerator and denominator by the same number. This keeps the value the same while changing the representation.
3) Students are asked to identify equivalent fractions for various values by applying this rule of multiplying the top and bottom numbers by the same amount.
Fractions
Fractions can represent parts of a whole or multiple units, written as a numerator over a denominator. Equivalent fractions have equal values and can be obtained by multiplying or dividing the numerator and denominator by the same number. To calculate a fraction of a quantity, multiply the quantity by the numerator and divide by the denominator. To add or subtract fractions, find a common denominator and then add or subtract the numerators. To multiply fractions, multiply the numerators and denominators, while to divide fractions invert the divisor and multiply the fractions.
Decimals
This document provides an introduction to decimals for students. It begins with an overview of decimals and then discusses how to write, read, and compare decimal values. Examples are provided such as writing amounts of money in decimal form. The document explains place value of decimals and how to use symbols like tenths, hundredths and thousandths. Students are given opportunities to practice writing, reading and comparing decimal values through interactive exercises.
Bm module lets begin part 2
Decimals represent fractional quantities and are written using a decimal point to separate the integer and fractional parts. The place values after the decimal point are tenths, hundredths, thousandths and so on. Trailing zeros after the decimal do not change a number's value as 3.27, 3.270 and 3.27000 are equivalent. Percents represent the number of parts per hundred and have a percent sign, with the document going on to provide more details on decimals and percents.
Fraction decimal equivalence
1) The document discusses the equivalence and relationships between fractions and decimals. It provides examples of how to convert fractions to decimals by dividing the numerator by the denominator.
2) Key questions are defined for fractions and decimals, with fractions describing parts of a whole using numbers and decimals using numbers and a decimal point.
3) Examples are given of converting common fractions such as 1/2, 1/4, and 1/10 to their decimal equivalents through division.
Decimals To Money Ppt
A decimal represents a part of a whole number, such as fractions of a dollar. Common fractions like quarters and halves can be written as decimals, with a quarter equal to 0.25 and a half equal to 0.50. Fractions have a numerator representing the parts and a denominator representing the whole amount.
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This document discusses improper and mixed fractions. Improper fractions have a numerator that is larger than the denominator. Mixed fractions are like improper fractions but where the numerator is larger than the denominator, the integer part is written before the fraction, such as 3 1/2 where 3 is the integer part and 1/2 is the fraction. Mixed fractions allow writing an improper fraction as a "normal" fraction by subtracting the denominator from the numerator until it fits in the denominator and writing the amount subtracted as the integer part.
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This document discusses mixed numbers and improper fractions. An improper fraction has a numerator greater than the denominator, while a mixed number is a whole number with a proper fraction. The document provides steps to convert between mixed numbers and improper fractions, such as multiplying the whole number by the denominator and adding it to the numerator to convert a mixed number to an improper fraction.
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This document discusses improper fractions and mixed numbers. It defines improper fractions as fractions where the numerator is greater than the denominator. Mixed numbers are defined as numbers with both a whole number and fractional part. It provides instructions for converting between improper fractions and mixed numbers by multiplying or dividing the numerator and denominator.
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The document defines fractions and their classifications including proper, improper, and mixed numbers. It explains that a fraction is the quotient of two rational numbers with a numerator and denominator. Proper fractions have a numerator smaller than the denominator, improper fractions have a numerator greater than or equal to the denominator, and mixed numbers contain a whole number and an improper fraction. The document also discusses how to identify equivalent fractions and how to order fractions with the same denominator by comparing their numerators.
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The document defines key fraction concepts such as the numerator, denominator, and converting fractions to decimals. It also explains how to perform operations with fractions such as addition, subtraction, multiplication, and division by finding common denominators or converting to improper fractions. Examples are provided to illustrate fraction conversions and the different steps for each mathematical operation.
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A decimal is a number written in the base ten system, with a decimal point separating the ones place from the tenths place. Places to the right of the decimal point show parts of a whole, with tenths being the first place and hundredths, thousandths, etc following. When ordering decimals from least to greatest, zeros at the end do not change the value, and the number of digits does not matter - only the first digit in each number is compared. Decimals are rounded the same as whole numbers, rounding up if over 5 and down if under 5. Adding and subtracting decimals involves lining up the decimal points and performing the operation as with whole numbers, while multiplying requires multiplying as usual and placing the decimal point
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1) A fraction represents a part of a whole or group, with the numerator above the fraction bar indicating the parts and the denominator below indicating the whole.
2) To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a fraction, determine the place value and use that number as the denominator with the original number as the numerator.
3) When adding or subtracting fractions, find a common denominator to convert the fractions before adding or subtracting the numerators and writing the final fraction over the common denominator.
Integers
Integers are whole numbers that can be positive, negative, or zero, but not fractions or decimals. A negative number is less than zero and is represented by a minus sign (-). The number line is used to show integer operations and the relative positions of positive and negative numbers. In the place value system, the value of each digit in a number depends on its place, with ones, tens, hundreds, and so on. Integer rules state that adding or subtracting two numbers of the same sign results in a positive number, while opposite signs can result in a positive or negative number depending on the values.
Subtracting fractions using a number line
To subtract fractions using a number line, first create a number line with appropriate units like the denominator. Then plot the first fraction on the number line. Finally, subtract the fractions by moving to the left on the number line and simplify if needed.
Dylan M
A fraction represents a part of a whole number, with the numerator representing the number of parts and the denominator representing the whole number. To convert a fraction to a decimal, divide the numerator by the denominator. To add or subtract fractions, find a common denominator. When multiplying fractions, multiply the numerators and denominators, and when dividing fractions invert the second fraction and multiply.
Multiplication lesson
This document explains how to multiply fractions. It shows that when multiplying fractions, the sizes of the fractional parts change rather than staying the same size as with addition and subtraction. Examples are provided of multiplying different fractions like 1/2 x 1/2 = 1/4, 1/2 x 3/4 = 3/8, and 2/3 x 4/5 = 8/15. Practice problems are also given for the student to try multiplying different fractions.
KS2 Year 3 equivalent fractions power point
1) This document discusses equivalent fractions, which are fractions that represent the same amount or value even though they are written with different numerators and denominators.
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3) Students are asked to identify equivalent fractions for various values by applying this rule of multiplying the top and bottom numbers by the same amount.
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Fractions can represent parts of a whole or multiple units, written as a numerator over a denominator. Equivalent fractions have equal values and can be obtained by multiplying or dividing the numerator and denominator by the same number. To calculate a fraction of a quantity, multiply the quantity by the numerator and divide by the denominator. To add or subtract fractions, find a common denominator and then add or subtract the numerators. To multiply fractions, multiply the numerators and denominators, while to divide fractions invert the divisor and multiply the fractions.
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This document provides an introduction to decimals for students. It begins with an overview of decimals and then discusses how to write, read, and compare decimal values. Examples are provided such as writing amounts of money in decimal form. The document explains place value of decimals and how to use symbols like tenths, hundredths and thousandths. Students are given opportunities to practice writing, reading and comparing decimal values through interactive exercises.
Bm module lets begin part 2
Decimals represent fractional quantities and are written using a decimal point to separate the integer and fractional parts. The place values after the decimal point are tenths, hundredths, thousandths and so on. Trailing zeros after the decimal do not change a number's value as 3.27, 3.270 and 3.27000 are equivalent. Percents represent the number of parts per hundred and have a percent sign, with the document going on to provide more details on decimals and percents.
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1) The document discusses the equivalence and relationships between fractions and decimals. It provides examples of how to convert fractions to decimals by dividing the numerator by the denominator.
2) Key questions are defined for fractions and decimals, with fractions describing parts of a whole using numbers and decimals using numbers and a decimal point.
3) Examples are given of converting common fractions such as 1/2, 1/4, and 1/10 to their decimal equivalents through division.
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A decimal represents a part of a whole number, such as fractions of a dollar. Common fractions like quarters and halves can be written as decimals, with a quarter equal to 0.25 and a half equal to 0.50. Fractions have a numerator representing the parts and a denominator representing the whole amount.
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This document provides an overview of multiplying fractions. It begins with a review of fractions, including the definition of a fraction as part of a whole and the meaning of the numerator and denominator. It then discusses how to multiply fractions by multiplying the numerators and denominators. Multiplying fractions means finding a fraction of a fraction. The document provides examples of multiplying fractions, mixed numbers, and cancelling common factors before multiplying. Students are given practice problems and homework assignments.
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Grace Garcia, her brother Louis, her best friend Caitlin, and Caitlin's dog Diego are kidnapped by a man calling himself The Watcher while visiting a store in Venice, Italy. The Watcher takes them to Rome and then Paris, holding them captive. The children work together to escape, finding food and water with the help of a doe in the forest. They make their way to the police and identify their kidnapper as John Cashy, using details they overheard. Police pursue Cashy and arrest him. The children are reunited with their parents and given a holiday in Paris by the police before returning safely home to Venice.
Monica's Narritave
The twins Paige and Chloe invent a time machine that transports them and their friend Kate to the year 2000. When they arrive, they discover doppelgangers of themselves also living in that time period. They question their doppelgangers but the conversation does not go well. Later, when Paige, Chloe, and Kate return to where they left their time machine, it has vanished, leaving them stranded in 2000.
Infographics 20
A survey of 18 people found that most average 1 conflict per day, with collaborating being the most common way of solving conflicts. Respondents reported having the most conflicts with family members, and said their values mostly come from family. The majority of conflicts revolve around family issues. People tend to look at opposing perspectives in conflicts and strongly agreed that differences in values can cause conflicts handled in various ways.
Clifford
Joe gets in trouble at school for punching another student. He is sent to the principal's office and faces expulsion. No other schools will accept Joe due to his past behavior. Joe eventually enrolls in a small rural school with one teacher, Rob. Rob helps Joe learn to control his emotions. Over time at the new school, Joe's behavior improves and he makes progress in his studies. Joe decides to transfer to a new larger school near his old one, where he is happy to reunite with old friends. However, years later when Joe visits, he discovers that Rob's small rural school has closed down.
Infographics 20
A survey of 18 people found that most have 1 conflict per day, usually with family members. The top ways of resolving conflicts reported were being collaborative (12 people) and compromise (9 people). Most people's values come from their family (15 people) and they reported usually considering the opposing perspective in a conflict. The document concludes that differences in values can cause conflicts, and people agreed that how those conflicts are dealt with can be a choice.
Cuatro Amigos Presentation
Juan, Carlos, Maria, and Anna each have a number between 5 and 15. Using clues about their numbers, the document solves for what each person's number is. Juan's number is 5, Carlos' number is 6, Maria's number is 9, and Anna's number is 18.
Cuatro Amigos Presentation
Juan, Carlos, Maria, and Anna each have a number between 5 and 15. Using clues about their numbers, the document solves for what each person's number is. Juan's number is 5, Carlos' number is 6, Maria's number is 9, and Anna's number is 18.
Cuatro amigos presentation
Juan, Carlos, Maria, and Anna each have a number between 5 and 15. Using clues about their numbers, the document solves for what each person's number is. Juan's number is 5, Carlos' number is 6, Maria's number is 9, and Anna's number is 18.
Pairadice
The document describes a dice game between Muhammed and Aly where Muhammed wins if the first die is a factor of the second, and Aly wins if one die is even and the other is odd. It calculates the chances of each player winning based on the possible die roll combinations, finding Aly has a 36% chance of winning compared to Muhammed's 28% chance, with a 36% chance of a tie. The document concludes the game is unfair and apologizes to Muhammed.
Math investigation
The document discusses a game called Pair-a-Dice where rolling a 1 gives the advantage of automatically winning. It is deemed unfair because no matter the other number rolled, a 1 will always win since 1 is a factor of every other number. A solution is proposed but not described.
Pair-a-dice
Muhammad and Ally are playing a dice game where they each roll a pair of dice. The document lists Muhammad's possible rolls which give him 15 ways to win, while Ally has 18 possible ways to win. It is determined that the game is unfair because Ally has more chances to win than Muhammad.
Math Investigation
The document outlines a multi-step process for determining the distance traveled each day of a 7 day road trip given a total distance of 560 km. It describes calculating the average daily distance of 80 km, then constructing a table showing distances increasing by 15 km each subsequent day from 65 to 125 km to account for the total 560 km traveled over the 7 days.
Road trip key note
The document details a group's weekly road trip over 7 days. Each day they rode 35 km plus additional kilometers, with the total increasing each day. By the 7th day they had ridden a total of 125 km.
Road trip
A group of students investigated how far a rider traveled over 7 days of a road trip. They used a table to calculate the daily and total kilometers ridden, starting with random numbers. After testing different options, they determined the correct amounts were 35, 50, 65, 80, 95, 110, 125 kilometers respectively each day, totaling to 560 kilometers for the trip.
Road trip!
A group of students documented a math problem about determining how far a cyclist rode on the seventh day of a trip based on increasing daily distances that totaled to 560km for the week. They showed the calculation of adding up the increasing daily distances of 35, 50, 65, 80, 95, 110, and 125km to equal the total 560km, determining that the seventh day distance was 125km.
Sweet sixteen plus 1
This document describes a math problem where the authors placed the numbers 0 through 9 in a grid such that the sums of each row and column equaled 17. They presented two possible solutions by rearranging the numbers, such as switching the 1 and 0. The document expresses thanks for solving the "Sweet Sixteen Plus One" problem.
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- 2. Mixed Numbers A mixed number always has to have a whole, and a fraction next to the whole on the right On the left is a example of a Mixed fraction. Same thing as the guide on top.
- 3. Improper Fraction • A improper fraction is when the numerator is bigger than the Denominator On the left is a Improper faction
- 4. How to use a mixed number • Use the denominator to multiple the whole than add the numerator’s number and then you’ll have the fraction.
- 5. Parts of a Faction • These are two things that you should remember from a fraction • A numerator is the number on top of a fraction and a Denominator is the number under the line of a fraction
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