IntoMath Grade 5 Lessons

In this lesson you will learn about decimals and their properties. A decimal number can be defined as a number whose whole and part are separated by a decimal point. The digits following the decimal point show a value less than one. Decimals are based on the powers of 10. As we move from left to right, the place value of the subsequent digit is divided by 10, meaning the place value becomes tenths, hundredths and thousandths. One tenth is 1/10. In decimal form, it is 0.1. This concept is frequently used in everyday life and can represent many different quantities, relationships and situations. More free math help and activities here: intomath.org

We have looked at the concept of a simple fraction in one of the previous lessons. Fractions can be proper (when the value of a number in the numerator is lower than that in the denominator) or improper (when the value of a number in the numerator is greater than or equal to that in the denominator). An improper fraction is always 1 or greater than 1. Improper fractions can be converted into mixed numbers (also called mixed fractions) by isolating the whole in the improper fraction. A mixed number is a combination of a whole number and a proper fraction. Rewriting an improper fraction as a mixed number can be helpful. It helps us identify more easily how many whole components there are. Mixed numbers can be represented visually as several wholes and parts of something. For example, in the short animation below we use pizzas to demonstrate the concept. It is important to understand how to connect the visual representation of mixed numbers and their arithmetic representation on paper (tablet). We can add and subtract mixed numbers by first adding and subtracting their whole parts and then their fractional parts. If the sum of the fractions is an improper fraction, then we change it to a mixed number. When the denominators of the fractions are different, we need to find equivalent fractions with a common denominator before adding or subtracting. More free math help and activities here: intomath.org

In this Grade 5 lesson you will learn about simple fractions and their properties. A fraction is a part of a whole. It has a numerator and a denominator. The numerator above the fraction line (bar) is used to count the parts out of the total. The number below the fraction line (bar) is called the denominator. It is used to name the total number of parts (fifth, tenth, thousandth, etc). The denominator can never be 0, because we cannot divide by 0. We can compare fractions, order them and perform various operations. You will learn and practice how to add and subtract fractions with the same denominators, as well as how to compare them. For example, you will discover that when the denominators are the same, the largest fraction is the one with the most parts (only comparing the numerators). More free math help and activities here: intomath.org

In this lesson you will discover that 1 dollar equals 100 cents and that cents can be expressed as part of a dollar using fractions or decimals ($0.05 = 5 cents). You will learn and practice how to add and subtract dollars and cents, as well as how to multiply and divide them. For example, if one item costs $2 and 50 cents and the other item costs $3 and 14 cents, what is the total cost of both items? We would add dollars and cents separately and get: $2 + $3 = $5; 50 cents + 14 cents = 64 cents. The total cost is $5 and 64 cents. The lesson teaches how to group the digits based on their place value in order to do operations with money faster and without a calculator. It also discusses sales tax and how to calculate it when making a purchase in order to find the grand total. A sales tax is what a customer pays on top of the actual price of the item. In some countries it is included in the price right away, in others it need to be calculated and added at the check out. More free math help and activities here: intomath.org

Division is the opposite operation to multiplication. When we are trying to distribute something evenly or with a remainder among a group of people or split something into smaller components – we are dividing. We cannot divide by 0, since no splitting or sharing is taking place. We use the ÷ symbol, or sometimes the / symbol to demonstrate division. The symbol ÷, called obelus or obel (from the Greek οβελοσ), was introduced by the Swiss mathematician Johann Henrich Rhan in 1659. Knowing the multiplication tables can help with division. More free math help and activities here: intomath.org

100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In this math lesson you will learn about numbers up to 100,000 and how to do operations with these numbers. You will discover their properties (for example, that any number added to 0 is that number). In addition, you will learn about the importance of the place value of each digit within the number. Moreover, you will also learn how to pronounce and write these numbers in words correctly. In this lesson, we demonstrate how to add and subtract numbers up to 100,000, as well as how to multiply and divide them vertically. The process involves “borrowing” a digit or “carrying” a digit. Our place-value system is called the “decimal” system, because it’s based on 10 fingers and when we move to the next ten, we add another zero, thus creating a new place value for a new digit. More free math help and activities here: intomath.org

We use numbers everyday to count, to measure, to order and estimate and so on. Natural numbers are positive numbers that we use to count and order. 0, 3, 6, 10, 204, 1000… In mathematical terminology, numbers used for counting are called “cardinal numbers” and numbers used for ordering are called “ordinal numbers”. Mathematicians use N to represent a set of all natural numbers. The set of natural numbers is an infinite set. This infinity is called countable infinity. Properties of natural numbers: 1. 0 is a natural number (but some mathematicians do not include it in the list of natural numbers) 2. Every natural number has a number that comes after it and is also a natural number 3. 0 does not come after any natural number 4. If the number that comes after x is equal to the number that comes after y, then x = y More free math help here: intomath.org