Fraction
A fraction uses two numbers to represent part of a whole.
The bottom number, called the denominator, indicates how many parts are in the whole group or the number of parts into which one item is divided. The top number, called the numerator, indicates how many parts you are working with.
What is a fraction?
A fraction is part of one whole
Two equal parts make a whole
numerator: number of parts of the whole
denominator: number of total parts
Q. 1. There are 10 students who play soccer. Divide the group into two equal teams. How many players are on each team?
Answer: There are five (5) players in each team.
Q. 2. Which of the following shapes have one half shaded?
Four equal parts make a whole
Sarah ate a quater of the pie. How many pieces did she eat?
Answer: Sarah ate one (1) piece of the pie
How many pieces of pie remain from the whole pie?
There are 4 equal parts in this rectangle. Because 3 are shaded, we say that 3/4 of the rectangle is shaded.
⬜⬜⬜⬜
¾
In a proper fraction, the numerator is less than the denominator. A proper fraction represents a quantity less than 1. An improper fraction is equal to or greater than 1.
There are 6 equal parts in the figure below, and 6 are shaded; therefore, 3/4 of the figure is shaded:
6/6 = 1
If the divisor is also a decimal, you must move the decimal points in both the divisor and the dividend before you divide.
Divide 4.9 by 0.35.
You can also change an improper fraction to a whole number or mixed number.
Change 16/5 to a mixed number.
A proper fraction is a fraction whose numerator is less than its denominator, i.e. a fraction less than 1.
An improper fraction is a fraction whose numerator is greater than its denominator, i.e. a fraction greater than 1.
A fraction such as this, consisting of a whole number together with a proper fraction, is called a mixed number. For example,
2 5/8
Fraction Operations:
Addition and Subtraction:
Add 3/10 + 5/10
= 8/10
Because the denominators are the same, add the numerators.
Reduce the answer to the lowest terms.
8 ➗2
8/10 = -------------
10➗２
〓４/5
A fraction is reduced to the lowest terms when the two terms do not have any common factor except 1.
To raise a fraction, multiply both terms by the same number:
To reduce a fraction, divide both terms by the same number:
3 X 3
3/4 = -------------
4 X 3
〓 9/12
10 /5
10/15 = -------------
15 / 5
〓 2/3
Q. Jim has an 8-pound bag of nuts. He wants to fill smaller, 3/2-pound bags using the nuts. How many 3/2 pound bags can he fill?
Solution:
Divide 8 by 3/2. Set up the division problem. Always write the whole or mixed numbers as improper fractions.
Invert the fraction you are dividing by and change the operation sign to multiplication. Multiply, following the rules for multiplying fractions. Jim can fill 16 small bags.
8 ➗ ½ 〓 8／1 ➗ ½
= ８/1 ❌ 2／1
= 16
Q.1. Which of the following is a decomposition of 3/4?
Ans: 1/4 + 1/4 + 1/4 = 3/4
Q.2. Select all the expressions that are equivalent to 0.75.
Ans: 75/100
1 - 1/4
= 3/4
Q.3. In a recent survey of 60 people, 15% of the people responded that they eat dinner out more than twice a week. What fraction of people do not eat dinner out more than twice a week?
Solution:
To find the fraction of people who do not eat dinner out more than twice a week, we need to know the actual number of people this represents. To find this number, we need to first find the percentage of people who do not eat out more than twice a week. If 15% eat out more than twice a week, then 100% - 15% = 85% represents those who do not eat out more than twice a week.
Next, find 85% of 60 people.
0.85 X 60 = 51
Thus, 51 people don't eat out more than twice a week, which is 51/60 of those surveyed.
Q.4. Find the cost of carpeting a floor 4½ m long and 3½ m wide at $3.60 per m².
Solution:
Length of room = 4 ½ m
Width of room = 3 ½ m
Area of room = 4 ½ X 3½ m²
Cost per square metre = $3.60
= $ 3⅗
Total cost = 4 ½ m + 3 ½ + 3⅗(always delay working out as long as possible)
= $56.70
Q.5. Find in cubic meters the volume of air in a room 13½ m long, 12½ m. wide and 4.4 m high.
Fraction:
A symbol, such as 2/3, 5/1, or 8/5 used to describe one or more parts of a whole that are divided into equal parts. A fraction can name a part of a whole, a part of a set, a location on a number line, or a division of whole numbers.
Expanded notation:
A number is written as the sum of the values of its digits.
Factors:
Numbers that are multiplied to get a product.
Formula:
A rule that uses symbols to relate two or more quantities.
Parentheses:
The symbols are used to group numbers or variables in mathematical expressions.
Example: 3(15 - 7)
remainder:
The amount that is left after dividing a number into equal parts.
Yard:
A customary unit of length equal to 3 feet
Brackets:
The symbols ( and ) that are used to group numbers or variables in mathematical expressions.
Common denominator:
A number that is the denominator of two or more fractions
Q.1. Jack needs about 1½ yards of string. He has three pieces of string that are different lengths. Without finding the exact amount, which two pieces should he choose to get closest to 1½ yards of string?
Solution:
🍥
I⬅----½------➡I
🍥
I⬅---⅓--➡I
🍥
I⬅-------⅞--------------➡I
Q.2. Mr. Fish is welding together two copper pipes to repair a leak. He will use the pipes shown. Is the new pipe closer to 1/2 foot or 1 foot long? Explain.
Solution:
1/6 + 5/12
1/2
Q.3. Over the weekend, Eleni ate 1/4 box of cereal, and Freddie ate 3/8 of the same box. What portion of the box of cereal did they eat in all?
Solution:
1/4 = 2/8
3/8 = 3/8
2/8 + 3/8 = 5/8
Q.4. Clarisse has two lengths of fabric to make covers for a sofa and chair. The covers require 9⅔ yards of fabric. How much fabric will Clarisse have left?
Solution:
5 ¾ + 7⅚ = 13 7/12
- 9 2/3
------------------------------------------
3 11/12 yards of fabric left
Fraction Number Line
What is a number line?
In math, a number line can be defined as a pictorial representation of numbers on a straight line.
The numbers on a number line are placed sequentially at equal distances along its length.
Multiply both the numerator and denominator by the same number or divide both the numerator and denominator by the same number. Essentially, you are multiplying or dividing the fraction by 1, which doesn’t change the amount of the fraction.
➖➖➖➖➖➖ーーーーー➖➖➖➖➖➖➖➖➖➖➖➡
0. 1/2. 1