<<Recap/Refresh>>
Equivalent Fractions (Fractions with the same values)
Example
1 = 2 = 3
2 4 6
Reducing Fractions to its lowest terms
Example
Reduce 12 / 16 to its lowest term
Step1: Break the numbers to its factors
15 = 3 x 4
20 = 4 x 4
Step2: ‘strike’ out the common factors
15 = 3 x 5
20 = 4 x 5
Step3: Answer
15 = 3
20 = 4
Mixed numbers and Improper Fractions
Mixed number is a whole number and a fraction written together.
Eg: 5 ½
Improper Fraction : the numerator is greater than or equal to the denominator
Eg: 8/7 , 2/2 , 9/4
Converting mixed number and improper fraction
Example
Convert 2 ½ to improper fraction
Step 1 : Multiply the whole number with the fraction's denominator
2 x 2 = 4
Step 2 : Add the number to the numerator
4 + 1 = 5
Step 3 : Write the improper fraction - the added number / the denominator
5 / 2
Example
Convert 17/5 to mixed number
Step 1 : Divide the improper fraction with remainder
123/ 5 = 3 with remainder 2
Step 2 : Write the proper fraction with the remainder as the numerator
2/5
Step 3 : Write the mixed number
Comparing and Ordering Fractions
Example
Which fraction is greater, 2/5 or 3/5?
Step 1: Convert denominator to same value. Yes
Step 2: Which has a greater numerator value? 3
Step 3: Answer
3/5 > 2/5
Ascending and Descending Order
Example
Arrange the fractions 1/2, 2/5, 3/10 in ascending order.
Step 1: Convert denominator to same value
Common factor for denominator is 10
½ = ½ x 5/5 = 5/10, 2/5 x 2/2 = 4/10, 3/10
Step 2: In ascending order => Arrange numerator value from small to big
Step 3: Answer
3/10, 2/5, ½
(2) Converting Decimals and Fractions
Decimals to Fractions
Example
Convert 0.6 to fractions in the lowest terms
Step: Change to fractional part base on decimal place value, 10th = /10
0.6 = 6/10
= 3/5
Fractions to Decimals
Example
Convert 1 12/60 to decimal
Step1: Reduce fraction to lowest term
1 121/605
= 11/5
Step2: Use either long division or convert fraction to 10s base
= 1 1x2/5x2
= 1 2/10
Step3: Answer in decimal form
= 1.2
[** Use the sรณD button on calculator to convert between a decimal and a fraction]
Compare Fractions and Decimals
Example
Arrange the following in descending order
0.6, 4/5, 3/4
Step 1: Convert fractions to decimals (with a calculator)
0.5, 0.8, 0.75
Step 2: Arrange the numbers using place values position
0.6
0.8
0.75
Step 3: Compare and Answer
[Descending – from big to small]
0.8, 0.75, 0.6
Addition and Subtraction of Fractions
** Always reduce the final answer to the lowest terms (when there are common factors in the numerator and denominators
Example
Evaluate the following.
2 + 3
3 4
Step 1: Convert to same denominator.
2 x 4=8 + 3x3=9
3 x 4=12 4x3 12
Step 2: Add the numerator
8 + 9 = 17
12 12 12
Step3: Answer and reduce to lowest term
17/12 = 12/12 + 5/12
= 1 5/12
Multiplication of Fractions
a x c = ac
b d bd
Example
Evaluate 2 x 3
5 8
Step1: Any common factors to reduce
21 x 3
5 84
Step2: Multiple the numerator and denominator
= -1x 3 (-ve x +ve = -ve)
5 x 4
Step3: Answer in lowest term
= -3/20
To avoid mistake, always change a mixed number to improper fraction, then do the multiplication.
Division of Fractions
When we divide by a fraction, we multiply by the reciprocal of fraction => dividing by 3 = multiply x 1/3
Example
Evaluate -4 ÷ 2
9 3
Step1: ‘Convert’ ÷ to x and flip fraction to right of ÷
= -4 x 3
9 2
Step2: Reduce to lowest term
= -42 x 31
93 21
Step3: Check +/- sign and answer
** + x - = -
= -2/3
<<To avoid mistake, always change a mixed number to improper fraction, then do the multiplication>>
Combined Operations on Fractions
** The same rules of the order of operations apply
For Fractions
Do the numerator and the denominator of a fraction separately first.
a + b x c = a + bc 2 + 3 x 5 = 2 + 15 = 17
c x e ce 3 x 6 18 18
Example:
Calculate
1 + 2 – 5 – 3
3 5 x 2
Step 1: Write ORDER and Underline Operation BY ORDER
(BEDMAS)
= 1 + 2 – 5 – 3
3 5 x 2
Step 2: Do calculation using operation rules
= 1 + 2 – 5 – 3
3 10
= 1 + 2 – 2
3 10
Step 3: Repeat step 1-2 until question is solved.
= 3 – 2
3 10 5
= 1 – 1/5
= 4/5
Example
Evaluate the following.
2 - 1/4 ÷ (2 1/3 – 1 5/6)
Step1: Any bracket? First order of operation
2 – ¼ ÷ (2 1x2 / 3x2 – 1 5/6) [change denominator to same value]
= 2 – ¼ ÷ (2 2/6 – 1 5/6)
= 2 – ¼ ÷ (14 /6 – 11/6) [change to improper fraction to - ]
= 2 – ¼ ÷ (3/6)
= 2 – ¼ ÷ ½ [reduce to lowest term]
Step2: Any x ÷ ? Do
= 2 – 1/42 x 21 [‘flip’ ÷]
Step3: Any + - ?
= 2 – ½
= 1 ½
Practice
1. Arrange the following fractions in ascending order
a. 1/2, 1/4, 1/5, 1/3
b. 2/5, 5/6, 1/2, 3/4
2. Arrange the following fractions in descending order
a. 1/10, 3/4, 3/5, 1/2
b. 1/4, 1/6, 1/2, 1/3
3. Evaluate the following:
a. -(-¾) b. +(-⅓) c. ⅚ x (-½)
d. 3/8 ÷ 1/3 e. (-1/5) x (-10/7) f. (1/5) ÷ (-3/10)
4. 6 + (2/5 - 1/10) ÷ (-1/10)
5. 2 + 2/3 x (-1/4 + 1/8)
6. Calculate 4.53 – 1.18 [12/p2/1b/1]
6.13 – 2.39
7. Calculate 5.63 x 23.8 [09/2/1a/1]
12.7 + 3.21
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