This document provides steps for subtracting mixed numbers:
1. Find the lowest common denominator (LCD) of the fractions, which is the least common multiple of the denominators.
2. Write the mixed numbers as equivalent fractions using the LCD.
3. Subtract the fractions by subtracting the numerators and keeping the common denominator.
The document then works through examples of subtracting mixed numbers step-by-step using the process outlined.
Implicit differentiation allows us to find slopes of lines tangent to curves that are not graphs of functions. Almost all of the time (yes, that is a mathematical term!) we can assume the curve comprises the graph of a function and differentiate using the chain rule.
Implicit differentiation allows us to find slopes of lines tangent to curves that are not graphs of functions. Almost all of the time (yes, that is a mathematical term!) we can assume the curve comprises the graph of a function and differentiate using the chain rule.
5. 19 1
STEP ONE: Find the LCD
The LCD is the LCM of the
3
denominators.
9 11
12
6. 19 1
STEP ONE: Find the LCD
The LCD is the LCM of the
3
denominators.
9
3: 3, 6, 9, 12, 15
11 12: 12, 24, 36, 48
12
7. 19 1
STEP ONE: Find the LCD
The LCD is the LCM of the
3
denominators.
9
3: 3, 6, 9, 12, 15
11 12: 12, 24, 36, 48
12
8. 19 1
STEP ONE: Find the LCD
The LCD is the LCM of the
3
denominators.
9
3: 3, 6, 9, 12, 15
11 12: 12, 24, 36, 48
12
LCD = 12
9. 19 1
STEP ONE: Find the LCD
The LCD is the LCM of the
3
denominators.
9
3: 3, 6, 9, 12, 15
11 12: 12, 24, 36, 48
12
LCD = 12
STEP TWO: Write equivalent
fractions using the LCD
10. 19 1 =
STEP ONE: Find the LCD
The LCD is the LCM of the
3
denominators.
9
3: 3, 6, 9, 12, 15
11 = 12: 12, 24, 36, 48
12
LCD = 12
STEP TWO: Write equivalent
fractions using the LCD
11. 19 1 =
STEP ONE: Find the LCD
The LCD is the LCM of the
3 12
denominators.
9
3: 3, 6, 9, 12, 15
11 = 12: 12, 24, 36, 48
12 12
LCD = 12
STEP TWO: Write equivalent
fractions using the LCD
12. 19 1 x4
STEP ONE: Find the LCD
= The LCD is the LCM of the
3 x4 12
denominators.
9
3: 3, 6, 9, 12, 15
11 =
x1 12: 12, 24, 36, 48
12 x1 12
LCD = 12
STEP TWO: Write equivalent
fractions using the LCD
13. 19 1 x4 4
STEP ONE: Find the LCD
= The LCD is the LCM of the
3 x4 12
denominators.
9
3: 3, 6, 9, 12, 15
11 =
x1 12: 12, 24, 36, 48
12 x1 12
LCD = 12
STEP TWO: Write equivalent
fractions using the LCD
14. 19 1 x4 4
STEP ONE: Find the LCD
= The LCD is the LCM of the
3 x4 12
denominators.
9
3: 3, 6, 9, 12, 15
x1 11
11 = 12: 12, 24, 36, 48
12 x1 12
LCD = 12
STEP TWO: Write equivalent
fractions using the LCD
15. 19 1 x4 4
STEP ONE: Find the LCD
= The LCD is the LCM of the
3 x4 12
denominators.
9
3: 3, 6, 9, 12, 15
x1 11
11 = 12: 12, 24, 36, 48
12 x1 12
LCD = 12
STEP TWO: Write equivalent
fractions using the LCD
Can you subtract a smaller
fraction from a larger fraction?
31. 12 2
STEP ONE: Find the LCD
The LCD is the LCM of the
5
denominators.
6 1
2
32. 12 2
STEP ONE: Find the LCD
The LCD is the LCM of the
5
denominators.
6
5: 5, 10, 15, 20, 25
1 2: 2, 4, 6, 8, 10
2
33. 12 2
STEP ONE: Find the LCD
The LCD is the LCM of the
5
denominators.
6
5: 5, 10, 15, 20, 25
1 2: 2, 4, 6, 8, 10
2
34. 12 2
STEP ONE: Find the LCD
The LCD is the LCM of the
5
denominators.
6
5: 5, 10, 15, 20, 25
1 2: 2, 4, 6, 8, 10
2
LCD = 10
35. 12 2
STEP ONE: Find the LCD
The LCD is the LCM of the
5
denominators.
6
5: 5, 10, 15, 20, 25
1 2: 2, 4, 6, 8, 10
2
LCD = 10
STEP TWO: Write equivalent
fractions using the LCD
36. 12 2=
STEP ONE: Find the LCD
The LCD is the LCM of the
5
denominators.
6
5: 5, 10, 15, 20, 25
1 = 2: 2, 4, 6, 8, 10
2
LCD = 10
STEP TWO: Write equivalent
fractions using the LCD
37. 12 2=
STEP ONE: Find the LCD
The LCD is the LCM of the
5 10
denominators.
6
5: 5, 10, 15, 20, 25
1 = 2: 2, 4, 6, 8, 10
2 10
LCD = 10
STEP TWO: Write equivalent
fractions using the LCD
38. 12 2 x2
STEP ONE: Find the LCD
= The LCD is the LCM of the
5 x2 10
denominators.
6
5: 5, 10, 15, 20, 25
1 =
x5 2: 2, 4, 6, 8, 10
2 x510
LCD = 10
STEP TWO: Write equivalent
fractions using the LCD
39. 12 2 x2 4
STEP ONE: Find the LCD
= The LCD is the LCM of the
5 x2 10
denominators.
6
5: 5, 10, 15, 20, 25
1 =
x5 2: 2, 4, 6, 8, 10
2 x510
LCD = 10
STEP TWO: Write equivalent
fractions using the LCD
40. 12 2 x2 4
STEP ONE: Find the LCD
= The LCD is the LCM of the
5 x2 10
denominators.
6
5: 5, 10, 15, 20, 25
x5 5
1 = 2: 2, 4, 6, 8, 10
2 x510
LCD = 10
STEP TWO: Write equivalent
fractions using the LCD
41. 12 2 x2 4
STEP ONE: Find the LCD
= The LCD is the LCM of the
5 x2 10
denominators.
6
5: 5, 10, 15, 20, 25
x5 5
1 = 2: 2, 4, 6, 8, 10
2 x510
LCD = 10
STEP TWO: Write equivalent
fractions using the LCD
Can you subtract a smaller
fraction from a larger fraction?
57. 62
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
48
58. 62
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
48
6
59. 62
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
48
6
60. 62
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
48
6 5
61. 62
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
48
6 5 +
62. 62
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
48
6 5 1 +
63. 62
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
48
6 5 1 +
STEP TWO: Change the “1” in a
fraction. Take notice of
the denominator.
64. 62
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
48
6 5 1 +
STEP TWO: Change the “1” in a
fraction. Take notice of
the denominator.
65. 62
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
48
6 5 +
STEP TWO: Change the “1” in a
fraction. Take notice of
the denominator.
66. 62
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
4 6 5 8
+8
8 STEP TWO: Change the “1” in a
fraction. Take notice of
the denominator.
67. STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
4 6 5 8
+8
2
8 STEP TWO: Change the “1” in a
fraction. Take notice of
the denominator.
68. 5 8
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
8
4 6 5 8
+8
2
8 STEP TWO: Change the “1” in a
fraction. Take notice of
the denominator.
69. 5 8
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
8
4 6 5 8
+8
2
8 STEP TWO: Change the “1” in a
1
fraction. Take notice of
the denominator.
6
8
70. 5 8
STEP ONE: The whole number
doesn’t have a fraction.
So rename the whole number.
8
4 6 5 8
+8
2
8 STEP TWO: Change the “1” in a
1
fraction. Take notice of
the denominator.
6
8 STEP THREE: Don’t forget to
simplify your answer.