Mattingly "AI & Prompt Design: The Basics of Prompt Design"
Adding and subtracting like and unlike fractions
1.
2. To or like fractions, add
or subtract the and
write the sum over the .
3. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 1:
1
4
+
2
4
=
3
4
/ the
numerators.
1+2
Retain the
.
Simplify if possible.
4. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 1:
1
4
+
2
4
=
3
4
5. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 2:
5
11
−
2
11
=
3
11
/ the
numerators.
5 − 2
Retain the
.
Simplify if possible.
6. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 2:
5
11
−
2
11
=
3
11
7. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 3:
−
3
9
+
4
9
=
1
9
/ the
numerators.
−3 + 4
Retain the
.
Simplify if possible.
8. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 3:
+
4
9
=
1
9
−
3
9
9. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 4:
−
4
7
+
2
7
=
−2
7
/ the
numerators.
−4 + 2
Retain the
.
Simplify if possible.
−
2
7
10. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 4:
−
4
7
+
2
7
= −
2
7
11. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 5:
5
6
+
−3
6
=
2
6
/ the
numerators.
5 − 3
Retain the
.
Simplify if possible.
=
1
3
12. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 5:
5
6
+
−3
6
=
2
6
=
1
3
13. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 6:
1
13
−
−4
13
=
5
13
/ the
numerators.
1 + 4
Retain the
.
Simplify if possible.
14. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 6:
1
13
−
−4
13
=
5
13
15. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 7:
2
3
5
+ 1
1
5
=
4
5
/ the
numerators.
3 + 4
Retain the
.
Add/subtract the
whole numbers
3
Simplify if possible.
2 + 1
16. To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 7:
2
3
5
+ 1
1
5
=
4
5
3
22. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
1
9
+
2
3
Denominators should
be alike. Find LCD.
23. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
1
9
+
2
3
Denominators should
be alike. Find LCD.
Least Common Multiple
9: 9, 18, 27, 36, 45, …
3: 3, 6, 9, 12, 15, …
24. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
1
9
+
2
3
Denominators should
be alike. Find LCD.
Least Common Multiple
9: 9, 18, 27, 36, 45, …
3: 3, 6, 9, 12, 15, …
LCD: 9
25. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
1
9
+
2
3
=
LCD: 9 Convert all to . Change
each denominator to the LCD.
1
9
What should be
multiplied to the
denominator to
have the LCD?
26. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
1
9
+
2
3
=
LCD: 9 Convert all to . Change
each denominator to the LCD.
1
9
+
6
9
27. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
LCD: 9 Convert all to . Change
each denominator to the LCD.
1
9
+
2
3
=
1
9
+
6
9
28. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
LCD: 9 Convert all to . Change
each denominator to the LCD.
1
9
+
2
3
=
1
9
+
6
9
What should be
multiplied to the
denominator to
have the LCD?
× 3
× 3
Simplify!
29. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
LCD: 9 Convert all to . Change
each denominator to the LCD.
1
9
+
2
3
=
1
9
+
6
9× 3
× 3
Simplify!
30. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
LCD: 9
Simplify.
1. Add the
numerators.
2. Retain
denominator.
1
9
+
2
3
=
1
9
=
7
9
× 3
× 3
+
6
9
1 + 6
31. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
LCD: 9
1
9
+
2
3
=
1
9
=
7
9
× 3
× 3
+
6
9
Simplify.
1. Add the
numerators.
2. Retain
denominator.
32. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
1
9
+
2
3
=
1
9
=
7
9
× 3
× 3
+
6
9
34. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
35. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
Changing mixed fraction to
improper fraction.
Multiply the denominator
and whole number
12
3
4
=
51
4
48
4 12
36. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
Changing mixed fraction to
improper fraction.
Add up the product to the
numerator. The result will be the
new numerator.
12
3
4
=
51
4
48
48 + 3
37. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
Changing mixed fraction to
improper fraction.
Copy the denominator
12
3
4
=
51
4
38. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
Changing mixed fraction to
improper fraction.
Copy the denominator
12
3
4
=
51
4
39. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
Break the
groupings.
40. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
+(−)
Break the
groupings.
41. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
Denominators
should be alike.
Find LCD.
42. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
Denominators
should be alike.
Find LCD.
Least Common Multiple
4: 4, 8, 12, 16, …
2: 2, 4, 6, 8, …
LCD: 4
43. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
LCD: 4
=
51
4
−
2
4
What should be
multiplied to the
denominator to
have the LCD?
Convert all to . Change
each denominator to the LCD.
44. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
What should be
multiplied to the
denominator to
have the LCD?
LCD: 4
Convert all to . Change
each denominator to the LCD.
45. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
What should be
multiplied to the
denominator to
have the LCD?
LCD: 4
Convert all to . Change
each denominator to the LCD.
46. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
What should be
multiplied to the
denominator to
have the LCD?
LCD: 4
Convert all to . Change
each denominator to the LCD.
× 2
× 2
47. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
Simplify!
LCD: 4
Convert all to . Change
each denominator to the LCD.
× 2
× 2
48. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
Simplify!
LCD: 4
Convert all to . Change
each denominator to the LCD.
× 2
× 2
49. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
Now we’re ready!
1. Subtract the
numerator.
2. Copy denominator
LCD: 4
× 2
× 2
=
49
4
51 − 2
50. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
Now we’re ready!
1. Subtract the
numerator.
2. Copy denominator
LCD: 4
× 2
× 2
=
49
4
51. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
For final answers.
Change to mixed
fractions.
× 2
× 2
=
49
4
= 12
1
4
52. To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
× 2
× 2
=
49
4
= 12
1
4