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Changing Improper Fractions to Mixed number
Example :
Simplify
21
4
= 21 ÷ 4 = 5 remainder 1.
The quotient, 5, becomes the whole number portion of the mixed number.
21
4
1
= 5 4 The remainder, 1, becomes the top number of the fraction.
The bottom number of the fraction always remains the same.
Changing Mixed number to Improper Fractions
3
Example :
Change 4 4 to an improper fraction/
Step 1:
Multiply the whole number (4) by the bottom number of the fraction (5)
Step 2:
Add the top number to the product from Step 1 : 20 + 3 = 23
Step 3:
Put the answer from step 2 over the bottom number (5)
3
45=
23
5
Multiplying Fractions
1
3
2
4
Example 1:
Multiply : ×
Step 1:
Multiply the top number 1 × 3 = 3. The top of the fraction is 3
Step 2:
Multiply the bottom number 2 × 4 = 8. The bottom of the fraction is 8
1
2
2
3
3
4
3
3
4
8
× =
Example 2:
Multiply : ×
Step 1 :
In this problem, the 3’s are both divisible by 3, so they cancel. 3 ÷ 3 = 1
2
3
3
2
1
4
1
4
× = ×
Step 2:
2 and the 4 are both divisible by 2, so they cancel. 2 ÷ 4 = 2
2
1
2
1
×4=1×4
1
Step 3:
Multiply. × =
1
1
1
1
2
2
Multiplying Mixed Numbers
1
2
Example:
Multiply : 3 4 × 3
Step 1:
Change 3 4 to an improper fraction
1
1
34 =
Step 2:
(3×4+1)
4
=
13
4
When multiplying fractions, you can cancel and simplify terms that have a
common factor. The 4 in the first fraction will cancel with the 2 in the second
13
2
fraction.
×
4
3
The terms 4 and 2 are both divisible by 2, so divide the 4 and 2 by 2.
4 simplifies to 2, and 2 simplifies to 1.
Step 3:
Multiply the simplified fractions.
Step 4:
Change
13
6
13
2
13
2
×
1
3
1
×3=
13
6
1
back to a mixed number. 2 6
Reciprocals
3
Example:
Find the reciprocal of 8
Step 1:
Invert the fraction, so the numerator is now the denominator, and the
denominator is now the numerator.
3
8
𝑏𝑒𝑐𝑜𝑚𝑒𝑠 3
8
Answer:
The reciprocal of
3
𝑖𝑠
8
8
3
Dividing Fractions and Mixed Numbers
3
1
Example:
Divide: 3 4 ÷ 2 3
Step 1:
Change the mixed numbers in the problem to improper fractions.
3
34 =
(4×3)+3
4
=
15
4
1
and 2 3 =
The problem is now
15
4
(3×2)+1
3
7
=3
7
÷3
Step 2:
Change the sign from division to multiplication , and then change the second
15
7
number to its reciprocal. 4 × 3
Step 3 :
Cancel is possible (not needed in this problem) and multiply.
Step 4:
Simplify to 1 28
17
15
4
3
45
× 7 = 28