Multiplying by the Reciprocal
6/7 ÷ 1/4
6/7 × 4/1 = 24/7 = 3 3/7
(2/3 + 1/2) ÷ 1/4 =
(4/6 + 3/6) ÷ 1/4 =
7/6 × 4 = 14/3 = 4 2/3
2 3/4 × ? = 2 3/4
? = 1
Identity Property
a = 5/6
(2/3 × a) ÷ 1/2 =
(2/3 × 5/6) ÷ 1/2 =
5/9 ÷ 1/2 =
5/9 × 2 = 10/9 = 1 1/9
3 1/8 ÷ 1/4 =
25/8 × 4 = 25/2 = 12 1/2
1/6 ÷ 1/9 =
1/6 × 9 = 9/6 = 3/2 = 1 1/2
6 × 3/4 ÷ 1/8 =
6 × 3/4 ÷ 1/8 =
18/4 × 8/1 = 36
8 1/3 + 1 1/4 = 1 1/4 + ?
? = 8 1/3
Commutative Property
b = 3/4
(b ÷ 1/2) - (4 × 1/3) =
(3/4 ÷ 1/2) - (4 × 1/3) =
(3/4 × 2) - (4 × 1/3) =
3/2 - 4/3 =
9/6 - 8/6 = 1/6
2 5/6 ÷ 1 1/4 =
17/6 ÷ 5/4 =
17/6 × 4/5 = 34/15 = 2 4/15
5 ÷ 3/8 =
5 × 8/3 = 40/3 = 13 1/3
6 - 3/9 × 1/3 =
6 - 3/9 × 1/3 =
6- 1/9 = 5 9/9 - 1/9 =
5 8/9
2 × 4 5/6 = (2 × a) + (2 × b)
a = 4, b = 5/6
Distributive Property
Write the reciprocal for
2 3/7
7/17
1 1/5 ÷ 2 =
6/5 ÷ 2 =
6/5 × 1/2 = 3/5
2/5 ÷ 5 =
2/5 × 1/5 = 2/25
(4 × 1/5) + (3 × 1/2) =
(4 × 1/5) + (3 × 1/2) =
4/5 + 3/2 =
8/10 + 15/10 =
23/10 = 2 3/10
7/8 × ? = 0
? =0
Zero Property
Use multiplication to check, state whether the quotient is true. If false, find the correction quotient.
7/8 ÷ 1/6 = 5 1/4
True
21/4 × 1/6 = 7/8
8 ÷ 2 3/4 =
8 ÷ 11/4 =
8 × 4/11 = 32/11 = 2 10/11
After dinner, Mrs. Karl had 1/3 of a pan of brownies left. If 1/12 of the pan of brownies is a serving, how man servings were left?
1/3 ÷ 1/12 =
1/3 × 12 = 12/3 = 4
Jacob read 2/3 of a book that had 315 pages. Kevin read 1/2 of a book that had 414 pages. Who read more pages?
Jacob read 210 pages
315 × 2/3 = 210
Kevin read 207 pages
414 × 1/2 = 207
Jacob read 3 more pages (210-207 = 3)
3/4 + (2/3 + 1/6) = (? + 2/3) + 1/6
? = 3/4
Associative Property
Use multiplication to check, state whether the quotient is true. If false, find the correction quotient.
6 ÷ 5/6 = 6 2/3
False
20/3 × 5/6= 50/9 = 5 5/9
6 ÷ 5/6 = 7 1/5
James has a rope that is 15 3/4 ft long. If he cuts the rope into lengths of 6 1/4 ft, how many pieces of rope will he have?
15 3/4 ÷ 6 1/4 = ?
63/4 ÷ 25/4 =
63/4 × 4/25 = 63/25 = 2 13/25