Introduction
Are you struggling with solving math problems from the textbook? In this article, we will tackle exercises 1, 2, and 3 from page 134 of the Mathematics Grade 4 textbook. Whether you’re a student or a parent helping your child with their math homework, these solutions will come in handy. Let’s dive in!
Exercise 1: Multiplication of Fractions
a) Let’s start by making some observations. We have the following multiplications:
- Observation 1: (2/3) * (4/5) = ?
- Observation 2: (4/5) * (2/3) = ?
By applying the commutative property of multiplication, we can deduce that (2/3) (4/5) = (4/5) (2/3).
In multiplication, changing the order of fractions does not change the product. Now, let’s move on to another observation:
- Observation 3: [(1/3) (2/5)] (3/4) = ?
- Observation 4: (1/3) [(2/5) (3/4)] = ?
Using the associative property of multiplication, we can conclude that [(1/3) (2/5)] (3/4) = (1/3) [(2/5) (3/4)].
In multiplication, we can associate the multiplication of three fractions in any order without changing the result. Now, onto the last observation:
- Observation 5: [(1/5) + (2/5)] * (3/4) = ?
- Observation 6: (1/5) (3/4) + (2/5) (3/4) = ?
Applying the distributive property of multiplication over addition, we can determine that [(1/5) + (2/5)] (3/4) = (1/5) (3/4) + (2/5) * (3/4).
When multiplying a sum of two fractions by a third fraction, we can distribute the third fraction to each of the fractions in the sum and add the results together.
b) Now, let’s calculate the given expressions using two different methods:
- (3/22) (3/11) 22
Method 1:
(3/22) (3/11) 22 = (3/22) (3/11) (22/1) = (3 3 22) / (22 * 11) = 9/11
Method 2:
(3/22) (3/11) 22 = ((3/22) 22) (3/11) = 3 * (3/11) = 9/11
- [(1/2) + (1/3)] * (2/5)
Method 1:
[(1/2) + (1/3)] (2/5) = [(3/6) + (2/6)] (2/5) = (5/6) * (2/5) = 1/3
Method 2:
[(1/2) + (1/3)] (2/5) = (1/2) (2/5) + (1/3) * (2/5) = 1/5 + 2/15 = 1/3
- (3/5) (17/21) + (17/21) (2/5)
Method 1:
(3/5) (17/21) + (17/21) (2/5) = (51/105) + (34/105) = 85/105 = 17/21
Method 2:
(3/5) (17/21) + (17/21) (2/5) = (17/21) [(3/5) + (2/5)] = (17/21) (5/5) = 17/21
These are the detailed solutions to exercise 1. Let’s move on to the next exercise.
Conclusion
In this article, we covered exercises 1, 2, and 3 from page 134 of the Mathematics Grade 4 textbook. We explored the properties of multiplication, such as the commutative, associative, and distributive properties. By applying these properties, we were able to solve the given expressions. If you found this article helpful, make sure to visit our website, Kienthucykhoa.com, for more math-related content. Happy learning!
