5. Name the property under multiplication used in each of the following.
(i) [tex]$\frac{-4}{5} \times 1=1 \times \frac{-4}{5}=-\frac{4}{5}$[/tex]
(ii) [tex]$-\frac{13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17}$[/tex]
(iii) [tex]$\frac{-19}{29} \times \frac{29}{-19}=1$[/tex]
Answer (2)
The properties of multiplication in the given examples are as follows: (i) Identity Property, (ii) Commutative Property, and (iii) Multiplicative Inverse Property. Each of these properties demonstrates a fundamental aspect of multiplication that is consistent across all numbers. Understanding these properties is essential in mastering multiplication techniques.
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The Identity Property of Multiplication states that any number multiplied by 1 remains unchanged.
The Commutative Property of Multiplication states that the order of multiplication does not affect the result.
The Multiplicative Inverse Property states that a number multiplied by its reciprocal equals 1.
Therefore, the properties are: (i) Identity, (ii) Commutative, (iii) Multiplicative Inverse. I d e n t i t y , C o mm u t a t i v e , M u lt i pl i c a t i v e I n v erse
Explanation
Analyzing the Problem We are asked to identify the properties of multiplication demonstrated in the given equations. Let's analyze each one.
Identity Property (i) The equation 5 − 4 × 1 = 1 × 5 − 4 = 5 − 4 shows that when you multiply any number by 1, the number remains the same. This is the Identity Property of Multiplication .
Commutative Property (ii) The equation − 17 13 × 7 − 2 = 7 − 2 × 17 − 13 shows that the order in which you multiply two numbers does not change the result. This is the Commutative Property of Multiplication .
Multiplicative Inverse Property (iii) The equation 29 − 19 × − 19 29 = 1 shows that when you multiply a number by its reciprocal, the result is 1. The reciprocal of 29 − 19 is − 19 29 . This is the Multiplicative Inverse Property .
Final Answer In summary: (i) Identity Property of Multiplication (ii) Commutative Property of Multiplication (iii) Multiplicative Inverse Property
Examples
Understanding properties of multiplication is crucial in various real-life scenarios. For instance, when calculating the total cost of multiple items with the same price, the commutative property allows you to multiply the price by the quantity or vice versa without affecting the total cost. The identity property helps in maintaining quantities unchanged when scaling recipes or converting units. The inverse property is useful in solving problems involving ratios and proportions, such as determining the original quantity before a percentage decrease.
