a) b) \( 9(7-4)=(9 \times 5)-(9 \times[\square) \) c) \( 12(15+24)=(12 \times 15)+(12 \times[\square) \) d) \( 35(18-11)=(35 \times 18)-(35 \times \square) \)
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Let's dive into the fascinating world of algebraic expressions! When you see an equation like \( 9(7-4) \), it showcases the distributive property in action. This property states that you can distribute a multiplication over addition or subtraction, like turning \( a(b-c) \) into \( ab - ac \). So, in \( 9(7-4) \), you can simply calculate \( 9 \times 3 = 27 \). Now, for the second equation, we can find the missing part. Since \( 7 - 4 = 3 \), the expression becomes \( 9 \times 3 = (9 \times 5) - (9 \times[\square)\). To make both sides equal, the missing value is 2 (as \( 9 \times 2 = 18 \), which is \( 9 \times 5 - 27 \)). The fun doesn't stop there! If you take a look at \( 12(15+24) \), you're using the same principle. The sum within the brackets adds up to 39, so you're effectively saying \( 12 \times 39 = (12 \times 15) + (12 \times [\square) \). Here, to balance the equation, the missing number is 24 (because \( 12 \times 24 = 288 \)). And finally, in \( 35(18-11) \), subtracting gives you 7, so this becomes \( 35 \times 7 = (35 \times 18) - (35 \times \square) \). To solve for the missing value, we see that it is 11 (since \( 35 \times 11 = 385 \)). In summary, the missing numbers are 2, 24, and 11! Now doesn't that make algebra just a touch more exciting?
