Video: Use Properties of Multiplication to Balance the Equation

Fill in the blank: (3 × 7) + (3 × 9) = _ × (7 + 9).

02:18

Video Transcript

Fill in the blank. Three multiplied by seven plus three multiplied by nine is equal to blank multiplied by seven plus nine.

On the left-hand side of the equation, both terms have a three. We have three multiplied by seven and three multiplied by nine. This means that we can factor or factorise a three outside of the bracket or parentheses. Inside the bracket, we’ll be left with a seven and a nine. The addition sign between the two terms three multiplied by seven and three multiplied by nine will now be between the seven and the nine. We can rewrite this as three multiplied by seven plus nine. The missing number was a three, as three multiplied by seven plus three multiplied by nine is equal to three multiplied by seven plus nine.

We can check this answer by working at the left-hand side and right-hand side separately. On the left-hand side, three multiplied by seven is equal to 21, and three multiplied by nine equals 27. 21 plus 27 is equal to 48. Therefore, the left-hand side of the equation equals 48. On the right-hand side, we need to add the two numbers in the bracket first, seven plus nine. This is equal to 16, so we are left with three multiplied by 16. Three multiplied by 10 is equal to 30, and three multiplied by six is equal to 18. 30 plus 18 is equal to 48. Therefore, three multiplied by 16 is 48. As both the left-hand side and right-hand side equal 48, our answer is correct.

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