Video Transcript
Expand four-sevenths multiplied by three-quarters plus eight-ninths of 𝑥.
In order to expand any bracket or parenthesis, we need to multiply the term outside of the bracket by each of the terms inside the bracket. In this case, we need to multiply four-sevenths by three-quarters and four-sevenths by eight-ninths of 𝑥.
The easiest way to multiply two fractions is to multiply the two numerators — in this case, four and three — and the two denominators — seven and four. Four multiplied by three is equal to 12 and seven multiplied by four is equal to 28. This means that four-sevenths multiplied by three-quarters is equal to 12 28ths.
This answer can be simplified by dividing the numerator and denominator by four. Remember whatever you do to the top, you must do to the bottom of a fraction. 12 divided by four is equal to three and 28 divided by four is equal to seven. Therefore, our simplified fraction is three-sevenths.
An alternative way of multiplying the two fractions would be to at first cancelled. In this case, we could have divided the four on the numerator and the four on the denominator by four. Four divided by four is equal to one. This leaves us with one-seventh multiplied by three over one or three. One-seventh multiplied by three is equal to three-sevenths.
Either way by multiplying four-sevenths by three-quarters, we get an answer of three-sevenths.
The second part of our expansion involves multiplying four-sevenths by eight-ninths of 𝑥. Once again, we can multiply the two fractions by multiplying the numerators and then separately multiplying the denominators.
Four multiplied by eight is equal to 32 and seven multiplied by nine is equal to 63. This means that four-sevenths multiplied by eight-ninths of 𝑥 is equal to 32 over 63𝑥 or 32 63rds of 𝑥.
The expansion of four-sevenths multiplied by three-quarters plus eight-ninths 𝑥 is three-sevenths plus 32 63rds 𝑥.
