Question Video: Expanding Single Bracket Expressions Involving Fractions

Expand (2/3) ((4/5 π‘₯) βˆ’ (3/10)).

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Video Transcript

Expand two-thirds multiplied by four-fifths π‘₯ minus three tenths.

In order to expand or multiply out a bracket, we need to distribute the term outside across the terms inside the bracket. We need to multiply two-thirds by four-fifths of π‘₯. We also need to multiply two-thirds by negative three tenths. In order to multiply any two fractions, we multiply the numerators and then multiply the denominators separately. For example, the fractions π‘Ž over 𝑏 and 𝑐 over 𝑑 multiplied together give us π‘Žπ‘ over 𝑏𝑑.

In order to multiply two-thirds by four-fifths, we’ll multiply two by four and three by five. Two multiplied by four is equal to eight and three multiplied by five is equal to 15. This means that two-thirds multiplied by four-fifths π‘₯ is equal to eight 15ths π‘₯. This is the first term in our expansion. For the second calculation, two-thirds multiplied by negative three tenths, we could multiply two by negative three and three by 10.

However, sometimes, we can cross simplify or cross cancel first. In this case, three and negative three are both divisible by three. Three divided by three is equal to one and negative three divided by three is equal to negative one. Two and 10 also have a common factor. They’re both divisible by two. Two divided by two is equal to one and 10 divided by two equals five.

We can now multiply the two numerators and the two denominators. One multiplied by negative one is equal to negative one and one multiplied by five is equal to five. The second term in our expansion is negative one-fifth as two-thirds multiplied by negative three tenths is equal to negative one-fifth.

The expansion of two-thirds multiplied by four-fifths π‘₯ minus three tenths is eight 15ths π‘₯ minus one-fifth.

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