Question

How do you simplify `11.4 times 1 3/8 div 0.6`?

Answer 1

`26 1/8->26.125`

Explanation:

In this instance it does not matter if you do the multiplication first or the division. This is because multiply and divide have the same priority in 'BODMAS'. Consequently you can move the operations around. This is the property of being 'commutative'.

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Write as:`" "11.4-:0.6xx1 3/8" "->" "11.4/0.6xx1 3/8`

`color(blue)("Simplifying the decimal part")`

Multiply by 1 and you do not change the value. However 1 comes in many forms so you can change the way something works without changing its intrinsic value.

`[11.4/0.6color(magenta)(xx1)]xx1 3/8`

`[11.4/0.6color(magenta)(xx10/10)]xx1 3/8`

`114/6xx1 3/8`

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`color(blue)("Dealing with "1 3/8)`

Think of this as `1+3/8" "->" "8/8+3/8 = 11/8`

`color(brown)("Putting it all together we have")`

`(cancel(114)^57)/6xx11/(cancel(8)^4)" "=" "(cancel(57))^(19)/(2xxcancel(3)^1)xx11/4`

`=209/8 = 26 1/8`

In decimal form this is:`" "26.125`

Answer 2

`26 1/8`

Explanation:

Decimals and fractions are interchangeable and it is often surprising to students to learn that fractions are often easier than decimals!

Unfortunately with the regular use of calculators many students have lost their skills in mental math and are dependent on calculators!

This question works just fine using fractions!

`11.4 xx1 3/8 div0.6" "larr` convert to fractions

=`11 4/10 xx 1 3/8 div 6/10" "larr` simplify if possible

=`11 2/5 xx 1 3/8 div 3/5" "larr` improper fractions and flip the divide

=`cancel57^19/cancel5 xx11/8 xxcancel5/cancel3" "larr` cancel where possible

=`(19xx11)/8`

=`209/8 = 26 1/8" "larr` this is fine in this form