**Question**

**Introduction**

This
primary school mathematics question is slightly tricky as the pieces of fruit*
are packaged. I present two solutions:
the first uses the “assumption” or “supposition” method together with the
concept of unit costs. The second
solution illustrates my Distinguished Ratio Units (DRU) method.

**Solution 1**(using an Assumption / Supposition)

**Solution 2**(using my Distinguished Ratio Units method)

I use 3 “circle” units to denote the number of
oranges (since I know it can be divided by 3) and

I use 2 “triangle” units to denote the number of
apples (since the number is divisible by 2).
Then the cost of the oranges would is two “circle” units and the cost of
the apples is 3 “triangles” units. Let us equalise the “circle” units by
multiplying the first row by 2 and the second row by 3.
With both “circle” units equal to
6, the 6
“circle” units can be used as a stepping stone to connect 4
“triangle” units with 9 “triangle” units (highlighted in yellow). We now know that 5
“triangle” units corresponds to
20. It is easy now to work
one 1
“triangle” unit and then 2 “triangle” units, which corresponds to 8.

**Ans:**Abigail bought 8 Apples

**Commentary**

Note
that my DRU solution does not use any fractions! The astute reader will note that my DRU
method is actually the equivalent to the
Singapore teachers/tutors. Both are actually algebraic methods in
disguise, just as the bar modelling (“the model method”) is. In case you are wondering what the difference
between units and parts is: units and parts actually have the same meaning, except
that they refer to differently-sized unknowns and we need different names for
different units. Primary school mathematics
in Singapore
is actually rather challenging because many of these problems are equivalent to
solving a pair of simultaneous equations in two unknowns. It is possible to use one unknown unit, but
you would kill a few brain cells in the process of formulating the problem in
terms of only one unknown.

*u*and*p*(“units vs parts”) method used by many***A Note on Singlish and standard English**

Most
Singaporeans would call, for example, 2 apples and 3 oranges as 5
“fruits”. Actually, in standard English,
“fruit” (as an

*uncountable noun*) refers to general fleshy food that comes from flowering plants. So if you eat “2 apples and 3 oranges”, you are eating fruit. Yes, fruit is food. The word “fruit” can also be used as a*countable noun*. This refers to fruit coming from different botanical species. So in the aforementioned example, “2 apples and 3 oranges” would be considered as 2 fruits (2 types of fruit) and 5 pieces of fruit.
H02. Use a
diagram / model

H04. Look for
pattern(s)

H05. Work
backwards

H08. Make
suppositions (assume, “what if”, imagine if ...)

H09. Restate
the problem in another way

**Suitable Levels**

*****Primary School Mathematics

* other syllabuses that involve ratios,
fractions and money

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