A Part of a Part

Multiplying a fraction by a fraction — shade across, shade down, count the overlap.

MATHEMATICS 5 MATATAG · Key Stage 2
CG Quarter 1 · competency 8
Term 1 · Week 7

How to do it — 23  ×  34

1
Draw a grid.
4 columns, 3 rows.
12 cells altogether
2
Shade 3 of 4 columns one way, 2 of 3 rows the other.
two directions, one grid
3
Count the cells with both marks.
6 of 12  =  ½
first fraction — columns second fraction — rows the product
ab × cd = a × cb × d
Tops times tops. Bottoms times bottoms. Then simplify.

When it does not get smaller

Times exactly 1
35 ×1= 35
Unchanged. Not smaller.
Times more than 1
35 × 32 = 910
Bigger — the multiplier is over 1.
Times a whole number
35 ×4= 125
Bigger. That is 2 25.

The rule is about the size of the multiplier: under 1 → smaller · exactly 1 → the same · over 1 → bigger.

Products you should know by sight

× 12 13 14 15
12 14 16 18 110
13 16 19 112 115
23 13 29 16 215
34 38 14 316 320
35 310 15 320 325

Every answer here is smaller than both fractions that made it — twenty examples on the wall, all year. The table is symmetric, too.

Awkward factors

A whole number — put a 1 underneath
4=41 so4× 23 =83
A mixed number — make it improper first
112 =32 so 32× 23 =1
Simplify before you multiply — less work
89× 34 =23
Cancel 3 with 9, and 4 with 8 — never top with top.
“Of” means multiply. A part of a part is smaller than both.
MATATAG Mathematics CG (DepEd, August 2023), p. 44
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