Make It a Fraction First

Multiplying any combination — fractions, whole numbers, mixed numbers. One rule.

MATHEMATICS 6 MATATAG · Key Stage 2
CG Quarter 1 · competency 11
Term 1 · Week 7

Why it works — 212  ×  113

1
A product is an area. Draw it 2½ wide, 1⅓ tall.
one rectangle
2
Cut where the whole parts end. Four pieces, not two.
2
½
⅔
⅙
2 · ½ · ⅔ · ⅙
3
Add all four. Or convert and multiply — same thing.
2
½
⅔
⅙
= 20/6 = 3⅓
the two the wrong method keeps the two it drops
Make everything a fraction. Then there is only one rule.
212 = 52  ·  113 = 43  ·  52 × 43 = 206 = 3⅓

Three shapes, one method

Whole number
4= 41
4 × 23 =2⅔
Mixed number
235 = 135
× 5 + 3 over 5
Fraction — already done
34 = 34
nothing to change

Every pairing, same three steps — six in all

ShapesAs writtenAs fractionsAnswer
whole × mixed 4 × 134 41 × 74 7
fraction × mixed 45 × 212 45 × 52 2
mixed × mixed 214 × 115 94 × 65 2 7/10

Conversions to know by sight

MixedImproperMixedImproper
112 32 214 94
212 52 334 154
312 72 125 75
113 43 235 135
213 73 178 158
313 103 423 143

Whole × denominator, plus numerator, over the denominator. Going back: divide, and the remainder is the new numerator.

The error this week exists to kill

212 × 113 = 216
212 × 113 = 313

Multiplying the whole parts and the fraction parts separately keeps only two of the four pieces. The missing ½ and ⅔ come to 7/6 — exactly the gap.

A mixed number is one number, not two.
MATATAG Mathematics CG (DepEd, August 2023), p. 48
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